148:
32:
8395:
2705:
2275:
8381:
1223:
1918:
8419:
2700:{\displaystyle {\begin{bmatrix}1&B_{0;1,2}\\B_{0;2,1}&1\end{bmatrix}}{\begin{bmatrix}y_{1,t}\\y_{2,t}\end{bmatrix}}={\begin{bmatrix}c_{0;1}\\c_{0;2}\end{bmatrix}}+{\begin{bmatrix}B_{1;1,1}&B_{1;1,2}\\B_{1;2,1}&B_{1;2,2}\end{bmatrix}}{\begin{bmatrix}y_{1,t-1}\\y_{2,t-1}\end{bmatrix}}+{\begin{bmatrix}\epsilon _{1,t}\\\epsilon _{2,t}\end{bmatrix}},}
8407:
903:
4163:
1687:
5618:. Sims advocated VAR models as providing a theory-free method to estimate economic relationships, thus being an alternative to the "incredible identification restrictions" in structural models. VAR models are also increasingly used in health research for automatic analyses of diary data or sensor data.
4993:
Vector autoregression models often involve the estimation of many parameters. For example, with seven variables and four lags, each matrix of coefficients for a given lag length is 7 by 7, and the vector of constants has 7 elements, so a total of 49Ă4 + 7 = 203 parameters are estimated, substantially
3287:
From an economic point of view, if the joint dynamics of a set of variables can be represented by a VAR model, then the structural form is a depiction of the underlying, "structural", economic relationships. Two features of the structural form make it the preferred candidate to represent the
2834:
3584:
1218:{\displaystyle {\begin{bmatrix}y_{1,t}\\y_{2,t}\end{bmatrix}}={\begin{bmatrix}c_{1}\\c_{2}\end{bmatrix}}+{\begin{bmatrix}a_{1,1}&a_{1,2}\\a_{2,1}&a_{2,2}\end{bmatrix}}{\begin{bmatrix}y_{1,t-1}\\y_{2,t-1}\end{bmatrix}}+{\begin{bmatrix}e_{1,t}\\e_{2,t}\end{bmatrix}},}
3758:
4724:
4601:
4983:
4427:
3300:, which implies zero correlation between error terms as a desired property. This is helpful for separating out the effects of economically unrelated influences in the VAR. For instance, there is no reason why an oil price shock (as an example of a
3198:
2119:
1913:{\displaystyle {\begin{bmatrix}y_{t}\\y_{t-1}\end{bmatrix}}={\begin{bmatrix}c\\0\end{bmatrix}}+{\begin{bmatrix}A_{1}&A_{2}\\I&0\end{bmatrix}}{\begin{bmatrix}y_{t-1}\\y_{t-2}\end{bmatrix}}+{\begin{bmatrix}e_{t}\\0\end{bmatrix}},}
4859:
466:
294:, which refers to the number of earlier time periods the model will use. Continuing the above example, a 5th-order VAR would model each year's wheat price as a linear combination of the last five years of wheat prices. A
3909:
3973:
1537:
1385:
2264:
2716:
3350:
5437:
2974:
2903:
3595:
654:
1674:
4998:
of the regression (the number of data points minus the number of parameters to be estimated). This can hurt the accuracy of the parameter estimates and hence of the forecasts given by the model.
735:
4307:
5308:
5936:
van der Krieke; et al. (2016). "Temporal
Dynamics of Health and Well-Being: A Crowdsourcing Approach to Momentary Assessments and Automated Generation of Personalized Feedback (2016)".
5208:
4608:
590:
5077:
1562:
lags can always be equivalently rewritten as a VAR with only one lag by appropriately redefining the dependent variable. The transformation amounts to stacking the lags of the VAR(
4502:
4875:
2996:
4318:
177:
4450:
4222:
865:
5477:
5542:
5856:
5508:
1965:
7516:
8021:
5120:
5100:
5554:
infinitely far forward in time, although the effect will become smaller and smaller over time assuming that the AR process is stable â that is, that all the
9518:
9474:
8171:
7795:
4743:
6436:
5130:-th element of the state vector 2 periods later, which is a particular impulse response, first write the above equation of evolution one period lagged:
2209:) satisfy the conditions (1) - (3) in the definition above, with the particularity that all the elements in the off diagonal of the covariance matrix
328:
7569:
5588:, and the quality of the forecasts can be judged, in ways that are completely analogous to the methods used in univariate autoregressive modelling.
8008:
4158:{\displaystyle \Omega =\mathrm {E} (e_{t}e_{t}')=\mathrm {E} (B_{0}^{-1}\epsilon _{t}\epsilon _{t}'(B_{0}^{-1})')=B_{0}^{-1}\Sigma (B_{0}^{-1})'\,}
3775:
1391:
1242:
6036:
5989:
2829:{\displaystyle \Sigma =\mathrm {E} (\epsilon _{t}\epsilon _{t}')={\begin{bmatrix}\sigma _{1}^{2}&0\\0&\sigma _{2}^{2}\end{bmatrix}};}
6431:
6131:
3579:{\displaystyle y_{t}=B_{0}^{-1}c_{0}+B_{0}^{-1}B_{1}y_{t-1}+B_{0}^{-1}B_{2}y_{t-2}+\cdots +B_{0}^{-1}B_{p}y_{t-p}+B_{0}^{-1}\epsilon _{t},}
53:
8457:
7035:
6183:
8423:
5810:"Can the LR test be helpful in choosing the optimal lag order in the VAR model when information criteria suggest different lag orders?"
2212:
6004:
Holtz-Eakin, D., Newey, W., and Rosen, H. S. (1988). Estimating Vector
Autoregressions with Panel Data. Econometrica, 56(6):1371â1395.
5683:
541:
123:
118:
Like the autoregressive model, each variable has an equation modelling its evolution over time. This equation includes the variable's
5319:
9548:
7818:
7710:
6077:
6055:
199:
75:
2916:
2846:
1546:) observation of each variable depends on its own lagged values as well as on the lagged values of each other variable in the VAR.
3753:{\displaystyle B_{0}^{-1}c_{0}=c,\quad B_{0}^{-1}B_{i}=A_{i}{\text{ for }}i=1,\dots ,p{\text{ and }}B_{0}^{-1}\epsilon _{t}=e_{t}}
7996:
7870:
3273:
95:) is a statistical model used to capture the relationship between multiple quantities as they change over time. VAR is a type of
8054:
7715:
7460:
6831:
6421:
4995:
7045:
8956:
8105:
7317:
7124:
7013:
6971:
5699:
3967:, thus creating contemporaneous movement in all endogenous variables. Consequently, the covariance matrix of the reduced VAR
1575:
6210:
9137:
8926:
8916:
8609:
8348:
7307:
5781:
5639:
4479:
As the explanatory variables are the same in each equation, the multivariate least squares estimator is equivalent to the
7357:
4182:
891:
871:
601:
9076:
9049:
7899:
7848:
7833:
7823:
7692:
7564:
7531:
7312:
7142:
5219:
4493:
131:
127:
7968:
7269:
160:
9543:
9503:
9484:
9061:
8906:
8872:
8857:
8836:
8831:
8243:
8044:
7023:
6692:
6156:
6089:
5814:
4457:
1566:) variable in the new VAR(1) dependent variable and appending identities to complete the precise number of equations.
8128:
8095:
676:
170:
164:
156:
134:. The only prior knowledge required is a list of variables which can be hypothesized to affect each other over time.
46:
40:
9478:
9054:
8744:
8734:
8100:
7843:
7602:
7508:
7488:
7396:
7107:
6925:
6408:
6280:
825:
223:
7274:
7040:
6898:
8624:
7860:
7628:
7349:
7203:
7132:
7052:
6910:
6891:
6599:
6320:
5714:
7973:
4719:{\displaystyle {\hat {\Sigma }}={\frac {1}{T-kp-1}}\sum _{t=1}^{T}{\hat {\epsilon }}_{t}{\hat {\epsilon }}_{t}'}
259:) The vector is modelled as a linear function of its previous value. The vector's components are referred to as
181:
57:
9508:
9454:
9197:
9152:
8991:
8862:
8739:
8343:
8110:
7658:
7623:
7587:
7372:
6814:
6723:
6682:
6594:
6285:
6124:
5704:
5627:
5136:
4239:
3297:
668:
9212:
7380:
7364:
1936:
The equivalent VAR(1) form is more convenient for analytical derivations and allows more compact statements.
550:
9162:
8996:
8986:
8976:
8966:
8704:
8694:
8654:
8644:
8524:
8450:
8252:
7865:
7805:
7742:
7102:
6964:
6954:
6804:
6718:
5854:(1962). "An Efficient Method of Estimating Seemingly Unrelated Regressions and Tests for Aggregation Bias".
4229:
3316:
8013:
7950:
5777:"Optimal lag-length choice in stable and unstable VAR models under situations of homoscedasticity and ARCH"
5636:
includes functions for VAR models. Other R packages are listed in the CRAN Task View: Time Series
Analysis.
5017:
4596:{\displaystyle {\hat {\Sigma }}={\frac {1}{T}}\sum _{t=1}^{T}{\hat {\epsilon }}_{t}{\hat {\epsilon }}_{t}'}
9332:
9177:
9037:
8980:
8936:
8899:
8649:
8589:
8564:
8534:
8519:
8290:
8220:
7705:
7592:
6589:
6486:
6393:
6272:
6171:
5900:
5723:
5547:
4480:
3277:
796:
9147:
8411:
7289:
4978:{\displaystyle {\widehat {\mbox{Cov}}}({\mbox{Vec}}({\hat {B}}))=({ZZ'})^{-1}\otimes {\hat {\Sigma }}.\,}
3304:) should be related to a shift in consumers' preferences towards a style of clothing (as an example of a
280:
th variable. For example, if the first variable in the model measures the price of wheat over time, then
9464:
9122:
9107:
9081:
9020:
8699:
8639:
8619:
8614:
8315:
8257:
8200:
7919:
7828:
7554:
7438:
7297:
7179:
7171:
6986:
6882:
6860:
6819:
6784:
6751:
6697:
6672:
6627:
6566:
6526:
6328:
6151:
6018:
Asteriou, Dimitrios; Hall, Stephen G. (2011). "Vector
Autoregressive (VAR) Models and Causality Tests".
5611:
3193:{\displaystyle y_{1,t}=c_{0;1}-B_{0;1,2}y_{2,t}+B_{1;1,1}y_{1,t-1}+B_{1;1,2}y_{2,t-1}+\epsilon _{1,t}\,}
8394:
7284:
3296:. The structural, economic shocks which drive the dynamics of the economic variables are assumed to be
9513:
9217:
8961:
8931:
8884:
8847:
8773:
8724:
8689:
8629:
8594:
8529:
8238:
7813:
7762:
7738:
7700:
7618:
7597:
7549:
7428:
7406:
7375:
7161:
7112:
7030:
7003:
6959:
6915:
6677:
6453:
6333:
5579:
5575:
4422:{\displaystyle \operatorname {Vec} ({\hat {B}})=((ZZ')^{-1}Z\otimes I_{k})\ \operatorname {Vec} (Y),}
770:
256:
100:
20:
5905:
9443:
9252:
9112:
9071:
8971:
8951:
8911:
8867:
8852:
8808:
8749:
8674:
8664:
8634:
8557:
8385:
8310:
8233:
7914:
7678:
7671:
7633:
7541:
7521:
7493:
7226:
7092:
7087:
7077:
7069:
6887:
6848:
6738:
6728:
6637:
6416:
6372:
6290:
6215:
6117:
6065:
5886:
5596:
7960:
5966:
9498:
9469:
9427:
9232:
8941:
8921:
8889:
8803:
8798:
8778:
8729:
8669:
8659:
8604:
8599:
8443:
8399:
8210:
8064:
7909:
7785:
7682:
7666:
7643:
7420:
7154:
7137:
7097:
7008:
6903:
6865:
6836:
6796:
6756:
6702:
6619:
6305:
6300:
5918:
5809:
4472:
4168:
can have non-zero off-diagonal elements, thus allowing non-zero correlation between error terms.
746:
96:
5776:
5745:
9362:
9337:
9287:
9247:
9127:
9015:
8818:
8754:
8719:
8709:
8579:
8305:
8275:
8267:
8087:
8078:
8003:
7934:
7790:
7775:
7750:
7638:
7579:
7445:
7433:
7059:
6976:
6920:
6843:
6687:
6609:
6388:
6262:
6073:
6051:
6032:
5985:
5949:
5833:
5709:
4453:
4435:
4191:
2114:{\displaystyle B_{0}y_{t}=c_{0}+B_{1}y_{t-1}+B_{2}y_{t-2}+\cdots +B_{p}y_{t-p}+\epsilon _{t},}
834:
657:
5449:
9412:
9357:
9342:
9327:
9312:
9292:
9242:
9222:
9202:
9157:
8764:
8714:
8684:
8679:
8569:
8507:
8330:
8285:
8049:
8036:
7929:
7904:
7838:
7770:
7648:
7256:
7149:
7082:
6995:
6942:
6761:
6632:
6426:
6225:
6192:
6098:
5941:
5910:
5865:
5790:
5757:
5517:
126:. VAR models do not require as much knowledge about the forces influencing a variable as do
5486:
9523:
9417:
9382:
9347:
9282:
9207:
9192:
9086:
9042:
8879:
8813:
8788:
8783:
8759:
8502:
8487:
8247:
7991:
7853:
7780:
7455:
7329:
7302:
7279:
7248:
6875:
6870:
6824:
6554:
6205:
3235:
2987:
1930:
777:
All the variables are I(0) (stationary): this is in the standard case, i.e. a VAR in level
112:
5632:
5599:
has advocated VAR models, criticizing the claims and performance of earlier modeling in
4496:(MLE) of the covariance matrix differs from the ordinary least squares (OLS) estimator.
3321:. This is a desirable feature especially when using low frequency data. For example, an
3284:
parameter estimates. This problem can be overcome by rewriting the VAR in reduced form.
16:
Statistical model to calculate the value of multiple quantities as they change over time
9437:
9422:
9387:
9372:
9352:
9322:
9172:
9142:
8793:
8514:
8482:
8196:
8191:
6654:
6584:
6230:
5851:
5615:
5563:
5105:
5085:
3329:
the day the decision is announced, but one could find an effect in that quarter's data.
593:
516:
3914:
Note that in the reduced form all right hand side variables are predetermined at time
806:: first, the variables have to be differenced d times and one has a VAR in difference.
