The consequences of seasonal adjustment for periodic autoregressive processes

Abstract

Summary This paper examines the effect of X-11 seasonal adjustment on periodicautoregressive processes, using both analytic techniques and simulation. Analytical resultsshow that adjustment reduces (but does not eliminate) periodicity in the coefficients ofa stationary PAR(1) process, and it generally moves the coefficients towards unity. Anonstationary periodically integrated process is converted into a process with a conventionalunit root and induced periodic heteroscedasticity. Simulations confirm that, for finite samples,evidence of periodicity in the coefficients and in residual heteroscedasticity may remain afteradjustment,butperiodicvariationinlong-runcoefficientsisannihilated.Theoverallconclusionis that adjustment alters, but does not destroy, periodic properties. Keywords: Seasonal adjustment , X-11 , Periodic processes , Unit root tests . 1. INTRODUCTION Seasonality is an important feature of macroeconomic time series, but it is typically of littleinterest to economists. Consequently, empirical analysis of macroeconomic time series is almostalways undertaken using seasonally adjusted values, frequently based on the US Bureau of theCensus X-11 Method (see, for example, Dagum 1988) or its recent development X-12 (Findley