Diagnostic checking of nonlinear multivariate time series with multivariate arch errors

Multivariate time series with multivariate ARCH errors have been found useful in many applications. In order to check the adequacy of these models, we define the sum of squared (standardized) residual autocorrelations and derive their asymptotic distribution. The results are used to derive several new multivariate portmanteau tests. Simulation results show that the asymptotic standard errors are quite satisfactory compared with empirical standard errors and that the tests have reasonable empirical size and power. The distribution of the standardized residual autocorrelations is also derived.     

DIAGNOSTIC CHECKING OF PERIODIC AUTOREGRESSION MODELS WITH APPLICATION

Abstract. An overview of model building with periodic autoregression (PAR) models is given emphasizing the three stages of model development:identification, estimation and diagnostic checking. New results on the distribution of residual autocorrelations and suitable diagnostic checks are derived. The validity of these checks is demonstrated by simulation. The methodology discussed is illustrated with an application. It is pointed out that the PAR approach to model development offers some important advantages over the more general approach using periodic autoregressive moving-average models.     

Testing for serial dependence in time series models of counts

Abstract. In analysing time series of counts, the need to test for the presence of a dependence structure routinely arises. Suitable tests for this purpose are considered in this paper. Their size and power properties are evaluated under various alternatives taken from the class of INARMA processes. We find that all the tests considered except one are robust against extra binomial variation in the data and that tests based on the sample autocorrelations and the sample partial autocorrelations can help to distinguish between integer-valued first-order and second-order autoregressive as well as first-order moving average processes.     

An Improvement of the Portmanteau Statistic

Abstract. The portmanteau statistic is based on the first m‐residual autocorrelations, and is used for diagnostic checks on the adequacy of fit of a model. In this article, we propose a modified portmanteau statistic with a correction term that allows for the use of small values of m for the chi‐squared test. For this modification, we take a different approach to that suggested by Ljung [Biometrika (1986), Vol. 73, pp. 725–30]. Their empirical behaviour is clarified using asymptotic theory.