JOURNAL OF APPLIED ECONOMETRICS, VOL. 8, 231-247 (1993)
DETRENDING, STYLIZED FACTS AND THE BUSINESS CYCLE
A. C. HARVEY
Department of Statistics, London School of Economics, Houghton Street, London WC2A 2AE, UK
Austrian Institute of Economic Research, A-1103 Vienna, PO Box 91, Austria
The stylized facts of macroeconomic time series can be presented by fitting structural time series models. Within this framework, we analyse the consequences of the widely used detrending technique popularised by Hodrick and Prescott (1980). It is shown that mechanical detrending based on the Hodrick-Prescott filter can lead investigators to report spurious cyclical behaviour, and this point is illustrated with empirical examples. Structural time-series models also allow investigators to deal explicitly with seasonal and irregular movements that may distort estimated cyclical components. Finally, the structural framework provides a basis for exposing the limitations of ARIMA methodology and models based on a deterministic trend with a single break.
Establishing the ‘stylized facts’ associated with a set of time series is widely considered a crucial step in macroeconomic research (see e.g. Blanchard and Fischer, 1989 chapter 1). For such facts to be useful they should (1) be consistent with the stochastic properties of the data and (2) present meaningful information. Nevertheless, many stylized facts reported in the literature do not fulfil these criteria. In particular, information based on mechanically detrended series can easily give a spurious impression of cyclical behaviour. Analysis based on autoregressive-integrated-moving average (ARIMA) models can also be misleading if such models are chosen primarily on grounds of parsimony.
We argue here that structural time-series models provide the most useful framework within which to present stylized facts on time series. These models are explicitly based on the stochastic properties of the data. We illustrate how, when these models are fitted to various macroeconomic time series, they provide meaningful information and serve as a basis for exposing the limitations of other techniques. These arguments have, to some extent, been made before (Harvey, 1985, 1989; Clark, 1987). They are further elaborated here. In addition, we examine the consequences of the mechanical detrending method suggested by Hodrick and Prescott (1980), which has recently started to become popular in macroeconomics (see e.g. Danthine and Girardin, 1989; Backus and Kehoe, 1989; Kydland and Prescott, 1990; Brandner and Neusser, 1992). We show that the uncritical use of mechanical detrending can lead investigators to report spurious cyclical behaviour. This point has also been made by Cogley
Received September 1991
© 1993 by John Wiley & Sons, Ltd.
Revised June 1992