Recently, there has been a lot of interest in modelling real data with a heavy-tailed distribution. A popular candidate is the so-called generalized autoregressive conditional heteroscedastic (GARCH) model. Unfortunately, the tails of GARCH models are not thick enough in some applications. In...

In many situations, we want to verify the existence of a relationship between multivariate time series. Here, we propose a semiparametric approach for testing the independence between two infinite-order vector autoregressive (VAR(infinity)) series, which is an extension of Hong's [Biometrika...

We obtain new models and results for count data time series based on binomial thinning. Count data time series may have non-stationarity from trends or covariates, so we propose an extension of stationary time series based on binomial thinning such that the univariate marginal distributions are...

We propose the quasi-maximum likelihood method to estimate the parameters of an RCA(1) process, i.e. a random coefficient autoregressive time series of order 1. The strong consistency and the asymptotic normality of the estimators are derived under optimal conditions. Copyright 2006 Blackwell...

A symbolic method which can be used to obtain the asymptotic bias and variance coefficients to order O(1/n) for estimators in stationary time series is discussed. Using this method, the large-sample bias of the Burg estimator in the AR(p) for p = 1, 2, 3 is shown to be equal to that of the least...

A pth-order random coefficient integer-valued autoregressive [RCINAR(p)] model is proposed for count data. Stationarity and ergodicity properties are established. Maximum likelihood, conditional least squares, modified quasi-likelihood and generalized method of moments are used to estimate the...

Since the seminal paper by Dickey and Fuller in 1979, unit-root tests have conditioned the standard approaches to analysing time series with strong serial dependence in mean behaviour, the focus being placed on the detection of eventual unit roots in an autoregressive model fitted to the series....

A continuous Euler model has time-varying coefficients. Through a logarithmic time transformation, a continuous Euler model can be transformed to a continuous autoregressive (AR) model. By using the continuous Kalman filtering through the Laplace method, this article explores the data...

In this article, the problem of detecting the eventual existence of an exponential component in an AR(1) model, that is, the problem of testing ordinary AR(1) dependence against the alternative of an exponential autoregression [EXPAR(1)] model, was considered. A local asymptotic normality...