795:: the error correction term has to be included in the VAR. The model becomes a Vector
9537:
9402:
9392:
9367:
9307:
9302:
9297:
9277:
9267:
9237:
9227:
9132:
9032:
9005:
8769:
8353:
8320:
8183:
8144:
7955:
7924:
7388:
7342:
6947:
6649:
6476:
6240:
6235:
6102:
5600:
2176:
803:
792:
6506:
5011:
Consider the first-order case (i.e., with only one lag), with equation of evolution
4854:{\displaystyle {\hat {\Sigma }}={\frac {1}{T-kp-1}}(Y-{\hat {B}}Z)(Y-{\hat {B}}Z)'.}
3929:
However, the error terms in the reduced VAR are composites of the structural shocks
9432:
9377:
9272:
9262:
9257:
9182:
9027:
8552:
8492:
8295:
8228:
8205:
8120:
7450:
6746:
6644:
6579:
6521:
6443:
6398:
5891:
5869:
5653:
5603:
3326:
3322:
3305:
3301:
897:
A VAR(1) in two variables can be written in matrix form (more compact notation) as
237:
119:
5761:
5945:
9407:
9397:
9187:
9066:
9010:
8497:
8338:
8300:
7983:
7884:
7746:
7559:
7526:
7018:
6935:
6930:
6574:
6531:
6511:
6491:
6481:
6250:
5585:
3238:(all off-diagonal elements are zero â the case in the initial definition), when
742:
505:
104:
5978:
Hyndman, Rob J; Athanasopoulos, George (2018). "11.2: Vector
Autoregressions".
461:{\displaystyle y_{t}=c+A_{1}y_{t-1}+A_{2}y_{t-2}+\cdots +A_{p}y_{t-p}+e_{t},\,}
9317:
9117:
8894:
7184:
6664:
6364:
6295:
6245:
6220:
6140:
5967:
Bernhard Pfaff VAR, SVAR and SVEC Models: Implementation Within R Package vars
5794:
5746:"Multivariate tests for autocorrelation in the stable and unstable VAR models"
5718:
5607:
5555:
2910:
822:
122:(past) values, the lagged values of the other variables in the model, and an
9167:
9097:
8544:
8474:
8466:
7337:
7189:
6809:
6604:
6516:
6501:
6496:
6461:
4468:
4464:
3904:{\displaystyle y_{t}=c+A_{1}y_{t-1}+A_{2}y_{t-2}+\cdots +A_{p}y_{t-p}+e_{t}}
3308:); therefore one would expect these factors to be statistically independent.
3281:
758:
108:
5953:
5606:. He recommended VAR models, which had previously appeared in time series
1532:{\displaystyle y_{2,t}=c_{2}+a_{2,1}y_{1,t-1}+a_{2,2}y_{2,t-1}+e_{2,t}.\,}
8946:
6853:
6471:
6348:
6343:
6338:
6310:
2840:
1380:{\displaystyle y_{1,t}=c_{1}+a_{1,1}y_{1,t-1}+a_{1,2}y_{2,t-1}+e_{1,t}\,}
1236:
equal to 1), or, equivalently, as the following system of two equations
8358:
8059:
5922:
298:
is the value of a variable in a previous time period. So in general a
8280:
7261:
7235:
7215:
6466:
6257:
6031:(Third ed.). New York: John Wiley & Sons. pp. 272â355.
5677:
5665:
5914:
5313:
then repeat using the twice lagged equation of evolution, to obtain
3960:
can potentially lead to the occurrence of shocks in all error terms
302:
th-order VAR refers to a VAR model which includes lags for the last
5979:
5742:
For multivariate tests for autocorrelation in the VAR models, see
5671:
5659:
2172:
2259:{\displaystyle \mathrm {E} (\epsilon _{t}\epsilon _{t}')=\Sigma }
6200:
6022:(Second ed.). London: Palgrave MacMillan. pp. 319â333.
8439:
8169:
7736:
7483:
6782:
6552:
6169:
6113:
5580:
Autoregressive model § Evaluating the quality of forecasts
5432:{\displaystyle y_{t}=A^{3}y_{t-3}+A^{2}e_{t-2}+Ae_{t-1}+e_{t}.}
3922:
endogenous variables on the right hand side, no variable has a
1542:
Each variable in the model has one equation. The current (time
5550:
process that any shock will have an effect on the elements of
141:
99:
model. VAR models generalize the single-variable (univariate)
25:
6109:
2969:{\displaystyle \mathrm {cov} (\epsilon _{1},\epsilon _{2})=0}
2898:{\displaystyle \mathrm {var} (\epsilon _{i})=\sigma _{i}^{2}}
8435:
4869:
The covariance matrix of the parameters can be estimated as
5646:
package's tsa (time series analysis) module supports VARs.
4181:
Starting from the concise matrix notation (for details see
2266:
are zero. That is, the structural shocks are uncorrelated.
5213:
Use this in the original equation of evolution to obtain
3338:
By premultiplying the structural VAR with the inverse of
3926:
contemporaneous effect on other variables in the model.
6050:. New York: Oxford University Press. pp. 162â213.
1669:{\displaystyle y_{t}=c+A_{1}y_{t-1}+A_{2}y_{t-2}+e_{t}}
761:
is dependent on correctness of the selected lag order.
4897:
4882:
2768:
2647:
2580:
2468:
2413:
2358:
2284:
1879:
1824:
1774:
1745:
1696:
1232:
matrix appears because this example has a maximum lag
1165:
1098:
1010:
967:
912:
544:
terms. The error terms must satisfy three conditions:
5520:
5489:
5452:
5322:
5222:
5139:
5108:
5088:
5020:
4878:
4746:
4611:
4505:
4438:
4321:
4242:
4194:
3976:
3778:
3598:
3353:
2999:
2919:
2849:
2719:
2278:
2215:
1968:
1690:
1578:
1394:
1245:
906:
837:
679:
604:
553:
331:
8022:
Autoregressive conditional heteroskedasticity (ARCH)
5576:
Autoregressive model § n-step-ahead forecasting
757:
in the VAR model requires special attention because
287:
would indicate the price of wheat in the year 1998.
251:(Equivalently, this vector might be described as a (
9453:
9095:
8829:
8578:
8543:
8473:
8329:
8266:
8219:
8182:
8137:
8119:
8086:
8077:
8035:
7982:
7943:
7892:
7883:
7804:
7761:
7691:
7657:
7611:
7578:
7540:
7507:
7419:
7328:
7247:
7202:
7170:
7123:
7068:
6994:
6985:
6795:
6737:
6711:
6663:
6618:
6565:
6452:
6407:
6381:
6363:
6319:
6271:
6191:
6182:
6087:Qin, Duo (2011). "Rise of VAR Modelling Approach".
649:{\displaystyle \mathrm {E} (e_{t}e_{t}')=\Omega \,}
5536:
5502:
5471:
5431:
5303:{\displaystyle y_{t}=A^{2}y_{t-2}+Ae_{t-1}+e_{t};}
5302:
5202:
5114:
5094:
5071:
4977:
4853:
4718:
4595:
4444:
4421:
4301:
4216:
4157:
3903:
3752:
3578:
3227:is not zero. This is different from the case when
3192:
2979:Writing the first equation explicitly and passing
2968:
2897:
2828:
2699:
2269:For example, a two variable structural VAR(1) is:
2258:
2113:
1912:
1668:
1531:
1379:
1217:
859:
817:One can stack the vectors in order to write a VAR(
729:
648:
584:
460:
6070:New Introduction to Multiple Time Series Analysis
4488:Estimation of the covariance matrix of the errors
217:A VAR model describes the evolution of a set of
169:but its sources remain unclear because it lacks
7570:Multivariate adaptive regression splines (MARS)
5857:Journal of the American Statistical Association
4865:Estimation of the estimator's covariance matrix
3953:. Thus, the occurrence of one structural shock
769:Note that all variables have to be of the same
730:{\displaystyle \mathrm {E} (e_{t}e_{t-k}')=0\,}
4483:estimator applied to each equation separately.
228:, over time. Each period of time is numbered,
8451:
6125:
5126:-th element of the vector of shocks upon the
4471:. It is furthermore equal to the conditional
3280:estimation of the structural VAR would yield
799:(VECM) which can be seen as a restricted VAR.
8:
5122:of shocks. To find, say, the effect of the
8458:
8444:
8436:
8179:
8166:
8083:
7889:
7758:
7733:
7504:
7480:
7208:
6991:
6792:
6779:
6562:
6549:
6188:
6179:
6166:
6132:
6118:
6110:
5840:. Princeton University Press. p. 293.
485:time periods earlier and are called the "i
5904:
5525:
5519:
5494:
5488:
5457:
5451:
5420:
5401:
5379:
5369:
5350:
5340:
5327:
5321:
5291:
5272:
5250:
5240:
5227:
5221:
5203:{\displaystyle y_{t-1}=Ay_{t-2}+e_{t-1}.}
5185:
5166:
5144:
5138:
5107:
5087:
5060:
5041:
5025:
5019:
4974:
4960:
4959:
4947:
4930:
4907:
4906:
4896:
4880:
4879:
4877:
4826:
4825:
4799:
4798:
4762:
4748:
4747:
4745:
4707:
4696:
4695:
4688:
4677:
4676:
4669:
4658:
4627:
4613:
4612:
4610:
4584:
4573:
4572:
4565:
4554:
4553:
4546:
4535:
4521:
4507:
4506:
4504:
4437:
4389:
4370:
4332:
4331:
4320:
4302:{\displaystyle {\hat {B}}=YZ'(ZZ')^{-1}.}
4287:
4244:
4243:
4241:
4213:
4193:
4154:
4137:
4132:
4113:
4108:
4081:
4076:
4060:
4050:
4037:
4032:
4020:
4005:
3995:
3983:
3975:
3895:
3876:
3866:
3841:
3831:
3812:
3802:
3783:
3777:
3744:
3731:
3718:
3713:
3704:
3678:
3672:
3659:
3646:
3641:
3621:
3608:
3603:
3597:
3567:
3554:
3549:
3530:
3520:
3507:
3502:
3477:
3467:
3454:
3449:
3430:
3420:
3407:
3402:
3389:
3376:
3371:
3358:
3352:
3189:
3177:
3152:
3130:
3105:
3083:
3064:
3042:
3023:
3004:
2998:
2951:
2938:
2920:
2918:
2889:
2884:
2868:
2850:
2848:
2809:
2804:
2780:
2775:
2763:
2748:
2738:
2726:
2718:
2674:
2654:
2642:
2613:
2587:
2575:
2549:
2525:
2499:
2475:
2463:
2440:
2420:
2408:
2385:
2365:
2353:
2322:
2296:
2279:
2277:
2238:
2228:
2216:
2214:
2102:
2083:
2073:
2048:
2038:
2019:
2009:
1996:
1983:
1973:
1967:
1886:
1874:
1851:
1831:
1819:
1793:
1781:
1769:
1740:
1717:
1703:
1691:
1689:
1660:
1641:
1631:
1612:
1602:
1583:
1577:
1528:
1513:
1488:
1472:
1447:
1431:
1418:
1399:
1393:
1376:
1364:
1339:
1323:
1298:
1282:
1269:
1250:
1244:
1192:
1172:
1160:
1131:
1105:
1093:
1073:
1055:
1035:
1017:
1005:
988:
974:
962:
939:
919:
907:
905:
856:
836:
726:
702:
692:
680:
678:
645:
627:
617:
605:
603:
581:
566:
554:
552:
457:
448:
429:
419:
394:
384:
365:
355:
336:
330:
200:Learn how and when to remove this message
76:Learn how and when to remove this message
5570:Forecasting using an estimated VAR model
753:The process of choosing the maximum lag
745:across time. In particular, there is no
39:This article includes a list of general
5735:
5650:has support for VARs and Bayesian VARs.
5584:An estimated VAR model can be used for
4232:(MLS) approach for estimating B yields:
4177:Estimation of the regression parameters
585:{\displaystyle \mathrm {E} (e_{t})=0\,}
8096:KaplanâMeier estimator (product limit)
5889:(1980). "Macroeconomics and Reality".
5881:
5879:
4312:This can be written alternatively as:
3259:and subsequent future values, but not
290:VAR models are characterized by their
5072:{\displaystyle y_{t}=Ay_{t-1}+e_{t},}
3213:can have a contemporaneous effect on
2843:of the structural shocks are denoted
765:Order of integration of the variables
7:
8406:
8106:Accelerated failure time (AFT) model
5981:Forecasting: Principles and Practice
5808:Hatemi-J, A.; Hacker, R. S. (2009).
5775:Hacker, R. S.; Hatemi-J, A. (2008).
2135: Ă 1 vector of constants,
773:. The following cases are distinct:
504:-vector of constants serving as the
314:)" and sometimes called "a VAR with
8418:
7701:Analysis of variance (ANOVA, anova)
892:General matrix notation of a VAR(p)
236:. The variables are collected in a
7796:CochranâMantelâHaenszel statistics
6422:Pearson product-moment correlation
5684:Regression analysis of time series
4962:
4750:
4737:In a matrix notation, this gives:
4615:
4509:
4122:
4021:
3984:
3977:
2927:
2924:
2921:
2857:
2854:
2851:
2727:
2720:
2253:
2217:
1679:can be recast as the VAR(1) model
828:, with a concise matrix notation:
681:
642:
606:
555:
272:, meaning the observation at time
45:it lacks sufficient corresponding
14:
5002:Interpretation of estimated model
4864:
870:Details of the matrices are in a
322:th-order VAR model is written as
8981:neoclassicalâKeynesian synthesis
8417:
8405:
8393:
8380:
8379:
6103:10.1111/j.1467-6419.2010.00637.x
5717:, an extension of VAR models to
3274:parameter identification problem
2186:matrix (the coefficients on the
146:
30:
8055:Least-squares spectral analysis
6029:Applied Econometric Time Series
3636:
3325:rate increase would not affect
882:For a general example of a VAR(
481:indicate that variable's value
107:. VAR models are often used in
7036:Mean-unbiased minimum-variance
5870:10.1080/01621459.1962.10480664
5700:Bayesian vector autoregression
4965:
4944:
4927:
4921:
4918:
4912:
4903:
4893:
4841:
4831:
4816:
4813:
4804:
4789:
4753:
4701:
4682:
4618:
4578:
4559:
4512:
4413:
4407:
4395:
4367:
4352:
4349:
4343:
4337:
4328:
4284:
4269:
4249:
4147:
4125:
4098:
4091:
4069:
4025:
4014:
3988:
3294:Error terms are not correlated
2957:
2931:
2874:
2861:
2757:
2731:
2247:
2221:
1569:For example, the VAR(2) model
717:
685:
636:
610:
572:
559:
1:
8917:Critique of political economy
8349:Geographic information system
7565:Simultaneous equations models
5782:Journal of Applied Statistics
5762:10.1016/j.econmod.2003.09.005
5614:, a statistical specialty in
5442:From this, the effect of the
5082:for evolving (state) vector
4726:for a model with a constant,
4492:As in the standard case, the
310:th-order VAR is denoted "VAR(
103:by allowing for multivariate
19:For other uses of "Var", see
7532:Coefficient of determination
7143:Uniformly most powerful test
5984:. OTexts. pp. 333â335.
5946:10.1097/PSY.0000000000000378
4494:maximum likelihood estimator
4473:maximum likelihood estimator
669:positive-semidefinite matrix
8101:Proportional hazards models
8045:Spectral density estimation
8027:Vector autoregression (VAR)
7461:Maximum posterior estimator
6693:Randomized controlled trial
6090:Journal of Economic Surveys
5715:Panel vector autoregression
2194:equation) are scaled to 1.
