CHECKING STATIONARITY AND INVERTIBILITY IN TIME SERIES MODELS—FINDING THE INVERTIBLE FORM IN THE VECTOR CASE

Abstract

Some numerical methods for checking stationarity and invertibility of scalar and vector autoregressive-moving average schemes with exogenous covariates are revisited in this paper. A fast, recursive, and noniterative numerical procedure to check whether the roots of a polynomial operator are outside or on the unit circle is considered. This procedure may be used to improve computational efficiency in the parameter estimation stage of the Box-Jenkins approach. The problem of checking the roots of the determinant of a matrix polynomial operator is also considered. Furthermore, for any given noise covariance matrix and moving average square-matrix polynomial operator, an efficient numerical method to compute their equivalent invertible counterparts is provided.

Keywords:

• Controllability
• Dynamic system
• Forecastability
• Invertibility
• Stability
• Stationarity

ACKNOWLEDGMENTS

This research has been supported by the Spanish Grant DGES-PB97-0555, and by the National Science Foundation Grant DMI-9812839.