Abstract

We use the term ‘RegComponent’ model to refer to a regression model whose errors follow an ARIMA component time series model. This is a generalisation of ‘RegARIMA’ models for which the error term follows a standard ARIMA model. Specific forms of RegComponent models (e.g., ‘structural models’) have been used for some time in connection with modelling seasonal time series and for model-based seasonal adjustment, but this paper takes a broader view of RegComponent models. We discuss a general form for RegComponent models along with some theoretical considerations in their treatment regarding likelihood evaluation, likelihood maximisation, forecasting and signal extraction. We also illustrate the use of RegComponent models on some less familiar applications. These include: (i) modelling and seasonal adjustment of time series observed with sampling error; (ii) use of regression models with stochastically time-varying regression parameters and error terms that follow ARIMA or ARIMA component models; and (iii) using components present only occasionally to allow for seasonal or other types of heteroskedasticity. The examples presented illustrate both some of the general model capabilities and some of the capabilities of the US Census Bureau's REGCMPNT computer program, which handles general RegComponent models.

Introduction

This paper explores the use of RegComponent time series models. We use the term ‘RegComponent’ model to refer to a time series model with a regression mean function and an error term that follows an ARIMA component time series model. This is a generalisation of ‘RegARIMA’ models for which the error term follows a standard ARIMA (autoregressive-integrated-moving average) time series model (Box and Jenkins 1976). This paper provides an overview of RegComponent models and illustrates their use with three examples.