Trends, Cycles and Autoregressions

Abstract

A casual inspection of many economic time series shows that they have trends. It is equally apparent that, unless the time period is fairly short, these trends cannot be adequately captured by straight lines. In other words, a deterministic linear time trend is too restrictive. Despite this, a good deal of applied economic work starts off by detrending the data by regressing on time, thereby rendering all that follows invalid. In recent years, it has become fashionable to detrend using the Hodrick-Prescott filter. This allows the researcher to commit the same mistake in a more sophisticated way. Separating out the trend from the cycle is motivated by the idea that the economic theory which is relevant to the long run is different to the theory one wishes to apply in the short run. Irrespective of whether or not one accepts this view, an arbitrary separation into trend and cycle is clearly not to be recommended. The ideal way to proceed is by constructing a multivariate model using original data. If this proves too difficult, one should at least begin by separating out the long run in a way which pays attention to the properties of series. The first section looks at univariate models and discusses the way in which various formulations provide information about the long run. The next section looks at seasonality to make the point that seasonal effects are correctly viewed as a permanent component of a time series. Having established the background, multivariate models are discussed. I argue that the current fad for basing all dynamic econometrics on autoregressions is unfortunate. It can be misleading; it can focus attention on uninteresting questions; and it can detract from potentially more fruitful approaches.