1940:Structural vs. reduced form
9565:
9055:Real business-cycle theory
7861:Multivariate distributions
6281:Average absolute deviation
5573:
4230:multivariate least squares
1952:structural VAR with p lags
826:matrix difference equation
749:in individual error terms.
471:The variables of the form
18:
9495:
8375:
8178:
8165:
7849:Structural equation model
7757:
7732:
7503:
7479:
7211:
7185:Score/Lagrange multiplier
6791:
6778:
6600:Sample size determination
6561:
6548:
6178:
6165:
6147:
6048:Applied Macroeconometrics
6046:Favero, Carlo A. (2001).
5795:10.1080/02664760801920473
5546:It can be seen from this
4460:of the indicated matrix.
2171: Ă 1 vector of
592:. Every error term has a
9549:Multivariate time series
8344:Environmental statistics
7866:Elliptical distributions
7659:Generalized linear model
7588:Simple linear regression
7358:HodgesâLehmann estimator
6815:Probability distribution
6724:Stochastic approximation
6286:Coefficient of variation
5705:Convergent cross mapping
4469:asymptotically efficient
4445:{\displaystyle \otimes }
4217:{\displaystyle Y=BZ+U\,}
1228:(in which only a single
860:{\displaystyle Y=BZ+U\,}
784:) (non-stationary) with
780:All the variables are I(
155:This section includes a
8695:Industrial organization
8525:Computational economics
8004:Cross-correlation (XCF)
7612:Non-standard predictors
7046:LehmannâScheffĂ© theorem
6719:Adaptive clinical trial
6027:Enders, Walter (2010).
5472:{\displaystyle e_{t-2}}
3918:. As there are no time
1955:(sometimes abbreviated
813:Concise matrix notation
184:more precise citations.
60:more precise citations.
8900:Modern monetary theory
8565:Experimental economics
8535:Pluralism in economics
8520:Mathematical economics
8400:Mathematics portal
8221:Engineering statistics
8129:NelsonâAalen estimator
7706:Analysis of covariance
7593:Ordinary least squares
7517:Pearson product-moment
6921:Statistical functional
6832:Empirical distribution
6665:Controlled experiments
6394:Frequency distribution
6172:Descriptive statistics
5938:Psychosomatic Medicine
5724:Variance decomposition
5538:
5537:{\displaystyle A^{2}.}
5514:element of the matrix
5504:
5473:
5433:
5304:
5204:
5116:
5096:
5073:
4979:
4855:
4720:
4674:
4597:
4551:
4481:ordinary least squares
4446:
4423:
4303:
4218:
4159:
3905:
3754:
3580:
3317:contemporaneous impact
3288:underlying relations:
3278:ordinary least squares
3194:
2970:
2899:
2830:
2701:
2260:
2115:
1914:
1670:
1533:
1381:
1219:
861:
802:The variables are not
797:error correction model
731:
656:. The contemporaneous
650:
586:
462:
132:simultaneous equations
8316:Population statistics
8258:System identification
7992:Autocorrelation (ACF)
7920:Exponential smoothing
7834:Discriminant analysis
7829:Canonical correlation
7693:Partition of variance
7555:Regression validation
7399:(JonckheereâTerpstra)
7298:Likelihood-ratio test
6987:Frequentist inference
6899:Locationâscale family
6820:Sampling distribution
6785:Statistical inference
6752:Cross-sectional study
6739:Observational studies
6698:Randomized experiment
6527:Stem-and-leaf display
6329:Central limit theorem
5744:Hatemi-J, A. (2004).
5612:system identification
5539:
5505:
5503:{\displaystyle y_{t}}
5474:
5434:
5305:
5205:
5117:
5097:
5074:
4980:
4856:
4721:
4654:
4598:
4531:
4447:
4424:
4304:
4219:
4160:
3906:
3755:
3581:
3315:Variables can have a
3195:
2971:
2900:
2831:
2702:
2261:
2116:
1915:
1671:
1534:
1382:
1220:
862:
732:
651:
587:
463:
247:, which is of length
89:Vector autoregression
8774:Social choice theory
8530:Behavioral economics
8239:Probabilistic design
7824:Principal components
7667:Exponential families
7619:Nonlinear regression
7598:General linear model
7560:Mixed effects models
7550:Errors and residuals
7527:Confounding variable
7429:Bayesian probability
7407:Van der Waerden test
7397:Ordered alternative
7162:Multiple comparisons
7041:RaoâBlackwellization
7004:Estimating equations
6960:Statistical distance
6678:Factorial experiment
6211:Arithmetic-Geometric
6072:. Berlin: Springer.
6020:Applied Econometrics
5838:Time Series Analysis
5518:
5487:
5450:
5320:
5220:
5137:
5106:
5086:
5018:
4876:
4744:
4609:
4503:
4436:
4319:
4240:
4192:
3974:
3776:
3768:th order reduced VAR
3596:
3351:
3248:can impact directly
2997:
2917:
2847:
2717:
2276:
2213:
1966:
1688:
1576:
1392:
1243:
904:
835:
771:order of integration
677:
660:of error terms is a
602:
551:
329:
101:autoregressive model
21:Var (disambiguation)
8858:American (National)
8558:Economic statistics
8311:Official statistics
8234:Methods engineering
7915:Seasonal adjustment
7683:Poisson regressions
7603:Bayesian regression
7542:Regression analysis
7522:Partial correlation
7494:Regression analysis
7093:Prediction interval
7088:Likelihood interval
7078:Confidence interval
7070:Interval estimation
7031:Unbiased estimators
6849:Model specification
6729:Up-and-down designs
6417:Partial correlation
6373:Index of dispersion
6291:Interquartile range
5562:are less than 1 in
4715:
4592:
4145:
4121:
4089:
4068:
4045:
4013:
3726:
3654:
3616:
3562:
3515:
3462:
3415:
3384:
2894:
2814:
2785:
2756:
2246:
788: > 0:
716:
635:
9544:Time series models
8331:Spatial statistics
8211:Medical statistics
8111:First hitting time
8065:Whittle likelihood
7716:Degrees of freedom
7711:Multivariate ANOVA
7644:Heteroscedasticity
7456:Bayesian estimator
7421:Bayesian inference
7270:KolmogorovâSmirnov
7155:Randomization test
7125:Testing hypotheses
7098:Tolerance interval
7009:Maximum likelihood
6904:Exponential family
6837:Density estimation
6797:Statistical theory
6757:Natural experiment
6703:Scientific control
6620:Survey methodology
6306:Standard deviation
5834:Hamilton, James D.
5750:Economic Modelling
5534:
5500:
5469:
5429:
5300:
5200:
5112:
5092:
5069:
4996:degrees of freedom
4989:Degrees of freedom
4975:
4901:
4886:
4851:
4716:
4694:
4593:
4571:
4463:This estimator is
4442:
4419:
4299:
4214:
4155:
4128:
4104:
4072:
4056:
4028:
4001:
3901:
3750:
3709:
3637:
3599:
3576:
3545:
3498:
3445:
3398:
3367:
3319:on other variables
3190:
2966:
2895:
2880:
2826:
2817:
2800:
2771:
2744:
2697:
2688:
2633:
2569:
2454:
2399:
2347:
2256:
2234:
2150:matrix (for every
2111:
1910:
1901:
1865:
1813:
1760:
1731:
1666:
1529:
1377:
1215:
1206:
1151:
1087:
996:
953:
857:
791:The variables are
747:serial correlation
727:
698:
646:
623:
582:
458:
221:variables, called
157:list of references
97:stochastic process
9531:
9530:
9062:New institutional
8433:
8432:
8371:
8370:
8367:
8366:
8306:National accounts
8276:Actuarial science
8268:Social statistics
8161:
8160:
8157:
8156:
8153:
8152:
8088:Survival function
8073:
8072:
7935:Granger causality
7776:Contingency table
7751:Survival analysis
7728:
7727:
7724:
7723:
7580:Linear regression
7475:
7474:
7471:
7470:
7446:Credible interval
7415:
7414:
7198:
7197:
7014:Method of moments
6883:Parametric family
6844:Statistical model
6774:
6773:
6770:
6769:
6688:Random assignment
6610:Statistical power
6544:
6543:
6540:
6539:
6389:Contingency table
6359:
6358:
6226:Generalized/power
6066:LĂŒtkepohl, Helmut
6038:978-0-470-50539-7
5991:978-0-9875071-1-2
5887:Sims, Christopher
5815:Applied Economics
5710:Granger causality
5483:-th component of
5446:-th component of
5115:{\displaystyle e}
5095:{\displaystyle y}
4968:
4915:
4900:
4890:
4885:
4834:
4807:
4787:
4756:
4704:
4685:
4652:
4621:
4581:
4562:
4529:
4515:
4454:Kronecker product
4400:
4340:
4252:
3707:
3681:
2206:structural shocks
2197:The error terms Δ
737:for any non-zero
658:covariance matrix
210:
209:
202:
128:structural models
86:
85:
78:
9556:
8735:Natural resource
8570:Economic history
8508:Mechanism design
8460:
8453:
8446:
8437:
8421:
8420:
8409:
8408:
8398:
8397:
8383:
8382:
8286:Crime statistics
8180:
8167:
8084:
8050:Fourier analysis
8037:Frequency domain
8017:
7964:
7930:Structural break
7890:
7839:Cluster analysis
7786:Log-linear model
7759:
7734:
7675:
7649:Homoscedasticity
7505:
7481:
7400:
7392:
7384:
7383:(KruskalâWallis)
7368:
7353:
7308:Cross validation
7293:
7275:AndersonâDarling
7222:
7209:
7180:Likelihood-ratio
7172:Parametric tests
7150:Permutation test
7133:1- & 2-tails
7024:Minimum distance
6996:Point estimation
6992:
6943:Optimal decision
6894:
6793:
6780:
6762:Quasi-experiment
6712:Adaptive designs
6563:
6550:
6427:Rank correlation
6189:
6180:
6167:
6134:
6127:
6120:
6111:
6106:
6083:
6061:
6042:
6023:
6005:
6002:
5996:
5995:
5975:
5969:
5964:
5958:
5957:
5933:
5927:
5926:
5908:
5883:
5874:
5873:
5864:(298): 348â368.
5848:
5842:
5841:
5830:
5824:
5823:
5805:
5799:
5798:
5772:
5766:
5765:
5740:
5597:Christopher Sims
5543:
5541:
5540:
5535:
5530:
5529:
5509:
5507:
5506:
5501:
5499:
5498:
5478:
5476:
5475:
5470:
5468:
5467:
5438:
5436:
5435:
5430:
5425:
5424:
5412:
5411:
5390:
5389:
5374:
5373:
5361:
5360:
5345:
5344:
5332:
5331:
5309:
5307:
5306:
5301:
5296:
5295:
5283:
5282:
5261:
5260:
5245:
5244:
5232:
5231:
5209:
5207:
5206:
5201:
5196:
5195:
5177:
5176:
5155:
5154:
5121:
5119:
5118:
5113:
5101:
5099:
5098:
5093:
5078:
5076:
5075:
5070:
5065:
5064:
5052:
5051:
5030:
5029:
5007:Impulse response
4984:
4982:
4981:
4976:
4970:
4969:
4961:
4955:
4954:
4942:
4941:
4917:
4916:
4908:
4902:
4898:
4892:
4891:
4883:
4881:
4860:
4858:
4857:
4852:
4847:
4836:
4835:
4827:
4809:
4808:
4800:
4788:
4786:
4763:
4758:
4757:
4749:
4725:
4723:
4722:
4717:
4711:
4706:
4705:
4697:
4693:
4692:
4687:
4686:
4678:
4673:
4668:
4653:
4651:
4628:
4623:
4622:
4614:
4602:
4600:
4599:
4594:
4588:
4583:
4582:
4574:
4570:
4569:
4564:
4563:
4555:
4550:
4545:
4530:
4522:
4517:
4516:
4508:
4451:
4449:
4448:
4443:
4428:
4426:
4425:
4420:
4398:
4394:
4393:
4378:
4377:
4365:
4342:
4341:
4333:
4308:
4306:
4305:
4300:
4295:
4294:
4282:
4268:
4254:
4253:
4245:
4223:
4221:
4220:
4215:
4164:
4162:
4161:
4156:
4153:
4144:
4136:
4120:
4112:
4097:
4088:
4080:
4064:
4055:
4054:
4044:
4036:
4024:
4009:
4000:
3999:
3987:
3910:
3908:
3907:
3902:
3900:
3899:
3887:
3886:
3871:
3870:
3852:
3851:
3836:
3835:
3823:
3822:
3807:
3806:
3788:
3787:
3763:one obtains the
3759:
3757:
3756:
3751:
3749:
3748:
3736:
3735:
3725:
3717:
3708:
3705:
3682:
3679:
3677:
3676:
3664:
3663:
3653:
3645:
3626:
3625:
3615:
3607:
3585:
3583:
3582:
3577:
3572:
3571:
3561:
3553:
3541:
3540:
3525:
3524:
3514:
3506:
3488:
3487:
3472:
3471:
3461:
3453:
3441:
3440:
3425:
3424:
3414:
3406:
3394:
3393:
3383:
3375:
3363:
3362:
3334:Reduced-form VAR
3199:
3197:
3196:
3191:
3188:
3187:
3169:
3168:
3147:
3146:
3122:
3121:
3100:
3099:
3075:
3074:
3059:
3058:
3034:
3033:
3015:
3014:
2975:
2973:
2972:
2967:
2956:
2955:
2943:
2942:
2930:
2909:= 1, 2) and the
2904:
2902:
2901:
2896:
2893:
2888:
2873:
2872:
2860:
2835:
2833:
2832:
2827:
2822:
2821:
2813:
2808:
2784:
2779:
2752:
2743:
2742:
2730:
2706:
2704:
2703:
2698:
2693:
2692:
2685:
2684:
2665:
2664:
2638:
2637:
2630:
2629:
2604:
2603:
2574:
2573:
2566:
2565:
2542:
2541:
2516:
2515:
2492:
2491:
2459:
2458:
2451:
2450:
2431:
2430:
2404:
2403:
2396:
2395:
2376:
2375:
2352:
2351:
2339:
2338:
2313:
2312:
2265:
2263:
2262:
2257:
2242:
2233:
2232:
2220:
2190:variable in the
2120:
2118:
2117:
2112:
2107:
2106:
2094:
2093:
2078:
2077:
2059:
2058:
2043:
2042:
2030:
2029:
2014:
2013:
2001:
2000:
1988:
1987:
1978:
1977:
1919:
1917:
1916:
1911:
1906:
1905:
1891:
1890:
1870:
1869:
1862:
1861:
1842:
1841:
1818:
1817:
1798:
1797:
1786:
1785:
1765:
1764:
1736:
1735:
1728:
1727:
1708:
1707:
1675:
1673:
1672:
1667:
1665:
1664:
1652:
1651:
1636:
1635:
1623:
1622:
1607:
1606:
1588:
1587:
1538:
1536:
1535:
1530:
1524:
1523:
1505:
1504:
1483:
1482:
1464:
1463:
1442:
1441:
1423:
1422:
1410:
1409:
1386:
1384:
1383:
1378:
1375:
1374:
1356:
1355:
1334:
1333:
1315:
1314:
1293:
1292:
1274:
1273:
1261:
1260:
1224:
1222:
1221:
1216:
1211:
1210:
1203:
1202:
1183:
1182:
1156:
1155:
1148:
1147:
1122:
1121:
1092:
1091:
1084:
1083:
1066:
1065:
1046:
1045:
1028:
1027:
1001:
1000:
993:
992:
979:
978:
958:
957:
950:
949:
930:
929:
866:
864:
863:
858:
736:
734:
733:
728:
712:
697:
696:
684:
655:
653:
652:
647:
631:
622:
621:
609:
591:
589:
588:
583:
571:
570:
558:
467:
465:
464:
459:
453:
452:
440:
439:
424:
423:
405:
404:
389:
388:
376:
375:
360:
359:
341:
340:
306:time periods. A
255: Ă 1)-
205:
198:
194:
191:
185:
180:this section by
171:inline citations
150:
149:
142:
113:natural sciences
81:
74:
70:
67:
61:
56:this article by
47:inline citations
34:
33:
26:
9564:
9563:
9559:
9558:
9557:
9555:
9554:
9553:
9534:
9533:
9532:
9527:
9524:Business portal
9491:
9490:
9489:
9449:
9213:von Böhm-Bawerk
9101:
9100:
9091:
8863:Ancient thought
8841:
8840:
8834:
8825:
8824:
8823:
8574:
8539:
8503:Contract theory
8488:Decision theory
8469:
8464:
8434:
8429:
8392:
8363:
8325:
8262:
8248:quality control
8215:
8197:Clinical trials
8174:
8149:
8133:
8121:Hazard function
8115:
8069:
8031:
8015:
7978:
7974:BreuschâGodfrey
7962:
7939:
7879:
7854:Factor analysis
7800:
7781:Graphical model
7753:
7720:
7687:
7673:
7653:
7607:
7574:
7536:
7499:
7498:
7467:
7411:
7398:
7390:
7382:
7366:
7351:
7330:Rank statistics
7324:
7303:Model selection
7291:
7249:Goodness of fit
7243:
7220:
7194:
7166:
7119:
7064:
7053:Median unbiased
6981:
6892:
6825:Order statistic
6787:
6766:
6733:
6707:
6659:
6614:
6557:
6555:Data collection
6536:
6448:
6403:
6377:
6355:
6315:
6267:
6184:Continuous data
6174:
6161:
6143:
6138:
6086:
6080:
6064:
6058:
6045:
6039:
6026:
6017:
6014:
6012:Further reading
6009:
6008:
6003:
5999:
5992:
5977:
5976:
5972:
5965:
5961:
5935:
5934:
5930:
5915:10.2307/1912017
5906:10.1.1.163.5425
5885:
5884:
5877:
5852:Zellner, Arnold
5850:
5849:
5845:
5832:
5831:
5827:
5822:(9): 1489â1500.
