Autocorrelation in an unobservable global trend: Does it help to forecast market returns?
In this paper, we empirically test the dependence of the Russian stock market on the world stock market, world oil prices and Russian political and economic news during the period 2001–2010. We find that oil prices are not significant after 2006, and the Japan stock index is significant over the whole period, since it is the nearest market index in terms of closing time to the Russian stock index. We find that political news like the Yukos arrests or news on the Georgian war have a short-term impact, since there are many other shocks. These factors confirm the structural instability of the Russian financial market.
This paper examines the dynamic beta of Russian companies within the framework of the market model. The closing weekly prices of 29 Russian stocks, six Russian sector indices and the MICEX Index as a market index during the period from January 2009 to June 2015 are used to estimate time-varying beta using various econometric techniques. According to the results for the analyzed period, semiparametric regressions are confirmed to be the most effective model. As regards the forecast period, multivariate GARCH models surprisingly outperform all the other methods. An analysis of beta dynamics shows that most of time-varying betas are non-stationary.
In this paper we consider the behavior of Kalman Filter state estimates in the case of distribution with heavy tails .The simulated linear state space models with Gaussian measurement noises were used. Gaussian noises in state equation are replaced by components with alpha-stable distribution with different parameters alpha and beta. We consider the case when "all parameters are known" and two methods of parameters estimation are compared: the maximum likelihood estimator (MLE) and the expectation- maximization algorithm (EM). It was shown that in cases of large deviation from Gaussian distribution the total error of states estimation rises dramatically. We conjecture that it can be explained by underestimation of the state equation noises covariance matrix that can be taken into account through the EM parameters estimation and ignored in the case of ML estimation.
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.