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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2022, Number 8, Pages 93–96
DOI: https://doi.org/10.26907/0021-3446-2022-8-93-96 (Mi ivm9806) 		 
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On a statistical criterion for the heterogeneity of second-order moments

S. G. Khaliullin

N.I. Lobachevsky Institute of Mathematics and Mechanics, Kazan Federal University, 18 Kremlyovskaya str., Kazan, 420008 Russia
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DOI: https://doi.org/10.26907/0021-3446-2022-8-93-96
Abstract: In this paper we consider the problem of heteroscedasticity in the theory of time series. The presence of heteroscedasticity (heterogeneity in second-order moments) in various data leads to known errors in statistical conclusions if it is not possible to notice this problem in time. This problem is most often encountered in the tasks of verifying the adequacy of a particular model in regression analysis or time series analysis. If the model is adequate, the residuals should be homoscedastic.
When studying the financial market, it is quite common to find heterogeneity of second-order moments in some financial indices, such as logarithmic profit in stock prices.
The paper considers a criterion for testing the hypothesis of homoscedasticity in statistical data.
Keywords: heteroscedasticity, conditionally Gaussian models, volatility.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation
Received: 02.06.2022
Revised: 02.06.2022
Accepted: 29.06.2022
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2022, Volume 66, Issue 8, Pages 76–78
DOI: https://doi.org/10.3103/S1066369X22080047
Document Type: Article
UDC: 519.226
Language: Russian
Citation: S. G. Khaliullin, “On a statistical criterion for the heterogeneity of second-order moments”, Izv. Vyssh. Uchebn. Zaved. Mat., 2022, no. 8, 93–96; Russian Math. (Iz. VUZ), 66:8 (2022), 76–78
Citation in format AMSBIB
\Bibitem{Kha22}
\by S.~G.~Khaliullin
\paper On a statistical criterion for the heterogeneity of second-order moments
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2022
\issue 8
\pages 93--96
\mathnet{http://mi.mathnet.ru/ivm9806}
\crossref{https://doi.org/10.26907/0021-3446-2022-8-93-96}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2022
\vol 66
\issue 8
\pages 76--78
\crossref{https://doi.org/10.3103/S1066369X22080047}
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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