5807:
5806:
5802:
5774:
5773:
5769:
5743:
5741:
5737:
5732:
5696:
5624:
5594:
5582:
5574:Main articles:
5572:
5521:
5516:
5515:
5490:
5485:
5484:
5453:
5448:
5447:
5416:
5397:
5375:
5365:
5346:
5336:
5323:
5318:
5317:
5287:
5268:
5246:
5236:
5223:
5218:
5217:
5181:
5162:
5140:
5135:
5134:
5104:
5103:
5084:
5083:
5056:
5037:
5021:
5016:
5015:
5009:
5004:
4991:
4943:
4934:
4874:
4873:
4867:
4840:
4767:
4742:
4741:
4675:
4632:
4607:
4606:
4605:OLS estimator:
4552:
4501:
4500:
4499:MLE estimator:
4490:
4434:
4433:
4385:
4366:
4358:
4317:
4316:
4283:
4275:
4261:
4238:
4237:
4190:
4189:
4179:
4174:
4146:
4090:
4046:
3991:
3972:
3971:
3965:
3958:
3952:
3944:
3937:
3891:
3872:
3862:
3837:
3827:
3808:
3798:
3779:
3774:
3773:
3740:
3727:
3706: and
3680: for
3668:
3655:
3617:
3594:
3593:
3563:
3526:
3516:
3473:
3463:
3426:
3416:
3385:
3354:
3349:
3348:
3344:
3336:
3272:Because of the
3268:
3258:
3247:
3236:identity matrix
3233:
3226:
3218:
3212:
3173:
3148:
3126:
3101:
3079:
3060:
3038:
3019:
3000:
2995:
2994:
2988:right hand side
2984:
2947:
2934:
2915:
2914:
2864:
2845:
2844:
2816:
2815:
2798:
2792:
2791:
2786:
2764:
2734:
2715:
2714:
2687:
2686:
2670:
2667:
2666:
2650:
2643:
2632:
2631:
2609:
2606:
2605:
2583:
2576:
2568:
2567:
2545:
2543:
2521:
2518:
2517:
2495:
2493:
2471:
2464:
2453:
2452:
2436:
2433:
2432:
2416:
2409:
2398:
2397:
2381:
2378:
2377:
2361:
2354:
2346:
2345:
2340:
2318:
2315:
2314:
2292:
2290:
2280:
2274:
2273:
2224:
2211:
2210:
2201:
2185:
2166:
2140:
2130:
2098:
2079:
2069:
2044:
2034:
2015:
2005:
1992:
1979:
1969:
1964:
1963:
1947:
1942:
1931:identity matrix
1900:
1899:
1893:
1892:
1882:
1875:
1864:
1863:
1847:
1844:
1843:
1827:
1820:
1812:
1811:
1806:
1800:
1799:
1789:
1787:
1777:
1770:
1759:
1758:
1752:
1751:
1741:
1730:
1729:
1713:
1710:
1709:
1699:
1692:
1686:
1685:
1656:
1637:
1627:
1608:
1598:
1579:
1574:
1573:
1556:
1509:
1484:
1468:
1443:
1427:
1414:
1395:
1390:
1389:
1360:
1335:
1319:
1294:
1278:
1265:
1246:
1241:
1240:
1205:
1204:
1188:
1185:
1184:
1168:
1161:
1150:
1149:
1127:
1124:
1123:
1101:
1094:
1086:
1085:
1069:
1067:
1051:
1048:
1047:
1031:
1029:
1013:
1006:
995:
994:
984:
981:
980:
970:
963:
952:
951:
935:
932:
931:
915:
908:
902:
901:
890:variables, see
880:
833:
832:
815:
767:
688:
675:
674:
613:
600:
599:
562:
549:
548:
535:
513:
496:. The variable
495:
480:
444:
425:
415:
390:
380:
361:
351:
332:
327:
326:
286:
271:
245:
215:
206:
195:
189:
186:
175:
161:related reading
151:
147:
140:
82:
71:
65:
62:
52:Please help to
51:
35:
31:
24:
17:
12:
11:
5:
9562:
9560:
9552:
9551:
9546:
9536:
9535:
9529:
9528:
9526:
9521:
9516:
9511:
9506:
9501:
9496:
9493:
9492:
9488:
9487:
9482:
9472:
9467:
9461:
9460:
9459:
9457:
9451:
9450:
9448:
9447:
9440:
9435:
9430:
9425:
9420:
9415:
9410:
9405:
9400:
9395:
9390:
9385:
9380:
9375:
9370:
9365:
9360:
9355:
9350:
9345:
9340:
9335:
9330:
9325:
9320:
9315:
9310:
9305:
9300:
9295:
9290:
9285:
9280:
9275:
9270:
9265:
9260:
9255:
9250:
9245:
9240:
9235:
9230:
9225:
9220:
9215:
9210:
9205:
9200:
9195:
9190:
9185:
9180:
9175:
9170:
9165:
9160:
9155:
9150:
9145:
9140:
9135:
9130:
9125:
9120:
9115:
9110:
9104:
9102:
9096:
9093:
9092:
9090:
9089:
9084:
9079:
9074:
9069:
9064:
9059:
9058:
9057:
9047:
9046:
9045:
9035:
9030:
9025:
9024:
9023:
9013:
9008:
9003:
9002:
9001:
9000:
8999:
8989:
8984:
8969:
8964:
8959:
8954:
8949:
8944:
8939:
8934:
8929:
8927:Disequilibrium
8924:
8919:
8914:
8909:
8904:
8903:
8902:
8892:
8887:
8882:
8877:
8876:
8875:
8865:
8860:
8855:
8850:
8844:
8842:
8830:
8827:
8826:
8822:
8821:
8816:
8811:
8806:
8801:
8796:
8791:
8786:
8781:
8776:
8767:
8762:
8757:
8752:
8747:
8742:
8740:Organizational
8737:
8732:
8727:
8722:
8717:
8712:
8707:
8702:
8697:
8692:
8687:
8682:
8677:
8672:
8667:
8662:
8657:
8652:
8647:
8642:
8637:
8632:
8627:
8622:
8617:
8612:
8607:
8602:
8597:
8592:
8586:
8585:
8584:
8582:
8576:
8575:
8573:
8572:
8567:
8562:
8561:
8560:
8549:
8547:
8541:
8540:
8538:
8537:
8532:
8527:
8522:
8517:
8515:Macroeconomics
8512:
8511:
8510:
8505:
8500:
8495:
8490:
8483:Microeconomics
8479:
8477:
8471:
8470:
8465:
8463:
8462:
8455:
8448:
8440:
8431:
8430:
8428:
8427:
8415:
8403:
8389:
8376:
8373:
8372:
8369:
8368:
8365:
8364:
8362:
8361:
8356:
8351:
8346:
8341:
8335:
8333:
8327:
8326:
8324:
8323:
8318:
8313:
8308:
8303:
8298:
8293:
8288:
8283:
8278:
8272:
8270:
8264:
8263:
8261:
8260:
8255:
8250:
8241:
8236:
8231:
8225:
8223:
8217:
8216:
8214:
8213:
8208:
8203:
8194:
8192:Bioinformatics
8188:
8186:
8176:
8175:
8170:
8163:
8162:
8159:
8158:
8155:
8154:
8151:
8150:
8148:
8147:
8141:
8139:
8135:
8134:
8132:
8131:
8125:
8123:
8117:
8116:
8114:
8113:
8108:
8103:
8098:
8092:
8090:
8081:
8075:
8074:
8071:
8070:
8068:
8067:
8062:
8057:
8052:
8047:
8041:
8039:
8033:
8032:
8030:
8029:
8024:
8019:
8011:
8006:
8001:
8000:
7999:
7997:partial (PACF)
7988:
7986:
7980:
7979:
7977:
7976:
7971:
7966:
7958:
7953:
7947:
7945:
7944:Specific tests
7941:
7940:
7938:
7937:
7932:
7927:
7922:
7917:
7912:
7907:
7902:
7896:
7894:
7887:
7881:
7880:
7878:
7877:
7876:
7875:
7874:
7873:
7858:
7857:
7856:
7846:
7844:Classification
7841:
7836:
7831:
7826:
7821:
7816:
7810:
7808:
7802:
7801:
7799:
7798:
7793:
7791:McNemar's test
7788:
7783:
7778:
7773:
7767:
7765:
7755:
7754:
7737:
7730:
7729:
7726:
7725:
7722:
7721:
7719:
7718:
7713:
7708:
7703:
7697:
7695:
7689:
7688:
7686:
7685:
7669:
7663:
7661:
7655:
7654:
7652:
7651:
7646:
7641:
7636:
7631:
7629:Semiparametric
7626:
7621:
7615:
7613:
7609:
7608:
7606:
7605:
7600:
7595:
7590:
7584:
7582:
7576:
7575:
7573:
7572:
7567:
7562:
7557:
7552:
7546:
7544:
7538:
7537:
7535:
7534:
7529:
7524:
7519:
7513:
7511:
7501:
7500:
7497:
7496:
7491:
7485:
7484:
7477:
7476:
7473:
7472:
7469:
7468:
7466:
7465:
7464:
7463:
7453:
7448:
7443:
7442:
7441:
7436:
7425:
7423:
7417:
7416:
7413:
7412:
7410:
7409:
7404:
7403:
7402:
7394:
7386:
7370:
7367:(MannâWhitney)
7362:
7361:
7360:
7347:
7346:
7345:
7334:
7332:
7326:
7325:
7323:
7322:
7321:
7320:
7315:
7310:
7300:
7295:
7292:(ShapiroâWilk)
7287:
7282:
7277:
7272:
7267:
7259:
7253:
7251:
7245:
7244:
7242:
7241:
7233:
7224:
7212:
7206:
7204:Specific tests
7200:
7199:
7196:
7195:
7193:
7192:
7187:
7182:
7176:
7174:
7168:
7167:
7165:
7164:
7159:
7158:
7157:
7147:
7146:
7145:
7135:
7129:
7127:
7121:
7120:
7118:
7117:
7116:
7115:
7110:
7100:
7095:
7090:
7085:
7080:
7074:
7072:
7066:
7065:
7063:
7062:
7057:
7056:
7055:
7050:
7049:
7048:
7043:
7028:
7027:
7026:
7021:
7016:
7011:
7000:
6998:
6989:
6983:
6982:
6980:
6979:
6974:
6969:
6968:
6967:
6957:
6952:
6951:
6950:
6940:
6939:
6938:
6933:
6928:
6918:
6913:
6908:
6907:
6906:
6901:
6896:
6880:
6879:
6878:
6873:
6868:
6858:
6857:
6856:
6851:
6841:
6840:
6839:
6829:
6828:
6827:
6817:
6812:
6807:
6801:
6799:
6789:
6788:
6783:
6776:
6775:
6772:
6771:
6768:
6767:
6765:
6764:
6759:
6754:
6749:
6743:
6741:
6735:
6734:
6732:
6731:
6726:
6721:
6715:
6713:
6709:
6708:
6706:
6705:
6700:
6695:
6690:
6685:
6680:
6675:
6669:
6667:
6661:
6660:
6658:
6657:
6655:Standard error
6652:
6647:
6642:
6641:
6640:
6635:
6624:
6622:
6616:
6615:
6613:
6612:
6607:
6602:
6597:
6592:
6587:
6585:Optimal design
6582:
6577:
6571:
6569:
6559:
6558:
6553:
6546:
6545:
6542:
6541:
6538:
6537:
6535:
6534:
6529:
6524:
6519:
6514:
6509:
6504:
6499:
6494:
6489:
6484:
6479:
6474:
6469:
6464:
6458:
6456:
6450:
6449:
6447:
6446:
6441:
6440:
6439:
6434:
6424:
6419:
6413:
6411:
6405:
6404:
6402:
6401:
6396:
6391:
6385:
6383:
6382:Summary tables
6379:
6378:
6376:
6375:
6369:
6367:
6361:
6360:
6357:
6356:
6354:
6353:
6352:
6351:
6346:
6341:
6331:
6325:
6323:
6317:
6316:
6314:
6313:
6308:
6303:
6298:
6293:
6288:
6283:
6277:
6275:
6269:
6268:
6266:
6265:
6260:
6255:
6254:
6253:
6248:
6243:
6238:
6233:
6228:
6223:
6218:
6216:Contraharmonic
6213:
6208:
6197:
6195:
6186:
6176:
6175:
6170:
6163:
6162:
6160:
6159:
6154:
6148:
6145:
6144:
6139:
6137:
6136:
6129:
6122:
6114:
6108:
6107:
6097:(1): 156â174.
