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The asymptotic distribution of the likelihood ratio for autoregressive time series with a regression trend

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  • Swensen, Anders Rygh

Abstract

It is shown that the likelihood ratio of an autoregressive time series of finite order with a regression trend is asymptotically normal. This result is used to derive the power of a test for positive correlation of the residuals under local autoregressive alternatives. The test is based on the Durbin-Watson statistics.

Suggested Citation

  • Swensen, Anders Rygh, 1985. "The asymptotic distribution of the likelihood ratio for autoregressive time series with a regression trend," Journal of Multivariate Analysis, Elsevier, vol. 16(1), pages 54-70, February.
    • Handle: RePEc:eee:jmvana:v:16:y:1985:i:1:p:54-70
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    1. Brandts, Jordi & El Baroudi, Sabrine & Huber, Stefanie J. & Rott, Christina, 2021. "Gender differences in private and public goal setting," Journal of Economic Behavior & Organization, Elsevier, vol. 192(C), pages 222-247.
    2. Lukas Hoesch & Adam Lee & Geert Mesters, 2022. "Robust inference for non-Gaussian SVAR models," Economics Working Papers 1847, Department of Economics and Business, Universitat Pompeu Fabra.
    3. Kara-Terki, Nesrine & Mourid, Tahar, 2016. "On local asymptotic normality for functional autoregressive processes," Journal of Multivariate Analysis, Elsevier, vol. 148(C), pages 120-140.
    4. Francq, Christian & Zakoian, Jean-Michel, 2023. "Local Asymptotic Normality Of General Conditionally Heteroskedastic And Score-Driven Time-Series Models," Econometric Theory, Cambridge University Press, vol. 39(5), pages 1067-1092, October.
    5. Schick, Anton, 1996. "Efficient estimation in a semiparametric additive regression model with autoregressive errors," Stochastic Processes and their Applications, Elsevier, vol. 61(2), pages 339-361, February.
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    7. Marc Hallin & Abdeslam Serroukh, 1998. "Adaptive Estimation of the Lag of a Long–memory Process," Statistical Inference for Stochastic Processes, Springer, vol. 1(2), pages 111-129, May.
    8. Ley, Christophe & Paindaveine, Davy, 2010. "On the singularity of multivariate skew-symmetric models," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1434-1444, July.
    9. Bennala, Nezar & Hallin, Marc & Paindaveine, Davy, 2012. "Pseudo-Gaussian and rank-based optimal tests for random individual effects in large n small T panels," Journal of Econometrics, Elsevier, vol. 170(1), pages 50-67.
    10. Lukas Hoesch & Adam Lee & Geert Mesters, 2022. "Locally Robust Inference for Non-Gaussian SVAR Models," Working Papers 1367, Barcelona School of Economics.
    11. Oliver Linton & Douglas Steigerwald, 2000. "Adaptive testing in arch models," Econometric Reviews, Taylor & Francis Journals, vol. 19(2), pages 145-174.
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    14. Marc Hallin & Catherine Vermandele & Bas J. M. Werker, 2008. "Semiparametrically efficient inference based on signs and ranks for median‐restricted models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(2), pages 389-412, April.
    15. Marc Hallin & Bas Werker, 2003. "Semiparametric efficiency, distribution-freeness, and invariance," ULB Institutional Repository 2013/2119, ULB -- Universite Libre de Bruxelles.
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    17. Bramati, Maria Caterina, 2013. "Optimal rank-based tests for block exogeneity in vector autoregressions," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 141-162.
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    19. Ciccarelli, Nicola, 2016. "Semiparametric Efficient Adaptive Estimation of the PTTGARCH model," MPRA Paper 72021, University Library of Munich, Germany.
    20. Sonja Rieder, 2012. "Robust parameter estimation for the Ornstein–Uhlenbeck process," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 21(4), pages 411-436, November.
    21. Ciccarelli Nicola, 2018. "Semiparametric efficient adaptive estimation of the GJR-GARCH model," Statistics & Risk Modeling, De Gruyter, vol. 35(3-4), pages 141-160, July.
    22. Masanobu Taniguchi & Shogo Kato & Hiroaki Ogata & Arthur Pewsey, 2020. "Models for circular data from time series spectra," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(6), pages 808-829, November.
    23. Nezar Bennala & Marc Hallin & Davy Paindaveine, 2010. "Rank‐based Optimal Tests for Random Effects in Panel Data," Working Papers ECARES ECARES 2010-018, ULB -- Universite Libre de Bruxelles.

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