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Inference on Nonstationary Time Series with Moving Mean

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  • Jiti Gao
  • Peter M. Robinson

Abstract

A semiparametric model is proposed in which a parametric filtering of a non-stationary time series, incorporating fractionally differencing with short memory correction, removes correlation but leaves a nonparametric deterministic trend. Estimates of the memory parameter and other dependence parameters are proposed, and shown to be consistent and asymptotically normally distributed with parametric rate. Unit root tests with standard asymptotics are thereby justified. Estimation of the trend function is also considered. We include a Monte Carlo study of finite-sample performance.

Suggested Citation

  • Jiti Gao & Peter M. Robinson, 2013. "Inference on Nonstationary Time Series with Moving Mean," Monash Econometrics and Business Statistics Working Papers 15/13, Monash University, Department of Econometrics and Business Statistics.
    • Handle: RePEc:msh:ebswps:2013-15
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    References listed on IDEAS

    as
    1. Roussas, George G. & Tran, Lanh T. & Ioannides, D. A., 1992. "Fixed design regression for time series: Asymptotic normality," Journal of Multivariate Analysis, Elsevier, vol. 40(2), pages 262-291, February.
    2. Cătălin Stărică & Clive Granger, 2005. "Nonstationarities in Stock Returns," The Review of Economics and Statistics, MIT Press, vol. 87(3), pages 503-522, August.
    3. Deo, R. S., 1997. "Nonparametric regression with long-memory errors," Statistics & Probability Letters, Elsevier, vol. 33(1), pages 89-94, April.
    4. Jan Beran & Yuanhua Feng, 2002. "Local Polynomial Fitting with Long-Memory, Short-Memory and Antipersistent Errors," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(2), pages 291-311, June.
    5. Robinson, Peter M., 2012. "Nonparametric trending regression with cross-sectional dependence," Journal of Econometrics, Elsevier, vol. 169(1), pages 4-14.
    6. Robinson, Peter M., 1997. "Large-sample inference for nonparametric regression with dependent errors," LSE Research Online Documents on Economics 302, London School of Economics and Political Science, LSE Library.
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    Cited by:

    1. Marlon Fritz, 2019. "Data-Driven Local Polynomial Trend Estimation for Economic Data - Steady State Adjusting Trends," Working Papers Dissertations 49, Paderborn University, Faculty of Business Administration and Economics.
    2. Fritz, Marlon, 2019. "Steady state adjusting trends using a data-driven local polynomial regression," Economic Modelling, Elsevier, vol. 83(C), pages 312-325.

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    More about this item

    Keywords

    fractional time series; fixed design nonparametric regression; non-stationary time series; unit root tests.;
    All these keywords.

    JEL classification:

    • J1 - Labor and Demographic Economics - - Demographic Economics

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