6084:
6078:
6062:
6056:
6043:
6037:
6024:
6013:
6010:
6007:
6006:
5997:
5990:
5970:
5959:
5928:
5875:
5843:
5825:
5800:
5789:(6): 601â615.
5767:
5756:(4): 661â683.
5734:
5733:
5731:
5728:
5727:
5726:
5721:
5712:
5707:
5702:
5695:
5692:
5691:
5690:
5687:
5681:
5675:
5669:
5663:
5657:
5651:
5637:
5630:: The package
5623:
5620:
5616:control theory
5593:
5590:
5571:
5568:
5564:absolute value
5558:of the matrix
5533:
5528:
5524:
5497:
5493:
5466:
5463:
5460:
5456:
5440:
5439:
5428:
5423:
5419:
5415:
5410:
5407:
5404:
5400:
5396:
5393:
5388:
5385:
5382:
5378:
5372:
5368:
5364:
5359:
5356:
5353:
5349:
5343:
5339:
5335:
5330:
5326:
5311:
5310:
5299:
5294:
5290:
5286:
5281:
5278:
5275:
5271:
5267:
5264:
5259:
5256:
5253:
5249:
5243:
5239:
5235:
5230:
5226:
5211:
5210:
5199:
5194:
5191:
5188:
5184:
5180:
5175:
5172:
5169:
5165:
5161:
5158:
5153:
5150:
5147:
5143:
5111:
5091:
5080:
5079:
5068:
5063:
5059:
5055:
5050:
5047:
5044:
5040:
5036:
5033:
5028:
5024:
5008:
5005:
5003:
5000:
4990:
4987:
4986:
4985:
4973:
4967:
4964:
4958:
4953:
4950:
4946:
4940:
4937:
4933:
4929:
4926:
4923:
4920:
4914:
4911:
4905:
4895:
4889:
4866:
4863:
4862:
4861:
4850:
4846:
4843:
4839:
4833:
4830:
4824:
4821:
4818:
4815:
4812:
4806:
4803:
4797:
4794:
4791:
4785:
4782:
4779:
4776:
4773:
4770:
4766:
4761:
4755:
4752:
4730:variables and
4714:
4710:
4703:
4700:
4691:
4684:
4681:
4672:
4667:
4664:
4661:
4657:
4650:
4647:
4644:
4641:
4638:
4635:
4631:
4626:
4620:
4617:
4591:
4587:
4580:
4577:
4568:
4561:
4558:
4549:
4544:
4541:
4538:
4534:
4528:
4525:
4520:
4514:
4511:
4489:
4486:
4485:
4484:
4441:
4430:
4429:
4418:
4415:
4412:
4409:
4406:
4403:
4397:
4392:
4388:
4384:
4381:
4376:
4373:
4369:
4364:
4361:
4357:
4354:
4351:
4348:
4345:
4339:
4336:
4330:
4327:
4324:
4310:
4309:
4298:
4293:
4290:
4286:
4281:
4278:
4274:
4271:
4267:
4264:
4260:
4257:
4251:
4248:
4234:
4233:
4225:
4224:
4212:
4209:
4206:
4203:
4200:
4197:
4178:
4175:
4173:
4170:
4166:
4165:
4152:
4149:
4143:
4140:
4135:
4131:
4127:
4124:
4119:
4116:
4111:
4107:
4103:
4100:
4096:
4093:
4087:
4084:
4079:
4075:
4071:
4067:
4063:
4059:
4053:
4049:
4043:
4040:
4035:
4031:
4027:
4023:
4019:
4016:
4012:
4008:
4004:
3998:
3994:
3990:
3986:
3982:
3979:
3963:
3956:
3948:
3942:
3933:
3912:
3911:
3898:
3894:
3890:
3885:
3882:
3879:
3875:
3869:
3865:
3861:
3858:
3855:
3850:
3847:
3844:
3840:
3834:
3830:
3826:
3821:
3818:
3815:
3811:
3805:
3801:
3797:
3794:
3791:
3786:
3782:
3761:
3760:
3747:
3743:
3739:
3734:
3730:
3724:
3721:
3716:
3712:
3703:
3700:
3697:
3694:
3691:
3688:
3685:
3675:
3671:
3667:
3662:
3658:
3652:
3649:
3644:
3640:
3635:
3632:
3629:
3624:
3620:
3614:
3611:
3606:
3602:
3587:
3586:
3575:
3570:
3566:
3560:
3557:
3552:
3548:
3544:
3539:
3536:
3533:
3529:
3523:
3519:
3513:
3510:
3505:
3501:
3497:
3494:
3491:
3486:
3483:
3480:
3476:
3470:
3466:
3460:
3457:
3452:
3448:
3444:
3439:
3436:
3433:
3429:
3423:
3419:
3413:
3410:
3405:
3401:
3397:
3392:
3388:
3382:
3379:
3374:
3370:
3366:
3361:
3357:
3342:
3335:
3332:
3331:
3330:
3310:
3309:
3263:
3252:
3242:
3231:
3224:
3216:
3207:
3201:
3200:
3186:
3183:
3180:
3176:
3172:
3167:
3164:
3161:
3158:
3155:
3151:
3145:
3142:
3139:
3136:
3133:
3129:
3125:
3120:
3117:
3114:
3111:
3108:
3104:
3098:
3095:
3092:
3089:
3086:
3082:
3078:
3073:
3070:
3067:
3063:
3057:
3054:
3051:
3048:
3045:
3041:
3037:
3032:
3029:
3026:
3022:
3018:
3013:
3010:
3007:
3003:
2982:
2965:
2962:
2959:
2954:
2950:
2946:
2941:
2937:
2933:
2929:
2926:
2923:
2892:
2887:
2883:
2879:
2876:
2871:
2867:
2863:
2859:
2856:
2853:
2837:
2836:
2825:
2820:
2812:
2807:
2803:
2799:
2797:
2794:
2793:
2790:
2787:
2783:
2778:
2774:
2770:
2769:
2767:
2762:
2759:
2755:
2751:
2747:
2741:
2737:
2733:
2729:
2725:
2722:
2708:
2707:
2696:
2691:
2683:
2680:
2677:
2673:
2669:
2668:
2663:
2660:
2657:
2653:
2649:
2648:
2646:
2641:
2636:
2628:
2625:
2622:
2619:
2616:
2612:
2608:
2607:
2602:
2599:
2596:
2593:
2590:
2586:
2582:
2581:
2579:
2572:
2564:
2561:
2558:
2555:
2552:
2548:
2544:
2540:
2537:
2534:
2531:
2528:
2524:
2520:
2519:
2514:
2511:
2508:
2505:
2502:
2498:
2494:
2490:
2487:
2484:
2481:
2478:
2474:
2470:
2469:
2467:
2462:
2457:
2449:
2446:
2443:
2439:
2435:
2434:
2429:
2426:
2423:
2419:
2415:
2414:
2412:
2407:
2402:
2394:
2391:
2388:
2384:
2380:
2379:
2374:
2371:
2368:
2364:
2360:
2359:
2357:
2350:
2344:
2341:
2337:
2334:
2331:
2328:
2325:
2321:
2317:
2316:
2311:
2308:
2305:
2302:
2299:
2295:
2291:
2289:
2286:
2285:
2283:
2255:
2252:
2249:
2245:
2241:
2237:
2231:
2227:
2223:
2219:
2199:
2183:
2162:
2138:
2128:
2122:
2121:
2110:
2105:
2101:
2097:
2092:
2089:
2086:
2082:
2076:
2072:
2068:
2065:
2062:
2057:
2054:
2051:
2047:
2041:
2037:
2033:
2028:
2025:
2022:
2018:
2012:
2008:
2004:
1999:
1995:
1991:
1986:
1982:
1976:
1972:
1946:
1945:Structural VAR
1943:
1941:
1938:
1923:
1922:
1921:
1920:
1909:
1904:
1898:
1895:
1894:
1889:
1885:
1881:
1880:
1878:
1873:
1868:
1860:
1857:
1854:
1850:
1846:
1845:
1840:
1837:
1834:
1830:
1826:
1825:
1823:
1816:
1810:
1807:
1805:
1802:
1801:
1796:
1792:
1788:
1784:
1780:
1776:
1775:
1773:
1768:
1763:
1757:
1754:
1753:
1750:
1747:
1746:
1744:
1739:
1734:
1726:
1723:
1720:
1716:
1712:
1711:
1706:
1702:
1698:
1697:
1695:
1677:
1676:
1663:
1659:
1655:
1650:
1647:
1644:
1640:
1634:
1630:
1626:
1621:
1618:
1615:
1611:
1605:
1601:
1597:
1594:
1591:
1586:
1582:
1555:
1548:
1540:
1539:
1527:
1522:
1519:
1516:
1512:
1508:
1503:
1500:
1497:
1494:
1491:
1487:
1481:
1478:
1475:
1471:
1467:
1462:
1459:
1456:
1453:
1450:
1446:
1440:
1437:
1434:
1430:
1426:
1421:
1417:
1413:
1408:
1405:
1402:
1398:
1387:
1373:
1370:
1367:
1363:
1359:
1354:
1351:
1348:
1345:
1342:
1338:
1332:
1329:
1326:
1322:
1318:
1313:
1310:
1307:
1304:
1301:
1297:
1291:
1288:
1285:
1281:
1277:
1272:
1268:
1264:
1259:
1256:
1253:
1249:
1226:
1225:
1214:
1209:
1201:
1198:
1195:
1191:
1187:
1186:
1181:
1178:
1175:
1171:
1167:
1166:
1164:
1159:
1154:
1146:
1143:
1140:
1137:
1134:
1130:
1126:
1125:
1120:
1117:
1114:
1111:
1108:
1104:
1100:
1099:
1097:
1090:
1082:
1079:
1076:
1072:
1068:
1064:
1061:
1058:
1054:
1050:
1049:
1044:
1041:
1038:
1034:
1030:
1026:
1023:
1020:
1016:
1012:
1011:
1009:
1004:
999:
991:
987:
983:
982:
977:
973:
969:
968:
966:
961:
956:
948:
945:
942:
938:
934:
933:
928:
925:
922:
918:
914:
913:
911:
879:
876:
868:
867:
855:
852:
849:
846:
843:
840:
814:
811:
810:
809:
808:
807:
800:
778:
766:
763:
751:
750:
741:. There is no
725:
722:
719:
715:
711:
708:
705:
701:
695:
691:
687:
683:
672:
644:
641:
638:
634:
630:
626:
620:
616:
612:
608:
597:
580:
577:
574:
569:
565:
561:
557:
531:
517:time-invariant
511:
508:of the model.
