Theory and Inference for a Class of Observation-driven Models with Application to Time Series of Counts

Abstract

This paper studies theory and inference related to a class of time series models that incorporates nonlinear dynamics. It is assumed that the observations follow a one-parameter exponential family of distributions given an accompanying process that evolves as a function of lagged observations. We employ an iterated random function approach and a special coupling technique to show that, under suitable conditions on the parameter space, the conditional mean process is a geometric moment contracting Markov chain and that the observation process is absolutely regular with geometrically decaying coefficients. Moreover the asymptotic theory of the maximum likelihood estimates of the parameters is established under some mild assumptions. These models are applied to two examples; the first is the number of transactions per minute of Ericsson stock and the second is related to return times of extreme events of Goldman Sachs Group stock.

32 pages, 7 figures

References in corpus (2)

• Absolute regularity and ergodicity of Poisson count processes
• Stochastic Ordering of Exponential Family Distributions and Their Mixtures

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• Density power divergence for general integer-valued time series with multivariate exogenous covariate
• Self-excited Threshold Poisson Autoregression
• ARMA Models for Zero Inflated Count Time Series
• General-order observation-driven models: ergodicity and consistency of the maximum likelihood estimator
• Handy sufficient conditions for the convergence of the maximum likelihood estimator in observation-driven models