Testing for Deterministic Components in Vector Seasonal Time Series

José Luis Gallego, Carlos Díaz

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DOI: 10.4236/ojs.2011.13017                

Abstract

Certain locally optimal tests for deterministic components in vector time series have associated sampling distributions determined by a linear combination of Beta variates. Such distributions are nonstandard and must be tabulated by Monte Carlo simulation. In this paper, we provide closed form expressions for the mean and variance of several multivariate test statistics, moments that can be used to approximate unknown distributions. In particular, we find that the two-moment Inverse Gaussian approximation provides a simple and fast method to compute accurate quantiles and p-values in small and asymptotic samples. To illustrate the scope of this approximation we review some standard tests for deterministic trends and/or seasonal patterns in VARIMA and structural time series models.

Keywords

Vector Time Series, Deterministic Components, Parametric Stability, Non-Invertibility, Unit Roots

Conflicts of Interest

The authors declare no conflicts of interest.

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