Theory of Probability and Mathematical Statistics
An Lp-criterion for testing a hypothesis about the covariance function of a random sequence
T. O. Yanevich
Download PDF
Abstract: An Lp-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.
Keywords: Square Gaussian random variables, random sequences, time series, covariance functions
Bibliography: 1. T. W. Anderson, The Statistical Analysis of Time Series, John Wiley & Sons, New York, 1971.
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.
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.
4. P. J. Brockwell and R. A. Davis, Time Series: Theory and Methods, Second Edition, Springer Series in Statistics, Springer-Verlag, New York, 2009.
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.
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.
7. O. E. Kamenshchikova and T. O. Yanevich, An approximation of L_p(Ω) processes, Teor. Ĭmovir. Mat. Stat. 83 (2010), 59-68; English transl in Theor. Probability and Math. Statist. 83 (2011), 71-82.
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.
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.
12. S. E. Rasmussen and C. K. I. Williams, Gaussian Processes for Machine Learning, The MIT press, 2006.
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)