Trends versus Random Walks in Time Series Analysis

Steven N. Durlauf · Peter C.B. Phillips

264 citations0/0 files storedEconometrica

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Monetary Policy and Economic Impact Financial Risk and Volatility Modeling Diverse Scientific and Economic Studies

Abstract

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.

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References

1987Co-Integration and Error Correction: Representation, Estimation, and Testing 1979Distribution of the Estimators for Autoregressive Time Series with a Unit Root 1988Testing for a Unit Root in Time Series Regression 1982Trends and random walks in macroeconmic time series 1987Asymptotic Properties of Least Squares Estimators of Cointegrating Vectors 1986Multiple Time Series Regression with Integrated Processes 1979The Volatility of Long-Term Interest Rates and Expectations Models of the Term Structure

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1990Predicting Stock Returns in an Efficient Market 1999Non-stationary log-periodogram regression 2003Spurious Regressions in Econometrics 1994Chapter 46 Unit roots, structural breaks and trends 2000Long Memory in Stock-Market Trading Volume 1998New Tools for Understanding Spurious Regressions 1991On Bayesian routes to unit roots

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