Modelled approximations to the ideal filter with application to GDP and its components

Abstract

This paper examines cyclical fluctuations in a comprehensive statistical application, focusing on U.S. macroeconomic indicators related to real gross domestic product (real GDP). While GDP is generally viewed as the most widespread measure of economic activity available, our dataset also encompasses the primary GDP components, such as investment, together with leading (and regularly analyzed) subcomponent series, like residential and inventory investment. Analysis of the cycles in these major sectors provides a more informative perspective on the macroeconomic state and may improve a researcher’s ability to understand and forecast cyclical movements and growth in GDP. Adaptive time series modelling is used for each time series to derive the preferred band-pass filter for computing the optimal cycle. This contrasts with the rigid use of the ideal filter, whose gain function is perfectly sharp. Regarding the ideal filter, we provide an improved implementation compared to current practice. Thus, a set of approximating filters is derived that allow for a more attractive gain profile, a better match to the targeted passband, and a direct statistical way to extract signals near the sample endpoints. Our application study demonstrates that the commonly used ideal filter can perform quite poorly on a routine basis and lead to incorrect conclusions about even the most basic questions about empirical cyclical properties. The amplitude of filtered economic activity can have major distortions and become expanded or diminished (depending on the GDP component under consideration), and many essential divergences in path may occur and affect key signals, such as expansion or contraction in growth. Statistical measures of model performance very strongly favor the adaptive parameter approach. Our statistical analysis reveals diverse dynamic behavior among the series; such results may yield worthwhile insights for output sector analysts and, even for those primarily focused on GDP, may lead to possible modelling improvements by using the finer information content in the GDP-component dynamics.