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Regular version of the site

Article

Оценивание параметров моделей временных рядов с марковскими переключениями режимов

Силаева В. А., Силаева М. В., Силаев А. М.

The paper considers the problem of estimating the parameters of time series described by regression models
with Markov switching of two regimes at random instants of time with independent Gaussian noise. For the
solution, we propose a variant of the EM algorithm based on the iterative procedure, during which an estimation
of the regression parameters is performed for a given sequence of regime switching and an evaluation of the
switching sequence for the given parameters of the regression models. In contrast to the well-known methods of
estimating regression parameters in the models with Markov switching, which are based on the calculation of a
posteriori probabilities of discrete states of the switching sequence, in the paper the estimates are calculated of
the switching sequence, which are optimal by the criterion of the maximum of a posteriori probability. As a result,
the proposed algorithm turns out to be simpler and requires less calculations. Computer modeling allows to
reveal the factors influencing accuracy of estimation. Such factors include the number of observations, the number
of unknown regression parameters, the degree of their difference in different modes of operation, and the
signal-to-noise ratio which is associated with the coefficient of determination in regression models. The proposed
algorithm is applied to the problem of estimating parameters in regression models for the rate of daily return
of the RTS index, depending on the returns of the S&P 500 index and Gazprom shares for the period from
2013 to 2018. Comparison of the estimates of the parameters found using the proposed algorithm is carried out
with the estimates that are formed using the EViews econometric package and with estimates of the ordinary
least squares method without taking into account regimes switching. The account of regimes switching allows to
receive more exact representation about structure of a statistical dependence of investigated variables. In switching
models, the increase in the signal-to-noise ratio leads to the fact that the differences in the estimates produced
by the proposed algorithm and using the EViews program are reduced.