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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.<\/jats:p>","DOI":"10.1017\/s0266466620000134","type":"journal-article","created":{"date-parts":[[2020,3,17]],"date-time":"2020-03-17T09:54:25Z","timestamp":1584438865000},"page":"248-280","source":"Crossref","is-referenced-by-count":40,"title":["COUNT AND DURATION TIME SERIES WITH EQUAL CONDITIONAL STOCHASTIC AND MEAN ORDERS"],"prefix":"10.1017","volume":"37","author":[{"given":"Abdelhakim","family":"Aknouche","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Christian","family":"Francq","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2020,3,17]]},"reference":[{"key":"S0266466620000134_r37","first-page":"179","article-title":"Models for count data with many zeros","volume":"19","author":"Ridout","year":"1998","journal-title":"Proceedings of the XIXth International Biometric Conference"},{"key":"S0266466620000134_r39","unstructured":"Siakoulis, V. 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