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.

中文翻译：

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具有相等条件随机和平均顺序的计数和持续时间时间序列

我们考虑一个正值时间序列，其条件分布具有时变均值，这可能取决于外生变量。主要应用涉及计数或持续时间数据。在均值函数的收缩条件下，表明当条件分布的均值和随机阶数相同时，平稳性和遍历性成立。后一种条件适用于由均值参数化的指数族，但也适用于许多其他分布。我们还为边际矩的存在和β-混合系数的几何衰减提供了条件。我们给出条件均值参数的指数准最大似然估计量的一致性和渐近正态性条件。