COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 788 "Trends versus Random Walks in Time Series Analysis" Steven N. Durlauf and Peter C.B. Phillips April 1986 This paper studies the effects of spurious detrending in regression. The asymptotic
behavior of traditional least squares estimators and tests are examined in the context of
models where the generating mechanism is systematically misspecified by the presence of
deterministic time trends. Most previous work on the subject has relied upon Monte Carlo
studies to understand the issues involved in detrending data that is generated by
integrated processes and our analytical results help to shed light on many of the
simulation findings. Standard F tests and Hausman tests are shown to inadequately
discriminate between the competing hypotheses. Durbin-Watson statistics, on the other
hand, are shown to be valuable measures of series stationarity. The asymptotic properties
of regressions and excess volatility tests with detrended integrated time series are also
explored. |
