Новый способ обнаружения структурных сдвигов в GARCH-моделях
The article proposes a new method of structural breaks detection in time series in the piecewise-specified GARCH-models. The method is based on the moving likelihood ratio statistics. In case of absence of structural breaks lower and upper 95 %- and 99 %- bounds were found for the likelihood ratio statistics. The criterion of structural breaks based on these bounds has been worked out. Good properties of the proposed method are supported by Monte Carlo numerical experiments. In the framework of performed calculations it is obtained that the method detects the correct number of structural changes approximately in 88% of cases. In case of correct detection of number of structural changes the moments of the structural breaks are estimated quite accurately. In the absence of structural breaks the proposed method falsely detects structural breaks quite rarely — around 2,5 % of cases. The method is tested on the real data when detecting the structural breaks in the volatility of returns for “Gazprom” ordinary shares.
интеграционные процессы на финансовых рынках, эффект перетекания волатильности, динамическая корреляция рядов доходности
This paper is an empirical study of the changing nature of the dependence of fundamental factors on the stock market index, which is the trend identified earlier in the Russian stock market. We empirically test the impact of daily values of fundamental factors on the MOEX Russia Index from 2003 to 2018. The analysis of the ARIMA-GARCH (1,1) model with a rolling window reveals that the change in the power and direction of the influence of the fundamental factors on the Russian stock market persists. The Quandt-Andrews breakpoint test and Bai-Perron test identify the number and likely location of structural breaks. We find multiple breaks probably associated with the dramatic falls of the stock market index. The results of the regression models over the different regimes, defined by the structural breaks, can vary markedly over time. This research is of value in macroeconomic forecasting and in the investment strategy development
This paper presents the results of volatility forecasting for indices of the Russian stock market using existing and developed by the authors fuzzy asymmetric GARCH-models. These models consider various switching functions which are taking into account the positive and negative shocks and are built using the tools of fuzzy numbers. Furthermore, in some models there are used switching functions that consider expert macroeconomic information. It was shown that fuzzy asymmetric GARCH-models provide a more accurate prediction of volatility than similar crisp models.
The article considers the procedure of constructing COGARCH volatility models with continuous time based on the Levy processes. The article describes the procedure of constructing the model in the general case and in the case of compound Poisson process.
The paper aims at finding the most accurate VaR model for the four most liquid Russian stocks. Among the possible VaR modeling techniques, the estimates considered in this work are based on GARCH models with six different distributions. A back testing analysis is performed to evaluate the accuracy of the alternative models and to find the worst predictable period in terms of the volatility behavior.
We consider certain spaces of functions on the circle, which naturally appear in harmonic analysis, and superposition operators on these spaces. We study the following question: which functions have the property that each their superposition with a homeomorphism of the circle belongs to a given space? We also study the multidimensional case.
We consider the spaces of functions on the m-dimensional torus, whose Fourier transform is p -summable. We obtain estimates for the norms of the exponential functions deformed by a C1 -smooth phase. The results generalize to the multidimensional case the one-dimensional results obtained by the author earlier in “Quantitative estimates in the Beurling—Helson theorem”, Sbornik: Mathematics, 201:12 (2010), 1811 – 1836.
We consider the spaces of function on the circle whose Fourier transform is p-summable. We obtain estimates for the norms of exponential functions deformed by a C1 -smooth phase.