An $L_p$-criterion for testing a hypothesis about the covariance function of a random sequence
Author:
T. O. Yanevich
Translated by:
N. Semenov
Journal:
Theor. Probability and Math. Statist. 92 (2016), 163-173
MSC (2010):
Primary 60G15; Secondary 60G10
DOI:
https://doi.org/10.1090/tpms/990
Published electronically:
August 10, 2016
MathSciNet review:
3553433
Full-text PDF Free Access
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Additional Information
Abstract: An $L_p$-criterion for testing a hypothesis about the covariance function for a centered stationary Gaussian sequence is constructed in this paper. The criterion is analyzed for some particular cases by using the simulated data.
References
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- G. E. P. Box and David A. Pierce, Distribution of residual autocorrelations in autoregressive-integrated moving average time series models, J. Amer. Statist. Assoc. 65 (1970), 1509–1526. MR 273762
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- O. Ē. Kamenshchikova and T. O. Yanevich, Approximation of $L_p(\Omega )$-processes, Teor. Ĭmovīr. Mat. Stat. 83 (2010), 59–68 (Ukrainian, with English and Ukrainian summaries); English transl., Theory Probab. Math. Statist. 83 (2011), 71–82. MR 2768849, DOI 10.1090/S0094-9000-2012-00842-9
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- Yurij V. Kozachenko and Olexander V. Stus, Square-Gaussian random processes and estimators of covariance functions, Math. Commun. 3 (1998), no. 1, 83–94 (English, with English and Croatian summaries). MR 1648867
- G. M. Ljung and G. E. P. Box, On a measure on lack of fit in time series models, Biometrica 65 (1978), no. 2, 297–303.
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- Carl Edward Rasmussen and Christopher K. I. Williams, Gaussian processes for machine learning, Adaptive Computation and Machine Learning, MIT Press, Cambridge, MA, 2006. MR 2514435
- O. O. Vasylyk, Yu. V. Kozachenko, and T. O. Yakovenko, Simulation of stationary random sequences, Visnyk Kyiv Univ. Ser. Fiz. Mat. Nauk (2009), no. 1, 7–10. (Ukrainian)
- Yu. V. Kozachenko and T. O. Yakovenko, A criterion for testing hypothesis about the covariance function of a stationary Gaussian random sequence, Visnyk Uzhgorod Univ. Ser. Mat. Inform. (2010), no. 20, 39–43. (Ukrainian)
References
- T. W. Anderson, The Statistical Analysis of Time Series, John Wiley & Sons, New York, 1971. MR 0283939
- G. E. P. Box, G. M. Jenkins, and G. C. Reinsel, Time Series Analysis: Forecasting and Control, 4th Edition, Wiley Series in Probability and Statistics, 2011. MR 2419724
- G. E. P. Box and D. A. Pierce, Distribution of residual autocorrelations in autoregressive-integrated moving average time series models, J. Amer. Statist. Assoc. 65 (1970), 1509–1526. MR 0273762
- P. J. Brockwell and R. A. Davis, Time Series: Theory and Methods, Second Edition, Springer Series in Statistics, Springer-Verlag, New York, 2009. MR 1093459
- V. V. Buldygin and Yu. V. Kozachenko, Metric Characterization of Random Variables and Random Processes, “TViMS”, Kyiv, 1998; American Mathematical Society, Providence, RI, 2000. MR 1743716
- W. W. Chen and R. S. Deo, A generalized Portmanteau goodness-of-fit test for time series models, Econometric Theory 20 (2004), no. 2, 382–416. MR 2044276
- O. E. Kamenshchikova and T. O. Yanevich, An approximation of $L_p(\Omega )$ processes, Teor. Ĭmovir. Mat. Stat. 83 (2010), 59–68; English transl in Theor. Probability and Math. Statist. 83 (2011), 71–82. MR 2768849
- Yu. V. Kozachenko and T. O. Ianevych, Some goodness of fit tests for random sequences, Lith. J. Statist. 52 (2013), no. 1, 5–13.
- Yu. V. Kozachenko and O. V. Stus, Square-Gaussian random processes and estimators of covariance functions, Math. Commun. 3 (1998), no. 1, 83–94. MR 1648867
- G. M. Ljung and G. E. P. Box, On a measure on lack of fit in time series models, Biometrica 65 (1978), no. 2, 297–303.
- A. I. McLeod and W. K. Li, Diagnostic checking ARMA time series models using squared-residual autocorrelations, J. Time Series Anal. 4 (1983), 269–273. MR 738587
- S. E. Rasmussen and C. K. I. Williams, Gaussian Processes for Machine Learning, The MIT press, 2006. MR 2514435
- O. O. Vasylyk, Yu. V. Kozachenko, and T. O. Yakovenko, Simulation of stationary random sequences, Visnyk Kyiv Univ. Ser. Fiz. Mat. Nauk (2009), no. 1, 7–10. (Ukrainian)
- Yu. V. Kozachenko and T. O. Yakovenko, A criterion for testing hypothesis about the covariance function of a stationary Gaussian random sequence, Visnyk Uzhgorod Univ. Ser. Mat. Inform. (2010), no. 20, 39–43. (Ukrainian)
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Additional Information
T. O. Yanevich
Affiliation:
Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, Taras Shevchenko National University of Kyiv, Volodymyrs’ka Street, 64/13, 01601, Kyiv, Ukraine
Email:
yata452@univ.kiev.ua
Keywords:
Square Gaussian random variables,
random sequences,
time series,
covariance functions
Received by editor(s):
May 5, 2015
Published electronically:
August 10, 2016
Article copyright:
© Copyright 2016
American Mathematical Society
