523:
247:
518:{\displaystyle \theta _{t}=\alpha _{0}+\alpha _{1}\tau _{t-1}+\cdots +\alpha _{q}\tau _{t-q}+\beta _{1}\theta _{t-1}+\cdots +\beta _{p}\theta _{t-p}=\alpha _{0}+\sum _{i=1}^{q}\alpha _{i}\tau _{t-i}+\sum _{i=1}^{p}\beta _{i}\theta _{t-i}}
135:
207:
564:
597:
630:
240:
79:
659:
162:
28:, Engle and Russell (1998)) model considers irregularly spaced and autocorrelated intertrade durations. ACD is analogous to
698:
84:
167:
673:
and J.R. Russell. "Autoregressive
Conditional Duration: A New Model for Irregularly Spaced Transaction Data",
530:
569:
602:
693:
212:
51:
37:
635:
140:
670:
687:
17:
81:
denote the duration (the waiting time between consecutive trades) and assume that
164:
are independent and identically distributed random variables, positive and with
680:
N. Hautsch. "Modelling
Irregularly Spaced Financial Data", Springer, 2004.
33:
29:
40:) waiting times between two consecutive trades vary at random.
638:
605:
572:
533:
250:
215:
170:
143:
87:
54:
653:
624:
591:
558:
517:
234:
201:
156:
129:
73:
8:
130:{\displaystyle ~\tau _{t}=\theta _{t}z_{t}~}
202:{\displaystyle \operatorname {E} (z_{t})=1}
637:
610:
604:
577:
571:
541:
532:
503:
493:
483:
472:
453:
443:
433:
422:
409:
390:
380:
355:
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326:
316:
291:
281:
268:
255:
249:
223:
214:
184:
169:
148:
142:
118:
108:
95:
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62:
53:
7:
36:(a common trading mechanism in many
22:autoregressive conditional duration
559:{\displaystyle ~\alpha _{0}>0~}
171:
14:
592:{\displaystyle \alpha _{i}\geq 0}
625:{\displaystyle \beta _{i}\geq 0}
190:
177:
1:
235:{\displaystyle ~\theta _{t}~}
74:{\displaystyle ~\tau _{t}~}
715:
32:. In a continuous double
654:{\displaystyle ~i>0}
655:
626:
593:
560:
519:
488:
438:
236:
203:
158:
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75:
677:, 66:1127-1162, 1998.
656:
627:
594:
561:
520:
468:
418:
237:
209:and where the series
204:
159:
157:{\displaystyle z_{t}}
132:
76:
699:Mathematical finance
636:
603:
570:
531:
248:
213:
168:
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38:financial markets
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68:
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671:Robert F. Engle
667:
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633:
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452:
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399:
396:
393:
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383:
379:
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372:
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364:
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358:
354:
348:
344:
340:
335:
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329:
325:
319:
315:
311:
308:
305:
300:
297:
294:
290:
284:
280:
276:
271:
267:
263:
258:
254:
226:
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198:
195:
192:
187:
183:
179:
176:
173:
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147:
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9:
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288:
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265:
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256:
252:
243:
242:is given by:
224:
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16:In financial
675:Econometrica
674:
526:
244:
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25:
21:
18:econometrics
15:
694:Time series
688:Categories
665:References
527:and where
44:Definition
617:≥
608:β
584:≥
575:α
539:α
508:−
501:θ
491:β
470:∑
458:−
451:τ
441:α
420:∑
407:α
395:−
388:θ
378:β
371:⋯
360:−
353:θ
343:β
331:−
324:τ
314:α
307:⋯
296:−
289:τ
279:α
266:α
253:θ
221:θ
175:
106:θ
93:τ
60:τ
137:, where
34:auction
640:
554:
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230:
217:
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89:
69:
56:
30:GARCH
20:, an
646:>
548:>
48:Let
26:ACD
690::
661:.
632:,
599:,
566:,
649:0
643:i
620:0
612:i
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551:0
543:0
511:i
505:t
495:i
485:p
480:1
477:=
474:i
466:+
461:i
455:t
445:i
435:q
430:1
427:=
424:i
416:+
411:0
403:=
398:p
392:t
382:p
374:+
368:+
363:1
357:t
347:1
339:+
334:q
328:t
318:q
310:+
304:+
299:1
293:t
283:1
275:+
270:0
262:=
257:t
225:t
197:1
194:=
191:)
186:t
182:z
178:(
172:E
150:t
146:z
120:t
116:z
110:t
102:=
97:t
64:t
24:(
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