493:
475:
469:
468:
456:
451:
447:
443:
438:
435:
432:
428:
422:
418:
414:
411:
408:
403:
400:
397:
393:
387:
383:
379:
374:
371:
368:
364:
358:
354:
350:
347:
344:
339:
335:
284:
263:
243:
214:
211:
208:
207:
165:external links
154:
152:
145:
139:
136:
84:
83:
38:
36:
29:
15:
13:
10:
9:
6:
4:
3:
2:
9561:
9550:
9547:
9545:
9542:
9541:
9539:
9525:
9522:
9520:
9517:
9515:
9512:
9510:
9507:
9505:
9502:
9500:
9497:
9494:
9486:
9483:
9480:
9476:
9473:
9471:
9468:
9466:
9463:
9462:
9458:
9456:
9452:
9446:
9445:
9441:
9439:
9436:
9434:
9431:
9429:
9426:
9424:
9421:
9419:
9416:
9414:
9411:
9409:
9406:
9404:
9401:
9399:
9396:
9394:
9391:
9389:
9386:
9384:
9381:
9379:
9376:
9374:
9371:
9369:
9366:
9364:
9361:
9359:
9356:
9354:
9351:
9349:
9346:
9344:
9341:
9339:
9336:
9334:
9331:
9329:
9326:
9324:
9321:
9319:
9316:
9314:
9311:
9309:
9306:
9304:
9301:
9299:
9296:
9294:
9291:
9289:
9286:
9284:
9281:
9279:
9276:
9274:
9271:
9269:
9266:
9264:
9261:
9259:
9256:
9254:
9251:
9249:
9246:
9244:
9241:
9239:
9236:
9234:
9231:
9229:
9226:
9224:
9221:
9219:
9216:
9214:
9211:
9209:
9206:
9204:
9201:
9199:
9196:
9194:
9191:
9189:
9186:
9184:
9181:
9179:
9176:
9174:
9171:
9169:
9166:
9164:
9161:
9159:
9156:
9154:
9151:
9149:
9146:
9144:
9141:
9139:
9136:
9134:
9131:
9129:
9126:
9124:
9121:
9119:
9116:
9114:
9111:
9109:
9108:de Mandeville
9106:
9105:
9103:
9099:
9094:
9088:
9085:
9083:
9080:
9078:
9075:
9073:
9070:
9068:
9065:
9063:
9060:
9056:
9053:
9052:
9051:
9050:New classical
9048:
9044:
9041:
9040:
9039:
9036:
9034:
9031:
9029:
9026:
9022:
9019:
9018:
9017:
9014:
9012:
9009:
9007:
9006:Malthusianism
9004:
8998:
8995:
8994:
8993:
8990:
8988:
8985:
8982:
8978:
8975:
8974:
8973:
8970:
8968:
8967:Institutional
8965:
8963:
8960:
8958:
8955:
8953:
8950:
8948:
8945:
8943:
8940:
8938:
8935:
8933:
8930:
8928:
8925:
8923:
8920:
8918:
8915:
8913:
8910:
8908:
8905:
8901:
8898:
8897:
8896:
8893:
8891:
8888:
8886:
8883:
8881:
8878:
8874:
8871:
8870:
8869:
8866:
8864:
8861:
8859:
8856:
8854:
8851:
8849:
8846:
8845:
8843:
8838:
8833:
8828:
8820:
8817:
8815:
8812:
8810:
8807:
8805:
8802:
8800:
8797:
8795:
8792:
8790:
8787:
8785:
8782:
8780:
8777:
8775:
8771:
8770:Public choice
8768:
8766:
8763:
8761:
8758:
8756:
8753:
8751:
8748:
8746:
8745:Participation
8743:
8741:
8738:
8736:
8733:
8731:
8728:
8726:
8723:
8721:
8718:
8716:
8713:
8711:
8708:
8706:
8705:Institutional
8703:
8701:
8698:
8696:
8693:
8691:
8688:
8686:
8683:
8681:
8678:
8676:
8673:
8671:
8668:
8666:
8663:
8661:
8658:
8656:
8655:Expeditionary
8653:
8651:
8648:
8646:
8645:Environmental
8643:
8641:
8638:
8636:
8633:
8631:
8628:
8626:
8623:
8621:
8618:
8616:
8613:
8611:
8608:
8606:
8603:
8601:
8598:
8596:
8593:
8591:
8588:
8587:
8583:
8581:
8577:
8571:
8568:
8566:
8563:
8559:
8556:
8555:
8554:
8551:
8550:
8548:
8546:
8542:
8536:
8533:
8531:
8528:
8526:
8523:
8521:
8518:
8516:
8513:
8509:
8506:
8504:
8501:
8499:
8496:
8494:
8491:
8489:
8486:
8485:
8484:
8481:
8480:
8478:
8476:
8472:
8468:
8461:
8456:
8454:
8449:
8447:
8442:
8441:
8438:
8426:
8425:
8416:
8414:
8413:
8404:
8402:
8401:
8396:
8390:
8388:
8387:
8378:
8377:
8374:
8360:
8357:
8355:
8354:Geostatistics
8352:
8350:
8347:
8345:
8342:
8340:
8337:
8336:
8334:
8332:
8328:
8322:
8321:Psychometrics
8319:
8317:
8314:
8312:
8309:
8307:
8304:
8302:
8299:
8297:
8294:
8292:
8289:
8287:
8284:
8282:
8279:
8277:
8274:
8273:
8271:
8269:
8265:
8259:
8256:
8254:
8251:
8249:
8245:
8242:
8240:
8237:
8235:
8232:
8230:
8227:
8226:
8224:
8222:
8218:
8212:
8209:
8207:
8204:
8202:
8198:
8195:
8193:
8190:
8189:
8187:
8185:
8184:Biostatistics
8181:
8177:
8173:
8168:
8164:
8146:
8145:Log-rank test
8143:
8142:
8140:
8136:
8130:
8127:
8126:
8124:
8122:
8118:
8112:
8109:
8107:
8104:
8102:
8099:
8097:
8094:
8093:
8091:
8089:
8085:
8082:
8080:
8076:
8066:
8063:
8061:
8058:
8056:
8053:
8051:
8048:
8046:
8043:
8042:
8040:
8038:
8034:
8028:
8025:
8023:
8020:
8018:
8016:(BoxâJenkins)
8012:
8010:
8007:
8005:
8002:
7998:
7995:
7994:
7993:
7990:
7989:
7987:
7985:
7981:
7975:
7972:
7970:
7969:DurbinâWatson
7967:
7965:
7959:
7957:
7954:
7952:
7951:DickeyâFuller
7949:
7948:
7946:
7942:
7936:
7933:
7931:
7928:
7926:
7925:Cointegration
7923:
7921:
7918:
7916:
7913:
7911:
7908:
7906:
7903:
7901:
7900:Decomposition
7898:
7897:
7895:
7891:
7888:
7886:
7882:
7872:
7869:
7868:
7867:
7864:
7863:
7862:
7859:
7855:
7852:
7851:
7850:
7847:
7845:
7842:
7840:
7837:
7835:
7832:
7830:
7827:
7825:
7822:
7820:
7817:
7815:
7812:
7811:
7809:
7807:
7803:
7797:
7794:
7792:
7789:
7787:
7784:
7782:
7779:
7777:
7774:
7772:
7771:Cohen's kappa
7769:
7768:
7766:
7764:
7760:
7756:
7752:
7748:
7744:
7740:
7735:
7731:
7717:
7714:
7712:
7709:
7707:
7704:
7702:
7699:
7698:
7696:
7694:
7690:
7684:
7680:
7676:
7670:
7668:
7665:
7664:
7662:
7660:
7656:
7650:
7647:
7645:
7642:
7640:
7637:
7635:
7632:
7630:
7627:
7625:
7624:Nonparametric
7622:
7620:
7617:
7616:
7614:
7610:
7604:
7601:
7599:
7596:
7594:
7591:
7589:
7586:
7585:
7583:
7581:
7577:
7571:
7568:
7566:
7563:
7561:
7558:
7556:
7553:
7551:
7548:
7547:
7545:
7543:
7539:
7533:
7530:
7528:
7525:
7523:
7520:
7518:
7515:
7514:
7512:
7510:
7506:
7502:
7495:
7492:
7490:
7487:
7486:
7482:
7478:
7462:
7459:
7458:
7457:
7454:
7452:
7449:
7447:
7444:
7440:
7437:
7435:
7432:
7431:
7430:
7427:
7426:
7424:
7422:
7418:
7408:
7405:
7401:
7395:
7393:
7387:
7385:
7379:
7378:
7377:
7374:
7373:Nonparametric
7371:
7369:
7363:
7359:
7356:
7355:
7354:
7348:
7344:
7343:Sample median
7341:
7340:
7339:
7336:
7335:
7333:
7331:
7327:
7319:
7316:
7314:
7311:
7309:
7306:
7305:
7304:
7301:
7299:
7296:
7294:
7288:
7286:
7283:
7281:
7278:
7276:
7273:
7271:
7268:
7266:
7264:
7260:
7258:
7255:
7254:
7252:
7250:
7246:
7240:
7238:
7234:
7232:
7230:
7225:
7223:
7218:
7214:
7213:
7210:
7207:
7205:
7201:
7191:
7188:
7186:
7183:
7181:
7178:
7177:
7175:
7173:
7169:
7163:
7160:
7156:
7153:
7152:
7151:
7148:
7144:
7141:
7140:
7139:
7136:
7134:
7131:
7130:
7128:
7126:
7122:
7114:
7111:
7109:
7106:
7105:
7104:
7101:
7099:
7096:
7094:
7091:
7089:
7086:
7084:
7081:
7079:
7076:
7075:
7073:
7071:
7067:
7061:
7058:
7054:
7051:
7047:
7044:
7042:
7039:
7038:
7037:
7034:
7033:
7032:
7029:
7025:
7022:
7020:
7017:
7015:
7012:
7010:
7007:
7006:
7005:
7002:
7001:
6999:
6997:
6993:
6990:
6988:
6984:
6978:
6975:
6973:
6970:
6966:
6963:
6962:
6961:
6958:
6956:
6953:
6949:
6948:loss function
6946:
6945:
6944:
6941:
6937:
6934:
6932:
6929:
6927:
6924:
6923:
6922:
6919:
6917:
6914:
6912:
6909:
6905:
6902:
6900:
6897:
6895:
6889:
6886:
6885:
6884:
6881:
6877:
6874:
6872:
6869:
6867:
6864:
6863:
6862:
6859:
6855:
6852:
6850:
6847:
6846:
6845:
6842:
6838:
6835:
6834:
6833:
6830:
6826:
6823:
6822:
6821:
6818:
6816:
6813:
6811:
6808:
6806:
6803:
6802:
6800:
6798:
6794:
6790:
6786:
6781:
6777:
6763:
6760:
6758:
6755:
6753:
6750:
6748:
6745:
6744:
6742:
6740:
6736:
6730:
6727:
6725:
6722:
6720:
6717:
6716:
6714:
6710:
6704:
6701:
6699:
6696:
6694:
6691:
6689:
6686:
6684:
6681:
6679:
6676:
6674:
6671:
6670:
6668:
6666:
6662:
6656:
6653:
6651:
6650:Questionnaire
6648:
6646:
6643:
6639:
6636:
6634:
6631:
6630:
6629:
6626:
6625:
6623:
6621:
6617:
6611:
6608:
6606:
6603:
6601:
6598:
6596:
6593:
6591:
6588:
6586:
6583:
6581:
6578:
6576:
6573:
6572:
6570:
6568:
6564:
6560:
6556:
6551:
6547:
6533:
6530:
6528:
6525:
6523:
6520:
6518:
6515:
6513:
6510:
6508:
6505:
6503:
6500:
6498:
6495:
6493:
6490:
6488:
6485:
6483:
6480:
6478:
6477:Control chart
6475:
6473:
6470:
6468:
6465:
6463:
6460:
6459:
6457:
6455:
6451:
6445:
6442:
6438:
6435:
6433:
6430:
6429:
6428:
6425:
6423:
6420:
6418:
6415:
6414:
6412:
6410:
6406:
6400:
6397:
6395:
6392:
6390:
6387:
6386:
6384:
6380:
6374:
6371:
6370:
6368:
6366:
6362:
6350:
6347:
6345:
6342:
6340:
6337:
6336:
6335:
6332:
6330:
6327:
6326:
6324:
6322:
6318:
6312:
6309:
6307:
6304:
6302:
6299:
6297:
6294:
6292:
6289:
6287:
6284:
6282:
6279:
6278:
6276:
6274:
6270:
6264:
6261:
6259:
6256:
6252:
6249:
6247:
6244:
6242:
6239:
6237:
6234:
6232:
6229:
6227:
6224:
6222:
6219:
6217:
6214:
6212:
6209:
6207:
6204:
6203:
6202:
6199:
6198:
6196:
6194:
6190:
6187:
6185:
6181:
6177:
6173:
6168:
6164:
6158:
6155:
6153:
6150:
6149:
6146:
6142:
6135:
6130:
6128:
6123:
6121:
6116:
6115:
6112:
6104:
6100:
6096:
6092:
6091:
6085:
6081:
6079:3-540-40172-5
6075:
6071:
6067:
6063:
6059:
6057:0-19-829685-1
6053:
6049:
6044:
6040:
6034:
6030:
6025:
6021:
6016:
6015:
6011:
6001:
5998:
5993:
5987:
5983:
5982:
5974:
5971:
5968:
5963:
5960:
5955:
5951:
5947:
5943:
5939:
5932:
5929:
5924:
5920:
5916:
5912:
5907:
5902:
5898:
5894:
5893:
5888:
5882:
5880:
5876:
5871:
5867:
5863:
5859:
5858:
5853:
5847:
5844:
5839:
5835:
5829:
5826:
5821:
5817:
5816:
5811:
5804:
5801:
5796:
5792:
5788:
5784:
5783:
5778:
5771:
5768:
5763:
5759:
5755:
5751:
5747:
5739:
5736:
5729:
5725:
5722:
5720:
5716:
5713:
5711:
5708:
5706:
5703:
5701:
5698:
5697:
5693:
5688:
5685:
5682:
5679:
5676:
5673:
5670:
5667:
5664:
5661:
5658:
5655:
5652:
5649:
5645:
5641:
5638:
5635:
5634:
5629:
5626:
5625:
5621:
5619:
5617:
5613:
5609:
5605:
5602:
5601:macroeconomic
5598:
5591:
5589:
5587:
5581:
5577:
5569:
5567:
5565:
5561:
5557:
5553:
5549:
5544:
5531:
5526:
5522:
5513:
5495:
5491:
5482:
5464:
5461:
5458:
5454:
5445:
5426:
5421:
5417:
5413:
5408:
5405:
5402:
5398:
5394:
5391:
5386:
5383:
5380:
5376:
5370:
5366:
5362:
5357:
5354:
5351:
5347:
5341:
5337:
5333:
5328:
5324:
5316:
5315:
5314:
5297:
5292:
5288:
5284:
5279:
5276:
5273:
5269:
5265:
5262:
5257:
5254:
5251:
5247:
5241:
5237:
5233:
5228:
5224:
5216:
5215:
5214:
5197:
5192:
5189:
5186:
5182:
5178:
5173:
5170:
5167:
5163:
5159:
5156:
5151:
5148:
5145:
5141:
5133:
5132:
5131:
5129:
5125:
5109:
5089:
5066:
5061:
5057:
5053:
5048:
5045:
5042:
5038:
5034:
5031:
5026:
5022:
5014:
5013:
5012:
5006:
5001:
4999:
4997:
4994:lowering the
4988:
4971:
4956:
4951:
4948:
4938:
4935:
4931:
4924:
4909:
4887:
4872:
4871:
4870:
4848:
4844:
4837:
4828:
4822:
4819:
4810:
4801:
4795:
4792:
4783:
4780:
4777:
4774:
4771:
4768:
4764:
4759:
4740:
4739:
4738:
4735:
4733:
4729:
4712:
4708:
4698:
4689:
4679:
4670:
4665:
4662:
4659:
4655:
4648:
4645:
4642:
4639:
4636:
4633:
4629:
4624:
4603:
4589:
4585:
4575:
4566:
4556:
4547:
4542:
4539:
4536:
4532:
4526:
4523:
4518:
4497:
4495:
4487:
4482:
4478:
4477:
4476:
4474:
4470:
4466:
4461:
4459:
4458:vectorization
4455:
4439:
4416:
4410:
4404:
4401:
4390:
4386:
4382:
4379:
4374:
4371:
4362:
4359:
4355:
4346:
4334:
4325:
4322:
4315:
4314:
4313:
4296:
4291:
4288:
4279:
4276:
4272:
4265:
4262:
4258:
4255:
4246:
4236:
4235:
4231:
4227:
4226:
4210:
4207:
4204:
4201:
4198:
4195:
4188:
4187:
4186:
4184:
4176:
4171:
4169:
4150:
4141:
4138:
4133:
4129:
4117:
4114:
4109:
4105:
4101:
4094:
4085:
4082:
4077:
4073:
4065:
4061:
4057:
4051:
4047:
4041:
4038:
4033:
4029:
4017:
4010:
4006:
4002:
3996:
3992:
3980:
3970:
3969:
3968:
3966:
3959:
3951:
3947:
3941:
3936:
3932:
3927:
3925:
3921:
3917:
3896:
3892:
