P. Saikkonen and R. Luukkonen, “Testing for a Moving Average Unit Root in Autoregressive Integrated Moving Average Models,” Journal of the American Statistical Association, Vol. 88, No. 422, 1993, pp. 596-601. doi:10.2307/2290341

has been cited by the following article:

• TITLE: Testing for Deterministic Components in Vector Seasonal Time Series

  AUTHORS: José Luis Gallego, Carlos Díaz

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

  JOURNAL NAME: Open Journal of Statistics, Vol.1 No.3, October 20, 2011

  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.