An -criterion for testing a hypothesis about the covariance function of a random sequence

Author:
T. O. Yanevich

Translated by:
N. Semenov

Original publication:
Teoriya Imovirnostei ta Matematichna Statistika, tom **92** (2015).

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

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: An -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.

**1.**T. W. Anderson,*The Statistical Analysis of Time Series*, John Wiley & Sons, New York, 1971. MR**0283939****2.**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****3.**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****4.**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****5.**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****6.**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****7.**O. E. Kamenshchikova and T. O. Yanevich,*An approximation of processes*, Teor. Ĭmovir. Mat. Stat.**83**(2010), 59-68; English transl in Theor. Probability and Math. Statist.**83**(2011), 71-82. MR**2768849****8.**Yu. V. Kozachenko and T. O. Ianevych,*Some goodness of fit tests for random sequences*, Lith. J. Statist.**52**(2013), no. 1, 5-13.**9.**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****10.**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.**11.**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****12.**S. E. Rasmussen and C. K. I. Williams,*Gaussian Processes for Machine Learning*, The MIT press, 2006. MR**2514435****13.**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)**14.**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

DOI:
https://doi.org/10.1090/tpms/990

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