A common error in the treatment of trending time series
Danny T. Quah, Jeffrey M. Wooldridge · DSpace@MIT (Massachusetts Institute of Technology) · 1988
There are two common misconceptions in the analysis of trending time series.First, if a series is difference-stationary, removing a linear time trend introduces spurious cyclically.Second, regard- less of whether a series is difference-stationary or trend-stationary, taking Erst differences produces, in either case, a covariance stationary sequence, and bo is recommended econometric practice.We show that the Bret statement is incorrect and that the second can be misleading. Introduction.A number of recent papers have recommended taking first-differences of observed time series prior to econo- metric analysis (see for example Campbell and Mankiw (1988) and others).The reasoning is as follows.If a series is truly difference-stationary, then removing a linear time-trend produces spurious cyclicality in the residuals.Under the same condition, taking first differences produces a series that is covariance stationary, and so is convenient for econometric analysis.If, on the other hand, the series is truly trend-stationary, taking first-differences nevertheless produces a covariance stationary series, albeit one with a zero in the spectral density at frequency zero.This is still satisfactory however (the reasoning goes), as the unit root in the moving average part produced by over-differencing will manifest in the final estimates.Thus, if one is to remain agnostic as to the cyclicality of the observed time series, the recommended practice is always to take first-differences prior to econometric analysis.Put another way, the recommended practice is not to detrend for detrending leads to spurious "cyclical* behavior in the residuals.This view has become quite widely held by many macroeconomists.See for example Campbell (1987), Deaton (1986), Nelson (1987), Nelson and Kang (1981, 1984), Mankiw and Shapiro (1985), Romer (1987), and Shapiro (1986) among others.Nelson and Kang (1981) and Nelson and Plosser (1982) have forcefully argued that least squares detrend- ing of a unit root process produces spurious cyclicality.It is known that when the data are trend-stationary,