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Count and duration time series with equal conditional stochastic and mean orders

Abdelhakim Aknouche and Christian Francq ()

MPRA Paper from University Library of Munich, Germany

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. 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 the present paper.

Keywords: Absolute regularity; Autoregressive Conditional Duration; Count time series models; Distance covariance test; Ergodicity; Integer GARCH (search for similar items in EconPapers)
JEL-codes: C18 C5 C58 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-ore
Date: 2018-11-11
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