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COUNT AND DURATION TIME SERIES WITH EQUAL CONDITIONAL STOCHASTIC AND MEAN ORDERS

Published online by Cambridge University Press:  17 March 2020

Abdelhakim Aknouche  and
Christian Francq
Abdelhakim Aknouche*
Affiliation:
USTHB and Qassim University
Christian Francq
Affiliation:
CREST and University of Lille
*
Address correspondence to Abdelhakim Aknouche, Faculty of Mathematics, University of Science and Technology Houari Boumediene, Bab Ezzouar, Algeria; e-mail: aknouche_ab@yahoo.com.
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Abstract

We consider a positive-valued time series whose conditional distribution has a time-varying mean, which may depend on exogenous variables. The main applications concern count or duration data. Under a contraction condition on the mean function, it is shown that stationarity and ergodicity hold when the mean and stochastic orders of the conditional distribution are the same. The latter condition holds for the exponential family parametrized by the mean, but also for many other distributions. We also provide conditions for the existence of marginal moments and for the geometric decay of the beta-mixing coefficients. We give conditions for consistency and asymptotic normality of the Exponential Quasi-Maximum Likelihood Estimator of the conditional mean parameters. Simulation experiments and illustrations on series of stock market volumes and of greenhouse gas concentrations show that the multiplicative-error form of usual duration models deserves to be relaxed, as allowed in this paper.

Type
ARTICLES
Information
Econometric Theory , Volume 37 , Issue 2 , April 2021 , pp. 248 - 280
Copyright
© Cambridge University Press 2020

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Footnotes

We are deeply grateful to the Editor-in-Chief Peter Phillips, the Co-Editor Dennis Kristensen, and two anonymous referees for their careful reading, very stimulating comments, and helpful suggestions that have led to significant improvements of this manuscript. C.F. is grateful to the Agence Nationale de la Recherche (ANR), which supported this work via the Project MultiRisk (ANR-16-CE26-0015-02). He also thanks the labex ECODEC.

References

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