Cointegration, Seasonality, Encompassing, and the Demand for Money in the United Kingdom

Abstract

Virtually all previous narrow money demand studies for the United Kingdom have used seasonally adjusted data for money, prices, and expenditure. This paper develops a constant, data-coherent M1 demand equation for the United Kingdom with seasonally unadjusted data. For that model, we address issues of cointegration, error correction, general-to-specific modeling, dynamic specification, model evaluation and testing, parameter constancy, and exogeneity. We also establish theoretical and empirical relationships between seasonally adjusted and unadjusted data, and so between models using those data. Finally, we derive and implement encompassing tests for comparing models using adjusted data with models using unadjusted data. Unlike the "standard" encompassing framework, variance dominance is not always a necessary condition for encompassing.

Moving Average Detrending and the Analysis of Business Cycles†

“…Symmetric linear filters are quite general, with special cases yielding simple moving averages as considered in Section III, the Hodrick-Prescott filter analysed by King and Rebelo (1993) and seasonal adjustment filters considered by Wallis(1993). Although the discussion here assumes that filtering is applied for trend estimation, this is not necessarily the case and some of the results are analogous to those obtained by Ericsson et aL (1994) in the context of cointegration between seasonally adjusted and unadjusted series.…”

Assessing forecast performance in a cointegrated system

“…In addition, since the forecasting performance of the systems we examine may depend upon the use of seasonally adjusted data (as discussed by Ericsson, Hendry, and Tran (1994)), we obtained seasonally unadjusted data for the M1 series and the nominal GDP series and reexamined the case for cointegration. In this case the vector autoregressions were augmented with seasonal dummies to account for the non-seasonality in the data.…”

Testing for Cointegration with Temporally Aggregated and Mixed‐Frequency Time Series

“…First, seasonal adjustment filters affect the power of unit root tests, as noted by Ghysels (), among others, whereas Ericsson et al . () study the consequences of such filters on tests for cointegration.…”