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Testing for a Unit Root in a Near-Integrated Model with Skip-Sampled Data

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  • Neil Kellard
  • Denise Osborn
  • Jerry Coakley
  • Marcus J. Chambers

Abstract

type="main" xml:id="jtsa12097-abs-0001"> This article examines tests for a unit root in skip-sampled data. A generalization of the usual discrete time framework that allows for a continuous time detrending procedure prior to estimation of the resulting discrete time dynamic model that embodies exactly the restrictions imposed by the process of temporal aggregation is proposed. A simulation study reveals that taking these restrictions into account can yield improved size and power properties compared to a statistic based on a model that ignores the temporal aggregation, and an empirical illustration of the methods using monthly producer price data for the UK and the USA is provided. Further avenues for investigation in future work are also highlighted.

Suggested Citation

  • 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.
  • Handle: RePEc:bla:jtsera:v:36:y:2015:i:5:p:630-649
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    File URL: http://hdl.handle.net/10.1111/jtsa.12097
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    References listed on IDEAS

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    1. Qiankun Zhou & Jun Yu, 2010. "Asymptotic Distributions of the Least Squares Estimator for Diffusion Processes," Working Papers 20-2010, Singapore Management University, School of Economics.
    2. DeJong, David N. & Nankervis, John C. & Savin, N. E. & Whiteman, Charles H., 1992. "The power problems of unit root test in time series with autoregressive errors," Journal of Econometrics, Elsevier, vol. 53(1-3), pages 323-343.
    3. Chambers, Marcus J. & Thornton, Michael A., 2012. "Discrete Time Representation Of Continuous Time Arma Processes," Econometric Theory, Cambridge University Press, vol. 28(01), pages 219-238, February.
    4. Perron, Pierre & Rodriguez, Gabriel, 2003. "GLS detrending, efficient unit root tests and structural change," Journal of Econometrics, Elsevier, vol. 115(1), pages 1-27, July.
    5. DeJong, David N, et al, 1992. "Integration versus Trend Stationarity in Time Series," Econometrica, Econometric Society, vol. 60(2), pages 423-433, March.
    6. 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.
    7. Weiss, Andrew A., 1984. "Systematic sampling and temporal aggregation in time series models," Journal of Econometrics, Elsevier, vol. 26(3), pages 271-281, December.
    8. 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.
    9. repec:esx:essedp:727 is not listed on IDEAS
    10. Michael A. Thornton & Marcus J. Chambers, 2013. "Continuous-time autoregressive moving average processes in discrete time: representation and embeddability," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(5), pages 552-561, September.
    11. Phillips, P C B, 1991. "Error Correction and Long-Run Equilibrium in Continuous Time," Econometrica, Econometric Society, vol. 59(4), pages 967-980, July.
    12. 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.
    13. Sook Fwe Yap & Gregory C. Reinsel, 1995. "Results On Estimation And Testing For A Unit Root In The Nonstationary Autoregressive Moving-Average Model," Journal of Time Series Analysis, Wiley Blackwell, vol. 16(3), pages 339-353, May.
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    Cited by:

    1. repec:eee:ecosta:v:5:y:2018:i:c:p:45-66 is not listed on IDEAS
    2. Miller, J. Isaac, 2018. "Simple robust tests for the specification of high-frequency predictors of a low-frequency series," Econometrics and Statistics, Elsevier, vol. 5(C), pages 45-66.
    3. 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.

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