Chapter VI - FORMULATION OF UNOBSERVED-COMPONENTS MODELS AND CANONICAL FORMS

Abstract

This chapter discusses the formulation of unobserved-components (UC) models, their canonical forms, and the ordinary mixed autoregressive moving-average (ARMA) models for both single and multiple time series. The first step in the estimation of either an ARMA model or an UC model is the determination of the orders of the moving averages and autoregressions as well as the number of components in a UC model, which is itself made up of superimposed ARMA models. This process is called model identification. Identification problems in the ordinary econometric sense may arise in the estimation of both ARMA and UC models. The chapter discusses the form of ARMA models using the estimated autocorrelation and partial autocorrelation functions, as suggested by Box and Jenkins. It also describes the formulation of time-series models relating two or more interdependent time series. The formulation of a time-series model means the determination of the appropriate degrees of the polynomials in the lag operators that appear in both the autoregressive part and the moving-average part of an ARMA model.