3888:
3883:
3880:
3877:
3873:
3867:
3863:
3859:
3856:
3853:
3848:
3845:
3842:
3838:
3832:
3828:
3824:
3819:
3816:
3813:
3809:
3803:
3799:
3795:
3792:
3789:
3784:
3780:
3772:
3771:
3770:
3769:
3767:
3745:
3741:
3737:
3732:
3728:
3722:
3719:
3714:
3710:
3701:
3698:
3695:
3692:
3689:
3686:
3683:
3673:
3669:
3665:
3660:
3656:
3650:
3647:
3642:
3638:
3633:
3630:
3627:
3622:
3618:
3612:
3609:
3604:
3600:
3592:
3591:
3590:
3589:and denoting
3573:
3568:
3564:
3558:
3555:
3550:
3546:
3542:
3537:
3534:
3531:
3527:
3521:
3517:
3511:
3508:
3503:
3499:
3495:
3492:
3489:
3484:
3481:
3478:
3474:
3468:
3464:
3458:
3455:
3450:
3446:
3442:
3437:
3434:
3431:
3427:
3421:
3417:
3411:
3408:
3403:
3399:
3395:
3390:
3386:
3380:
3377:
3372:
3368:
3364:
3359:
3355:
3347:
3346:
3345:
3341:
3333:
3328:
3324:
3320:
3318:
3312:
3311:
3307:
3303:
3299:
3295:
3291:
3290:
3289:
3285:
3283:
3279:
3275:
3270:
3267:
3262:
3256:
3251:
3246:
3241:
3237:
3230:
3223:
3219:
3211:
3206:
3184:
3181:
3178:
3174:
3170:
3165:
3162:
3159:
3156:
3153:
3149:
3143:
3140:
3137:
3134:
3131:
3127:
3123:
3118:
3115:
3112:
3109:
3106:
3102:
3096:
3093:
3090:
3087:
3084:
3080:
3076:
3071:
3068:
3065:
3061:
3055:
3052:
3049:
3046:
3043:
3039:
3035:
3030:
3027:
3024:
3020:
3016:
3011:
3008:
3005:
3001:
2993:
2992:
2991:
2989:
2985:
2977:
2963:
2960:
2952:
2948:
2944:
2939:
2935:
2912:
2908:
2890:
2885:
2881:
2877:
2869:
2865:
2842:
2839:that is, the
2823:
2818:
2810:
2805:
2801:
2795:
2788:
2781:
2776:
2772:
2765:
2760:
2753:
2749:
2745:
2739:
2735:
2723:
2713:
2712:
2711:
2694:
2689:
2681:
2678:
2675:
2671:
2661:
2658:
2655:
2651:
2644:
2639:
2634:
2626:
2623:
2620:
2617:
2614:
2610:
2600:
2597:
2594:
2591:
2588:
2584:
2577:
2570:
2562:
2559:
2556:
2553:
2550:
2546:
2538:
2535:
2532:
2529:
2526:
2522:
2512:
2509:
2506:
2503:
2500:
2496:
2488:
2485:
2482:
2479:
2476:
2472:
2465:
2460:
2455:
2447:
2444:
2441:
2437:
2427:
2424:
2421:
2417:
2410:
2405:
2400:
2392:
2389:
2386:
2382:
2372:
2369:
2366:
2362:
2355:
2348:
2342:
2335:
2332:
2329:
2326:
2323:
2319:
2309:
2306:
2303:
2300:
2297:
2293:
2287:
2281:
2272:
2271:
2270:
2267:
2250:
2243:
2239:
2235:
2229:
2225:
2208:
2207:
2202:
2195:
2193:
2189:
2182:
2179:terms of the
2178:
2177:main diagonal
2174:
2170:
2165:
2161:
2157:
2153:
2149:
2146: Ă
2145:
2141:
2134:
2127:
2108:
2103:
2099:
2095:
2090:
2087:
2084:
2080:
2074:
2070:
2066:
2063:
2060:
2055:
2052:
2049:
2045:
2039:
2035:
2031:
2026:
2023:
2020:
2016:
2010:
2006:
2002:
1997:
1993:
1989:
1984:
1980:
1974:
1970:
1962:
1961:
1960:
1958:
1954:
1953:
1944:
1939:
1937:
1934:
1932:
1928:
1907:
1902:
1896:
1887:
1883:
1876:
1871:
1866:
1858:
1855:
1852:
1848:
1838:
1835:
1832:
1828:
1821:
1814:
1808:
1803:
1794:
1790:
1782:
1778:
1771:
1766:
1761:
1755:
1748:
1742:
1737:
1732:
1724:
1721:
1718:
1714:
1704:
1700:
1693:
1684:
1683:
1682:
1681:
1680:
1661:
1657:
1653:
1648:
1645:
1642:
1638:
1632:
1628:
1624:
1619:
1616:
1613:
1609:
1603:
1599:
1595:
1592:
1589:
1584:
1580:
1572:
1571:
1570:
1567:
1565:
1561:
1553:
1549:
1547:
1545:
1525:
1520:
1517:
1514:
1510:
1506:
1501:
1498:
1495:
1492:
1489:
1485:
1479:
1476:
1473:
1469:
1465:
1460:
1457:
1454:
1451:
1448:
1444:
1438:
1435:
1432:
1428:
1424:
1419:
1415:
1411:
1406:
1403:
1400:
1396:
1388:
1371:
1368:
1365:
1361:
1357:
1352:
1349:
1346:
1343:
1340:
1336:
1330:
1327:
1324:
1320:
1316:
1311:
1308:
1305:
1302:
1299:
1295:
1289:
1286:
1283:
1279:
1275:
1270:
1266:
1262:
1257:
1254:
1251:
1247:
1239:
1238:
1237:
1235:
1231:
1212:
1207:
1199:
1196:
1193:
1189:
1179:
1176:
1173:
1169:
1162:
1157:
1152:
1144:
1141:
1138:
1135:
1132:
1128:
1118:
1115:
1112:
1109:
1106:
1102:
1095:
1088:
1080:
1077:
1074:
1070:
1062:
1059:
1056:
1052:
1042:
1039:
1036:
1032:
1024:
1021:
1018:
1014:
1007:
1002:
997:
989:
985:
975:
971:
964:
959:
954:
946:
943:
940:
936:
926:
923:
920:
916:
909:
900:
899:
898:
895:
893:
889:
885:
877:
875:
873:
872:separate page
853:
850:
847:
844:
841:
838:
831:
830:
829:
827:
824:
820:
812:
805:
801:
798:
794:
790:
789:
787:
783:
779:
776:
775:
774:
772:
764:
762:
760:
756:
748:
744:
740:
723:
720:
713:
709:
706:
703:
699:
693:
689:
673:
670:
667:
664: Ă
663:
659:
639:
632:
628:
624:
618:
614:
598:
595:
578:
575:
567:
563:
547:
546:
545:
543:
539:
534:
530:
527:)-matrix and
526:
523: Ă
522:
518:
514:
507:
503:
499:
492:
488:
484:
478:
474:
454:
449:
445:
441:
436:
433:
430:
426:
420:
416:
412:
409:
406:
401:
398:
395:
391:
385:
381:
377:
372:
369:
366:
362:
356:
352:
348:
345:
342:
337:
333:
325:
324:
323:
321:
317:
313:
309:
305:
301:
297:
293:
288:
283:
279:
275:
270:
266:
262:
258:
254:
250:
246:
239:
235:
231:
227:
225:
220:
212:
204:
201:
193:
190:February 2012
183:
179:
173:
172:
166:
162:
158:
153:
144:
143:
138:Specification
137:
135:
133:
129:
125:
121:
116:
114:
110:
106:
102:
98:
94:
90:
80:
77:
69:
66:February 2012
59:
55:
49:
48:
42:
37:
28:
27:
22:
9519:Publications
9475:Publications
9442:
9038:Neoclassical
9028:Mercantilism
8937:Evolutionary
8799:Sociological
8772: /
8670:Geographical
8650:Evolutionary
8625:Digitization
8590:Agricultural
8553:Econometrics
8493:Price theory
8422:
8410:
8391:
8384:
8296:Econometrics
8246: /
8229:Chemometrics
8206:Epidemiology
8199: /
8172:Applications
8026:
8014:ARIMA model
7961:Q-statistic
7910:Stationarity
7806:Multivariate
7749: /
7745: /
7743:Multivariate
7741: /
7681: /
7677: /
7451:Bayes factor
7350:Signed rank
7262:
7236:
7228:
7216:
6911:Completeness
6747:Cohort study
6645:Opinion poll
6580:Missing data
6567:Study design
6522:Scatter plot
6444:Scatter plot
6437:Spearman's Ï
6399:Grouped data
6094:
6088:
6069:
6047:
6028:
6019:
6000:
5980:
5973:
5962:
5937:
5931:
5896:
5892:Econometrica
5890:
5861:
5855:
5846:
5837:
5828:
5819:
5813:
5803:
5786:
5780:
5770:
5753:
5749:
5738:
5647:
5643:
5631:
5604:econometrics
5595:
5592:Applications
5583:
5559:
5551:
5545:
5511:
5480:
5443:
5441:
5312:
5212:
5127:
5123:
5081:
5010:
4992:
4868:
4736:
4731:
4727:
4604:
4498:
4491:
4462:
4456:and Vec the
4452:denotes the
4431:
4311:
4180:
4167:
3961:
3954:
3949:
3945:
3939:
3934:
3930:
3928:
3923:
3919:
3915:
3913:
3765:
3764:
3762:
3588:
3339:
3337:
3327:tax revenues
3323:indirect tax
3314:
3306:demand shock
3302:supply shock
3293:
3286:
3282:inconsistent
3271:
3265:
3260:
3254:
3249:
3244:
3239:
3228:
3221:
3214:
3209:
3204:
3202:
2990:one obtains
2980:
2978:
2906:
2838:
2709:
2268:
2205:
2204:
2198:
2196:
2191:
2187:
2180:
2168:
2163:
2159:
2155:
2151:
2147:
2143:
2136:
2132:
2125:
2123:
1956:
1951:
1950:
1948:
1935:
1926:
1924:
1678:
1568:
1563:
1559:
1557:
1551:
1550:Writing VAR(
1543:
1541:
1233:
1229:
1227:
896:
887:
883:
881:
869:
818:
816:
804:cointegrated
793:cointegrated
785:
781:
768:
754:
752:
738:
665:
661:
537:
532:
528:
524:
520:
509:
501:
497:
490:
486:
482:
476:
472:
470:
319:
315:
311:
307:
303:
299:
295:
291:
289:
281:
277:
273:
268:
264:
260:
252:
248:
241:
233:
229:
222:
218:
216:
196:
187:
176:Please help
168:
117:
92:
88:
87:
72:
63:
44:
9313:von Neumann
9082:Supply-side
9067:Physiocracy
9011:Marginalism
8700:Information
8640:Engineering
8620:Development
8615:Demographic
8498:Game theory
8475:Theoretical
8424:WikiProject
8339:Cartography
8301:Jurimetrics
8253:Reliability
7984:Time domain
7963:(LjungâBox)
7885:Time-series
7763:Categorical
7747:Time-series
7739:Categorical
7674:(Bernoulli)
7509:Correlation
7489:Correlation
7285:JarqueâBera
7257:Chi-squared
7019:M-estimator
6972:Asymptotics
6916:Sufficiency
6683:Interaction
6595:Replication
6575:Effect size
6532:Violin plot
6512:Radar chart
6492:Forest plot
6482:Correlogram
6432:Kendall's Ï
5899:(1): 1â48.
5644:statsmodels
5586:forecasting
5556:eigenvalues
5102:and vector
3298:independent
2175:terms. The
1558:A VAR with
1554:) as VAR(1)
743:correlation
540:-vector of
182:introducing
105:time series
58:introducing
9538:Categories
9470:Economists
9343:Schumacher
9248:Schumpeter
9218:von Wieser
9138:von ThĂŒnen
9098:Economists
8997:Circuitism
8962:Humanistic
8957:Historical
8932:Ecological
8922:Democratic
8895:Chartalism
8885:Behavioral
8848:Mainstream
8809:Statistics
8804:Solidarity
8725:Managerial
8690:Humanistic
8685:Historical
8630:Ecological
8595:Behavioral
8291:Demography
8009:ARMA model
7814:Regression
7391:(Friedman)
7352:(Wilcoxon)
7290:Normality
7280:Lilliefors
7227:Student's
7103:Resampling
6977:Robustness
6965:divergence
6955:Efficiency
6893:(monotone)
6888:Likelihood
6805:Population
6638:Stratified
6590:Population
6409:Dependence
6365:Count data
6296:Percentile
6273:Dispersion
6206:Arithmetic
6141:Statistics
5719:panel data
5686:: "SYSTEM"
5608:statistics
4465:consistent
4183:this annex
4172:Estimation
3203:Note that
2911:covariance
2154:= 0, ...,
823:stochastic
671:denoted Ω.
232:= 1, ...,
224:endogenous
213:Definition
124:error term
41:references
9388:Greenspan
9353:Samuelson
9333:Galbraith
9303:Tinbergen
9243:von Mises
9238:Heckscher
9198:Edgeworth
9077:Stockholm
9072:Socialist
8972:Keynesian
8952:Happiness
8912:Classical
8873:Mutualism
8868:Anarchist
8853:Heterodox
8750:Personnel
8710:Knowledge
8675:Happiness
8665:Financial
8635:Education
8610:Democracy
8545:Empirical
8467:Economics
7672:Logistic
7439:posterior
7365:Rank sum
7113:Jackknife
7108:Bootstrap
6926:Bootstrap
6861:Parameter
6810:Statistic
6605:Statistic
6517:Run chart
6502:Pie chart
6497:Histogram
6487:Fan chart
6462:Bar chart
6344:L-moments
6231:Geometric
5901:CiteSeerX
5548:induction
5479:upon the
5462:−
5406:−
5384:−
5355:−
5277:−
5255:−
5190:−
5171:−
5149:−
5046:−
4966:^
4963:Σ
4957:⊗
4949:−
4913:^
4888:^
4832:^
4823:−
4805:^
4796:−
4781:−
4772:−
4754:^
4751:Σ
4702:^
4699:ϵ
4683:^
4680:ϵ
4656:∑
4646:−
4637:−
4619:^
4616:Σ
4579:^
4576:ϵ
4560:^
4557:ϵ
4533:∑
4513:^
4510:Σ
4440:⊗
4405:
4383:⊗
4372:−
4338:^
4326:
4289:−
4250:^
4139:−
4123:Σ
4115:−
4083:−
4058:ϵ
4048:ϵ
4039:−
3978:Ω
3881:−
3857:⋯
3846:−
3817:−
3729:ϵ
3720:−
3696:…
3648:−
3610:−
3565:ϵ
3556:−
3535:−
3509:−
3493:⋯
3482:−
3456:−
3435:−
3409:−
3378:−
3175:ϵ
3163:−
3116:−
3036:−
2949:ϵ
2936:ϵ
2882:σ
2866:ϵ
2841:variances
2802:σ
2773:σ
2746:ϵ
2736:ϵ
2721:Σ
2672:ϵ
2652:ϵ
2624:−
2598:−
2254:Σ
2236:ϵ
2226:ϵ
2100:ϵ
2088:−
2064:⋯
2053:−
2024:−
1856:−
1836:−
1722:−
1646:−
1617:−
1499:−
1458:−
1350:−
1309:−
1142:−
1116:−
759:inference
707:−
643:Ω
506:intercept
434:−
410:⋯
399:−
370:−
318:lags". A
226:variables
109:economics
9499:Category
9479:journals
9465:Glossary
9418:Stiglitz
9383:Rothbard
9363:Buchanan
9348:Friedman
9338:Koopmans
9328:Leontief
9308:Robinson
9193:Marshall
9043:Lausanne
8947:Georgism
8942:Feminist
8890:Buddhist
8880:Austrian
8779:Regional
8755:Planning
8730:Monetary
8660:Feminist
8605:Cultural
8600:Business
8386:Category
8079:Survival
7956:Johansen
7679:Binomial
7634:Isotonic
7221:(normal)
6866:location
6673:Blocking
6628:Sampling
6507:QâQ plot
6472:Box plot
6454:Graphics
6349:Skewness
6339:Kurtosis
6311:Variance
6241:Heronian
6236:Harmonic
6068:(2005).
