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The Effects of Sampling Frequency on Detrending Methods for Unit Root Tests

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  • Chambers, MJ

Abstract

This paper analyses the effects of sampling frequency on detrending methods based on an underlying continuous time representation of the process of interest. Such an approach has the advantage of allowing for the explicit - and different - treatment of the ways in which stock and flow variables are actually observed. Some general results are provided before the focus turns to three particular detrending methods that have found widespread use in the conduct of tests for a unit root, these being GLS detrending, OLS detrending, and first differencing, and which correspond to particular values of the generic detrending parameter. In addition, three different scenarios concerning sampling frequency and data span, in each of which the number of observations increases, are considered for each detrending method. The limit properties of the detrending coeffcient estimates, as well as an invariance principle for the detrended variable, are derived. An example of the application of the techniques to testing for a unit root, using GLS detrending on an intercept, is provided and the results of a simulation exercise to analyse the size and power properties of the test in the three different sampling scenarios are reported.

Suggested Citation

  • Chambers, MJ, 2016. "The Effects of Sampling Frequency on Detrending Methods for Unit Root Tests," Economics Discussion Papers 16062, University of Essex, Department of Economics.
    • Handle: RePEc:esx:essedp:16062
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    References listed on IDEAS

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    1. Chambers, Marcus J., 2004. "Testing for unit roots with flow data and varying sampling frequency," Journal of Econometrics, Elsevier, vol. 119(1), pages 1-18, March.
    2. Chambers, Marcus J., 2008. "Corrigendum to: "Testing for unit roots with flow data and varying sampling frequency" [J. Econom. 119 (1) (2004) 1-18]," Journal of Econometrics, Elsevier, vol. 144(2), pages 524-525, June.
    3. Davidson, James, 1994. "Stochastic Limit Theory: An Introduction for Econometricians," OUP Catalogue, Oxford University Press, number 9780198774037.
    4. Wang, Xiaohu & Yu, Jun, 2016. "Double asymptotics for explosive continuous time models," Journal of Econometrics, Elsevier, vol. 193(1), pages 35-53.
    5. Perron, Pierre, 1991. "Test Consistency with Varying Sampling Frequency," Econometric Theory, Cambridge University Press, vol. 7(3), pages 341-368, September.
    6. Marcus J. Chambers, 2011. "Cointegration and sampling frequency," Econometrics Journal, Royal Economic Society, vol. 14(2), pages 156-185, July.
    7. Chambers, Marcus J., 2005. "The purchasing power parity puzzle, temporal aggregation, and half-life estimation," Economics Letters, Elsevier, vol. 86(2), pages 193-198, February.
    8. P. C. B. Phillips & S. N. Durlauf, 1986. "Multiple Time Series Regression with Integrated Processes," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(4), pages 473-495.
    9. Chambers, Marcus J. & Thornton, Michael A., 2012. "Discrete Time Representation Of Continuous Time Arma Processes," Econometric Theory, Cambridge University Press, vol. 28(1), pages 219-238, February.
    10. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, vol. 64(4), pages 813-836, July.
    11. Marcus J. Chambers, 2015. "The Calculation of Some Limiting Distributions Arising in Near-Integrated Models with GLS Detrending," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(4), pages 562-586, July.
    12. Brewer, K. R. W., 1973. "Some consequences of temporal aggregation and systematic sampling for ARMA and ARMAX models," Journal of Econometrics, Elsevier, vol. 1(2), pages 133-154, June.
    13. Neil Kellard & Denise Osborn & Jerry Coakley & Marcus J. Chambers, 2015. "Testing for a Unit Root in a Near-Integrated Model with Skip-Sampled Data," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(5), pages 630-649, September.
    14. Zhou, Qiankun & Yu, Jun, 2015. "Asymptotic theory for linear diffusions under alternative sampling schemes," Economics Letters, Elsevier, vol. 128(C), pages 1-5.
    15. Weiss, Andrew A., 1984. "Systematic sampling and temporal aggregation in time series models," Journal of Econometrics, Elsevier, vol. 26(3), pages 271-281, December.
    16. Perron, Pierre, 1989. "The Calculation of the Limiting Distribution of the Least-Squares Estimator in a Near-Integrated Model," Econometric Theory, Cambridge University Press, vol. 5(2), pages 241-255, August.
    17. McCrorie, J. Roderick, 2000. "Deriving The Exact Discrete Analog Of A Continuous Time System," Econometric Theory, Cambridge University Press, vol. 16(6), pages 998-1015, December.
    18. Chambers, Marcus J., 2003. "The Asymptotic Efficiency Of Cointegration Estimators Under Temporal Aggregation," Econometric Theory, Cambridge University Press, vol. 19(1), pages 49-77, February.
    19. Marcellino, Massimiliano, 1999. "Some Consequences of Temporal Aggregation in Empirical Analysis," Journal of Business & Economic Statistics, American Statistical Association, vol. 17(1), pages 129-136, January.
    20. Westerlund, Joakim, 2014. "On the asymptotic distribution of the DF-GLS test statistic," Working Papers fe_2014_03, Deakin University, Department of Economics.
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    Keywords

    Continuous time; detrending; sampling frequency;
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