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. Examples of both linear and non-linear dynamic models are presented with some illustrative numerical results.


Richard A. Davis

Research Area

Columbia University


Fri, 08/11/2013 - 4:00pm to 5:00pm


Room 4082, Red Centre Centre Wing, University of New South Wales