Seasonal Adjustment Based on Structural Time Series Models

Abstract

The structural model decomposition method starts directly with an observation equation (sometimes called measurement equation) that relates the observed time series to the unobserved components. Simple ARIMA or stochastic trigonometric models are a priori assumed for each unobserved component. Structural Time series Analyzer, Modeler, and Predictor (STAMP) is the main software and includes several types of models for each component. This chapter discusses in detail the basic structural time series model with explicit specifications for each component. It deals also with the estimation of the parameters which is carried out by the method of maximum likelihood where the maximization is done by means of a numerical optimization method. Based on the parameter estimates, the components can be estimated using the observed time series. Model adequacy is generally diagnosed using classical test statistics applied to the standardized one-step ahead prediction errors. An illustrative example of the seasonal adjustment performed using the default option of the STAMP software is shown with the US Unemployment Rate for Males (16 years and over) series.