Academic journal article Quarterly Journal of Business and Economics

Seasonal and Non-Seasonal Long Memory in the US Interest Rate and the Monetary Aggregates

Academic journal article Quarterly Journal of Business and Economics

Seasonal and Non-Seasonal Long Memory in the US Interest Rate and the Monetary Aggregates

Article excerpt

Introduction

Many macroeconomic time series contain important seasonal components. It is a common belief that modelers need to pay specific attention to the nature of seasonality rather than essentially to ignore it. The concept of seasonality is seldom defined rigorously. It seems clear that any definition of seasonality must include something such as a systematic intra-year movement, though the relevant question is how systematic such movement is. (See, e.g., Thomas and Wallis, 1972; Granger, 1978; Hylleberg, 1986, 1992, etc.).

Traditionally, seasonal fluctuations have been considered as a nuisance that obscure the more important components of the series (presumably the growth and the cyclical components, e.g., Burns and Mitchell, 1946), and seasonal adjustment procedures have been implemented to eliminate seasonality. Thus, most of the empirical work on economic variables has been based on seasonally adjusted data, and little attention has been paid to the role of seasonality. In a number of papers, seasonal fluctuations have been found to play a significant role in accounting for most of the variation in many macroeconomic time series. Contributors to this view include Ghysels (1988), Barsky and Miron (1989), Faig (1989), Beaulieu and Miron (1992), Braun and Evans (1995), Lee and Siklos (1997), Bohl (2000), etc. The first two authors observe that seasonal adjustment might lead to mistaken inferences about economic relationships between time series data. Seasonal fluctuations have been found to be economically significant and an important source of variation in economic time series. For example, Bohl (2000) finds a stable long-run relationship between money demand (M2) and output only when using seasonally unadjusted data. Similarly, Lee and Siklos (1997) find evidence of some feedback from output to money when using seasonally unadjusted data and, consequently, suggest that researchers should use raw data instead of seasonally adjusted data for inference and forecasting purposes.

Nevertheless, there is little consensus on how seasonality should be treated in empirical research on economic modeling. While Barsky and Miron (1989) use seasonal dummy variables, Faig (1989) and Beaulieu and Miron (1993) emphasize the problem of using this adjustment procedure when the observed seasonality is generated by an integrated process. The use of a filter (1 - [L.sup.s]) to a series with a seasonal component is justified when the series is integrated at the zero and the seasonal frequencies. The application of the seasonal difference operator may produce serious misspecifications if unit roots are absent at some or at all of the seasonal frequencies. Several papers (Porter-Hudak, 1990; Franses and Ooms, 1997; Arteche and Robinson, 2000; Gil-Alana and Robinson, 2001; Gil-Alana, 2002) analyze the usefulness of seasonal fractional models in contrast to the procedure of seasonal (integer) differencing of the series. In most of these papers, they concentrate on the seasonal structure and pay no attention to the other possible (trend) structures underlying the series. Clearly, the polynomial (1 - [L.sup.s]) can be decomposed into (1 - L) (1 + L + [L.sup.2] + ... + [L.sup.s-1]), i.e., separating the roots at zero and the seasonal frequencies. The polynomial at zero may be important by itself, and first (or fractional) differences may be required before proceeding to the examination of the seasonal part.

In this paper we analyze the monetary aggregates M1, M2, and M3 as well as the interest rates for the US using monthly data based on fractional integration techniques. An extensive work has been done in modeling monetary aggregates in a variety of contexts: first, as a preliminary step before estimating some macroeconomic relationships (as the money demand function); second, the analysis of these series received great attention because they were significant variables used by the US Federal Reserve as targets of monetary policy; moreover, the impact on some real variables such as output has been an important issue in monetary economics. …

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