zbMATH — the first resource for mathematics

An \(L_p\)-criterion for testing a hypothesis about the covariance function of a random sequence. (English. Ukrainian original) Zbl 1346.60050
Theory Probab. Math. Stat. 92, 163-173 (2016); translation from Teor. Jmovirn. Mat. Stat. 92, 151-160 (2015).
Summary: 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 simulated data.

60G15 Gaussian processes
62G10 Nonparametric hypothesis testing
60G10 Stationary stochastic processes
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
Full Text: DOI
[1] Anderson T. W. Anderson, The Statistical Analysis of Time Series, John Wiley & Sons, New York, 1971. · Zbl 0225.62108
[2] Box_Jenkins 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] Box_Pierce G. E. P. Box and D. A. Pierce, Distribution of residual autocorrelations in autoregressive-integrated moving average time series models, J. Amer. Statist. Assoc. <span class=”textbf”>6</span>5 (1970), 1509–1526. · Zbl 0224.62041
[4] Brockwell P. J. Brockwell and R. A. Davis, Time Series: Theory and Methods, Second Edition, Springer Series in Statistics, Springer-Verlag, New York, 2009. · Zbl 1169.62074
[5] Buld_Koz 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] Chen_Deo1 W. W. Chen and R. S. Deo, A generalized Portmanteau goodness-of-fit test for time series models, Econometric Theory <span class=”textbf”>2</span>0 (2004), no. 2, 382–416. · Zbl 1072.62088
[7] Ian_Kam O. E. Kamenshchikova and T. O. Yanevich, An approximation of \(L_p(Ω )\) processes, Teor. \u Imovir. Mat. Stat. <span class=”textbf”>8</span>3 (2010), 59–68; English transl in Theor. Probability and Math. Statist. <span class=”textbf”>8</span>3 (2011), 71–82.
[8] Koz_Yakov2 Yu. V. Kozachenko and T. O. Ianevych, Some goodness of fit tests for random sequences, Lith. J. Statist. <span class=”textbf”>5</span>2 (2013), no. 1, 5–13.
[9] Koz_Stus Yu. V. Kozachenko and O. V. Stus, Square-Gaussian random processes and estimators of covariance functions, Math. Commun. <span class=”textbf”>3</span> (1998), no. 1, 83–94. · Zbl 0910.60021
[10] Ljung_Box G. M. Ljung and G. E. P. Box, On a measure on lack of fit in time series models, Biometrica <span class=”textbf”>6</span>5 (1978), no. 2, 297–303. · Zbl 0386.62079
[11] McLeod_Li A. I. McLeod and W. K. Li, Diagnostic checking ARMA time series models using squared-residual autocorrelations, J. Time Series Anal. <span class=”textbf”>4</span> (1983), 269–273. · Zbl 0536.62067
[12] ml S. E. Rasmussen and C. K. I. Williams, Gaussian Processes for Machine Learning, The MIT press, 2006. · Zbl 1177.68165
[13] Vas_Koz_Yakov 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) · Zbl 1199.60125
[14] Koz_Yakov1 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) · Zbl 1224.62037
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.