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Likelihood-Based Inference In Trending Time Series With A Root Near Unity

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  • Xiao, Zhijie

Abstract

This paper studies likelihood-based estimation and tests for autoregressive time series models with deterministic trends and general disturbance distributions. In particular, a joint estimation of the trend coefficients and the autoregressive parameter is considered. Asymptotic analysis on the M-estimators is provided. It is shown that the limiting distributions of these estimators involve nonlinear equation systems of Brownian motions even for the simple case of least squares regression. Unit root tests based on M-estimation are also considered, and extensions of the Neyman–Pearson test are studied. The finite sample performance of these estimators and testing procedures is examined by Monte Carlo experiments.

Suggested Citation

  • Xiao, Zhijie, 2001. "Likelihood-Based Inference In Trending Time Series With A Root Near Unity," Econometric Theory, Cambridge University Press, vol. 17(6), pages 1082-1112, December.
    • Handle: RePEc:cup:etheor:v:17:y:2001:i:06:p:1082-1112_17
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    Cited by:

    1. Lima Luiz Renato & Xiao Zhijie, 2010. "Testing Unit Root Based on Partially Adaptive Estimation," Journal of Time Series Econometrics, De Gruyter, vol. 2(1), pages 1-34, June.
    2. Bai, ChongEn & Li, Qi & Ouyang, Min, 2014. "Property taxes and home prices: A tale of two cities," Journal of Econometrics, Elsevier, vol. 180(1), pages 1-15.
    3. Distaso, Walter, 2008. "Testing for unit root processes in random coefficient autoregressive models," Journal of Econometrics, Elsevier, vol. 142(1), pages 581-609, January.
    4. Xiao, Zhijie, 2012. "Robust inference in nonstationary time series models," Journal of Econometrics, Elsevier, vol. 169(2), pages 211-223.
    5. Maxwell L. King & Sivagowry Sriananthakumar, 2015. "Point Optimal Testing: A Survey of the Post 1987 Literature," Monash Econometrics and Business Statistics Working Papers 5/15, Monash University, Department of Econometrics and Business Statistics.

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