5954:27551988
5836:(1994).
5694:See also
5680:: "varm"
5656:: VARMAX
5622:Software
4939:′
4845:′
4713:′
4590:′
4363:′
4280:′
4266:′
4151:′
4095:′
4066:′
4011:′
2754:′
2244:′
714:′
633:′
596:of zero.
489:lag" of
111:and the
9514:Outline
9485:Schools
9477: (
9438:Piketty
9433:Krugman
9298:Kuznets
9288:Kalecki
9263:Polanyi
9153:Cournot
9148:Bastiat
9133:Ricardo
9123:Malthus
9113:Quesnay
9016:Marxian
8907:Chicago
8837:history
8832:Schools
8819:Welfare
8789:Service
8580:Applied
8412:Commons
8359:Kriging
8244:Process
8201:studies
8060:Wavelet
7893:General
7060:Plug-in
6854:L space
6633:Cluster
6334:Moments
6152:Outline
5923:1912017
5674:: "var"
5668:: "VAR"
5662:: "var"
5610:and in
5510:is the
3234:is the
2986:to the
1929:is the
886:) with
878:Example
821:) as a
276:of the
257:matrix.
178:improve
54:improve
9423:Thaler
9403:Ostrom
9398:Becker
9393:Sowell
9373:Baumol
9278:Myrdal
9273:Sraffa
9268:Frisch
9258:Knight
9253:Keynes
9228:Fisher
9223:Veblen
9208:Pareto
9188:Menger
9183:George
9178:Jevons
9173:Walras
9163:Gossen
9087:Thermo
8765:Public
8760:Policy
8715:Labour
8680:Health
8281:Census
7871:Normal
7819:Manova
7639:Robust
7389:2-way
7381:1-way
7219:-test
6890:
6467:Biplot
6258:Median
6251:Lehmer
6193:Center
6076:
6054:
6035:
5988:
5952:
5921:
5903:
5678:Matlab
5666:EViews
5648:PyFlux
5642:: The
5640:Python
5578:, and
4734:lags.
4432:where
4399:
3924:direct
2710:where
2158:) and
2124:where
1925:where
285:1,1998
238:vector
120:lagged
43:, but
9509:Lists
9504:Index
9455:Lists
9428:Hoppe
9413:Lucas
9378:Solow
9368:Arrow
9358:Simon
9323:Lange
9318:Hicks
9293:Röpke
9283:Hayek
9233:Pigou
9203:Clark
9118:Smith
9033:Mixed
8992:Post-
8814:Urban
8794:Socio
8784:Rural
7905:Trend
7434:prior
7376:anova
7265:-test
7239:-test
7231:-test
7138:Power
7083:Pivot
6876:shape
6871:scale
6321:Shape
6301:Range
6246:Heinz
6221:Cubic
6157:Index
5940:: 1.
5919:JSTOR
5730:Notes
5672:Gretl
5660:Stata
3225:0;1,2
2173:error
2167:is a
2142:is a
2131:is a
1959:) is
542:error
536:is a
515:is a
500:is a
292:order
163:, or
130:with
9444:more
9168:Marx
9158:Mill
9143:List
9021:Neo-
8977:Neo-
8138:Test
7338:Sign
7190:Wald
6263:Mode
6201:Mean
6074:ISBN
6052:ISBN
6033:ISBN
5986:ISBN
5950:PMID
5633:vars
5512:i, j
4467:and
4228:The
1957:SVAR
594:mean
9408:Sen
9128:Say
8987:New
8720:Law
7318:BIC
7313:AIC
6099:doi
5942:doi
5911:doi
5866:doi
5791:doi
5758:doi
5689:LDT
5654:SAS
4899:Vec
4884:Cov
4402:Vec
4323:Vec
4185:):
3964:j,t
3957:i,t
3313:2.
3292:1.
3220:if
3217:1,t
2983:2,t
2913:is
296:lag
93:VAR
9540::
6095:25
6093:.
5948:.
5917:.
5909:.
5897:48
5895:.
5878:^
5862:57
5860:.
5820:41
5818:.
5812:.
5787:35
5785:.
5779:.
5754:21
5752:.
5748:.
5566:.
4475:.
3938:=
3276:,
3269:.
3264:1,
3257:+1
3253:1,
3243:2,
3208:2,
2976:.
1949:A
1933:.
894:.
874:.
487:th
479:âi
249:k.
240:,
167:,
159:,
115:.
9481:)
8983:)
8979:(
8839:)
8835:(
8459:e
8452:t
8445:v
7263:G
7237:F
7229:t
7217:Z
6936:V
6931:U
6133:e
6126:t
6119:v
6105:.
6101::
6082:.
6060:.
6041:.
5994:.
5956:.
5944::
5925:.
5913::
5872:.
5868::
5797:.
5793::
5764:.
5760::
5628:R
5560:A
5552:y
5532:.
5527:2
5523:A
5496:t
5492:y
5481:i
5465:2
5459:t
5455:e
5444:j
5427:.
5422:t
5418:e
5414:+
5409:1
5403:t
5399:e
5395:A
5392:+
5387:2
5381:t
5377:e
5371:2
5367:A
5363:+
5358:3
5352:t
5348:y
5342:3
5338:A
5334:=
5329:t
5325:y
5298:;
5293:t
5289:e
5285:+
5280:1
5274:t
5270:e
5266:A
5263:+
5258:2
5252:t
5248:y
5242:2
5238:A
5234:=
5229:t
5225:y
5198:.
5193:1
5187:t
5183:e
5179:+
5174:2
5168:t
5164:y
5160:A
5157:=
5152:1
5146:t
5142:y
5128:i
5124:j
5110:e
5090:y
5067:,
5062:t
5058:e
5054:+
5049:1
5043:t
5039:y
5035:A
5032:=
5027:t
5023:y
4972:.
4952:1
4945:)
4936:Z
4932:Z
4928:(
4925:=
4922:)
4919:)
4910:B
4904:(
4894:(
4849:.
4842:)
4838:Z
4829:B
4820:Y
4817:(
4814:)
4811:Z
4802:B
4793:Y
4790:(
4784:1
4778:p
4775:k
4769:T
4765:1
4760:=
4732:p
4728:k
4709:t
4690:t
4671:T
4666:1
4663:=
4660:t
4649:1
4643:p
4640:k
4634:T
4630:1
4625:=
4586:t
4567:t
4548:T
4543:1
4540:=
4537:t
4527:T
4524:1
4519:=
4417:,
4414:)
4411:Y
4408:(
4396:)
4391:k
4387:I
4380:Z
4375:1
4368:)
4360:Z
4356:Z
4353:(
4350:(
4347:=
4344:)
4335:B
4329:(
4297:.
4292:1
4285:)
4277:Z
4273:Z
4270:(
4263:Z
4259:Y
4256:=
4247:B
4211:U
4208:+
4205:Z
4202:B
4199:=
4196:Y
4148:)
4142:1
4134:0
4130:B
4126:(
4118:1
4110:0
4106:B
4102:=
4099:)
4092:)
4086:1
4078:0
4074:B
4070:(
4062:t
4052:t
4042:1
4034:0
4030:B
4026:(
4022:E
4018:=
4015:)
4007:t
4003:e
3997:t
3993:e
3989:(
3985:E
3981:=
3962:e
3955:Δ
3950:t
3946:Δ
3943:0
3940:B
3935:t
3931:e
3920:t
3916:t
3897:t
3893:e
3889:+
3884:p
3878:t
3874:y
3868:p
3864:A
3860:+
3854:+
3849:2
3843:t
3839:y
3833:2
3829:A
3825:+
3820:1
3814:t
3810:y
3804:1
3800:A
3796:+
3793:c
3790:=
3785:t
3781:y
3766:p
3746:t
3742:e
3738:=
3733:t
3723:1
3715:0
3711:B
3702:p
3699:,
3693:,
3690:1
3687:=
3684:i
3674:i
3670:A
3666:=
3661:i
3657:B
3651:1
3643:0
3639:B
3634:,
3631:c
3628:=
3623:0
3619:c
3613:1
3605:0
3601:B
3574:,
3569:t
3559:1
3551:0
3547:B
3543:+
3538:p
3532:t
3528:y
3522:p
3518:B
3512:1
3504:0
3500:B
3496:+
3490:+
3485:2
3479:t
3475:y
3469:2
3465:B
3459:1
3451:0
3447:B
3443:+
3438:1
3432:t
3428:y
3422:1
3418:B
3412:1
3404:0
3400:B
3396:+
3391:0
3387:c
3381:1
3373:0
3369:B
3365:=
3360:t
3356:y
3343:0
3340:B
3266:t
3261:y
3255:t
3250:y
3245:t
3240:y
3232:0
3229:B
3222:B
3215:y
3210:t
3205:y
3185:t
3182:,
3179:1
3171:+
3166:1
3160:t
3157:,
3154:2
3150:y
3144:2
3141:,
3138:1
3135:;
3132:1
3128:B
3124:+
3119:1
3113:t
3110:,
3107:1
3103:y
3097:1
3094:,
3091:1
3088:;
3085:1
3081:B
3077:+
3072:t
3069:,
3066:2
3062:y
3056:2
3053:,
3050:1
3047:;
3044:0
3040:B
3031:1
3028:;
3025:0
3021:c
3017:=
3012:t
3009:,
3006:1
3002:y
2981:y
2964:0
2961:=
2958:)
2953:2
2945:,
2940:1
2932:(
2928:v
2925:o
2922:c
2907:i
2905:(
2891:2
2886:i
2878:=
2875:)
2870:i
2862:(
2858:r
2855:a
2852:v
2824:;
2819:]
2811:2
2806:2
2796:0
2789:0
2782:2
2777:1
2766:[
2761:=
2758:)
2750:t
2740:t
2732:(
2728:E
2724:=
2695:,
2690:]
2682:t
2679:,
2676:2
2662:t
2659:,
2656:1
2645:[
2640:+
2635:]
2627:1
2621:t
2618:,
2615:2
2611:y
2601:1
2595:t
2592:,
2589:1
2585:y
2578:[
2571:]
2563:2
2560:,
2557:2
2554:;
2551:1
2547:B
2539:1
2536:,
2533:2
2530:;
2527:1
2523:B
2513:2
2510:,
2507:1
2504:;
2501:1
2497:B
2489:1
2486:,
2483:1
2480:;
2477:1
2473:B
2466:[
2461:+
2456:]
2448:2
2445:;
2442:0
2438:c
2428:1
2425:;
2422:0
2418:c
2411:[
2406:=
2401:]
2393:t
2390:,
2387:2
2383:y
2373:t
2370:,
2367:1
2363:y
2356:[
2349:]
2343:1
2336:1
2333:,
2330:2
2327:;
2324:0
2320:B
2310:2
2307:,
2304:1
2301:;
2298:0
2294:B
2288:1
2282:[
2251:=
2248:)
2240:t
2230:t
2222:(
2218:E
2203:(
2200:t
2192:i
2188:i
2184:0
2181:B
2169:k
2164:t
2160:Δ
2156:p
2152:i
2148:k
2144:k
2139:i
2137:B
2133:k
2129:0
2126:c
2109:,
2104:t
2096:+
2091:p
2085:t
2081:y
2075:p
2071:B
2067:+
2061:+
2056:2
2050:t
2046:y
2040:2
2036:B
2032:+
2027:1
2021:t
2017:y
2011:1
2007:B
2003:+
1998:0
1994:c
1990:=
1985:t
1981:y
1975:0
1971:B
1927:I
1908:,
1903:]
1897:0
1888:t
1884:e
1877:[
1872:+
1867:]
1859:2
1853:t
1849:y
1839:1
1833:t
1829:y
1822:[
1815:]
1809:0
1804:I
1795:2
1791:A
1783:1
1779:A
1772:[
1767:+
1762:]
1756:0
1749:c
1743:[
1738:=
1733:]
1725:1
1719:t
1715:y
1705:t
1701:y
1694:[
1662:t
1658:e
1654:+
1649:2
1643:t
1639:y
1633:2
1629:A
1625:+
1620:1
1614:t
1610:y
1604:1
1600:A
1596:+
1593:c
1590:=
1585:t
1581:y
1564:p
1560:p
1552:p
1544:t
1526:.
1521:t
1518:,
1515:2
1511:e
1507:+
1502:1
1496:t
1493:,
1490:2
1486:y
1480:2
1477:,
1474:2
1470:a
1466:+
1461:1
1455:t
1452:,
1449:1
1445:y
1439:1
1436:,
1433:2
1429:a
1425:+
1420:2
1416:c
1412:=
1407:t
1404:,
1401:2
1397:y
1372:t
1369:,
1366:1
1362:e
1358:+
1353:1
1347:t
1344:,
1341:2
1337:y
1331:2
1328:,
1325:1
1321:a
1317:+
1312:1
1306:t
1303:,
1300:1
1296:y
1290:1
1287:,
1284:1
1280:a
1276:+
1271:1
1267:c
1263:=
1258:t
1255:,
1252:1
1248:y
1234:p
1230:A
1213:,
1208:]
1200:t
1197:,
1194:2
1190:e
1180:t
1177:,
1174:1
1170:e
1163:[
1158:+
1153:]
1145:1
1139:t
1136:,
1133:2
1129:y
1119:1
1113:t
1110:,
1107:1
1103:y
1096:[
1089:]
1081:2
1078:,
1075:2
1071:a
1063:1
1060:,
1057:2
1053:a
1043:2
1040:,
1037:1
1033:a
1025:1
1022:,
1019:1
1015:a
1008:[
1003:+
998:]
990:2
986:c
976:1
972:c
965:[
960:=
955:]
947:t
944:,
941:2
937:y
927:t
924:,
921:1
917:y
910:[
888:k
884:p
854:U
851:+
848:Z
845:B
842:=
839:Y
819:p
786:d
782:d
755:p
739:k
724:0
721:=
718:)
710:k
704:t
700:e
694:t
690:e
686:(
682:E
666:k
662:k
640:=
637:)
629:t
625:e
619:t
615:e
611:(
607:E
579:0
576:=
573:)
568:t
564:e
560:(
556:E
538:k
533:t
529:e
525:k
521:k
519:(
512:i
510:A
502:k
498:c
494:t
491:y
483:i
477:t
473:y
455:,
450:t
446:e
442:+
437:p
431:t
427:y
421:p
417:A
413:+
407:+
402:2
396:t
392:y
386:2
382:A
378:+
373:1
367:t
363:y
357:1
353:A
349:+
346:c
343:=
338:t
334:y
320:p
316:p
312:p
308:p
304:p
300:p
282:y
278:i
274:t
269:t
267:,
265:i
261:y
253:k
244:t
242:y
234:T
230:t
219:k
203:)
197:(
192:)
188:(
174:.
91:(
79:)
73:(
68:)
64:(
50:.
23:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.