Seasonal cointegration

Abstract

This chapter reviews the principal methods used by researchers when forecasting seasonal time series. In addition, the often overlooked implications of forecasting and feedback for seasonal adjustment are discussed. After an introduction in Section 1, Section 2 examines traditional univariate linear models, including methods based on SARIMA models, seasonally integrated models and deterministic seasonality models. As well as examining how forecasts are computed in each case, the forecast implications of misspecifying the class of model (deterministic versus nonstationary stochastic) are considered. The linear analysis concludes with a discussion of the nature and implications of cointegration in the context of forecasting seasonal time series, including merging short-term seasonal forecasts with those from long-term (nonseasonal) models.Periodic (or seasonally varying parameter) models, which often arise from theoretical models of economic decision-making, are examined in Section 3. As periodic models may be highly parameterized, their value for forecasting can be open to question. In this context, modelling procedures for periodic models are critically examined, as well as procedures for forecasting.Section 3 discusses less traditional models, specifically nonlinear seasonal models and models for seasonality in variance. Such nonlinear models primarily concentrate on interactions between seasonality and the business cycle, either using a threshold specification to capture changing seasonality over the business cycle or through regime transition probabilities being seasonally varying in a Markov switching framework. Seasonality heteroskedasticity is considered for financial time series, including deterministic versus stochastic seasonality, periodic GARCH and periodic stochastic volatility models for daily or intra-daily series.Economists typically consider that seasonal adjustment rids their analysis of the “nuisance” of seasonality. Section 5 shows this to be false. Forecasting seasonal time series is an inherent part of seasonal adjustment and, further, decisions based on seasonally adjusted data affect future outcomes, which destroys the assumed orthogonality between seasonal and nonseasonal components of time series.