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Estimating Autocorrelations in the Presence of Deterministic Trends


  • Wang Shin-Huei

    (Université catholique de Louvain and Beijing Normal University)

  • Hafner Christian

    (Université catholique de Louvain)


This paper considers the impact of ordinary least squares (OLS) detrending and the first difference (FD) detrending on autocorrelation estimation in the presence of long memory and deterministic trends. We show that the FD detrending results in inconsistent autocorrelation estimates when the error term is stationary. Thus, the FD detrending should not be employed for autocorrelation estimation of the detrended series when constructing e.g. portmanteau-type tests. In an empirical application of volume in Dow Jones stocks, we show that for some stocks, OLS and FD detrending result in substantial differences in ACF estimates.

Suggested Citation

  • Wang Shin-Huei & Hafner Christian, 2011. "Estimating Autocorrelations in the Presence of Deterministic Trends," Journal of Time Series Econometrics, De Gruyter, vol. 3(2), pages 1-25, April.
  • Handle: RePEc:bpj:jtsmet:v:3:y:2011:i:2:n:4

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    References listed on IDEAS

    1. Eugene Canjels & Mark W. Watson, 1997. "Estimating Deterministic Trends In The Presence Of Serially Correlated Errors," The Review of Economics and Statistics, MIT Press, vol. 79(2), pages 184-200, May.
    2. Maeshiro, Asatoshi, 1976. "Autoregressive Transformation, Trended Independent Variables and Autocorrelated Disturbance Terms," The Review of Economics and Statistics, MIT Press, vol. 58(4), pages 497-500, November.
    3. Granger, C. W. J., 1980. "Long memory relationships and the aggregation of dynamic models," Journal of Econometrics, Elsevier, vol. 14(2), pages 227-238, October.
    4. Chipman, John S, 1979. "Efficiency of Least-Squares Estimation of Linear Trend when Residuals are Autocorrelated," Econometrica, Econometric Society, vol. 47(1), pages 115-128, January.
    5. Tauchen, George E & Pitts, Mark, 1983. "The Price Variability-Volume Relationship on Speculative Markets," Econometrica, Econometric Society, vol. 51(2), pages 485-505, March.
    6. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
    7. Granger, C. W. J., 1981. "Some properties of time series data and their use in econometric model specification," Journal of Econometrics, Elsevier, vol. 16(1), pages 121-130, May.
    8. Granger, Clive W J, 1986. "Developments in the Study of Cointegrated Economic Variables," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 48(3), pages 213-228, August.
    9. Cheung, Yin-Wong & Lai, Kon S, 1993. "A Fractional Cointegration Analysis of Purchasing Power Parity," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(1), pages 103-112, January.
    10. Tsay, Wen-Jen, 2000. "Estimating Trending Variables In The Presence Of Fractionally Integrated Errors," Econometric Theory, Cambridge University Press, vol. 16(03), pages 324-346, June.
    11. Gallant, A Ronald & Rossi, Peter E & Tauchen, George, 1992. "Stock Prices and Volume," Review of Financial Studies, Society for Financial Studies, vol. 5(2), pages 199-242.
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    More about this item

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes


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