ESTIMATION OF PARTIALLY NONSTATIONARY VECTOR AUTOREGRESSIVE MODELS WITH SEASONAL BEHAVIOR

In this paper the concept of multivariate partial nonstationarity considered by Ahn and Reinsel (1990) is extended to nonstationary seasonal models. The relationship between the partially non-stationary vector autoregressive model with seasonal behavior and seasonal cointegration and the error correction model is presented. The Gaussian reduced rank estimation procedure along with asymptotic properties of its estimator are studied. This estimation procedure yields an estimated model in which the same nonstationary characteristics are imposed as those possessed by the underlying process. Therefore, we can achieve better understanding of the nature of the process, improved forecasts, and better seasonal adjustment. We also study a two-step reduced rank estimation procedure that yields an estimator which is asymptotically as efficient as the Gaussian reduced rank estimator. Asymptotic properties of the Gaussian reduced rank estimator are also studied when deterministic seasonal components are included in the model. The finite sample properties of the estimators are briefly examined through a simulation. An example is presented to illustrate the methods and concepts.