This paper derives the autocorrelation function of the squared values of long-memory GARCH processes. Such processes are of much interest as they can produce the long-memory conditional heteroskedasticity that many high-frequency financial time series exhibit. An empirical application...

Dynamic models with parameters that are allowed to depend on the state of a hidden Markov chain have become a popular tool for modelling time series subject to changes in regime. An important question that arises in applications involving such models is how to determine the number of states...

This article considers the problem of selecting among competing nonlinear time series models by using complexity-penalized likelihood criteria. An extensive simulation study is undertaken to assess the small-sample performance of several popular criteria in selecting among nonlinear...

This article considers a simple procedure for assessing whether a weakly dependent univariate stochastic process is time-reversible. Our approach is based on a simple index of the deviation from zero of the median of the one-dimensional marginal law of differenced data. An attractive feature of...

This paper is concerned with the problem of joint determination of the state dimension and autoregressive order of models with Markov-switching parameters. A model selection procedure is proposed which is based on optimization of complexity-penalized likelihood criteria. The efficacy of the...