PROBABILISTIC MODELS AND METHODS OF REGRESSION ANALYSIS OF VOLATILE FINANCIAL TIME SERIES
DOI:
https://doi.org/10.18372/2310-5461.57.17439Keywords:
financial time series, homoscedasticityhomoscedasticity, heteroscedasticity, regression, auto regression and moving averageAbstract
The article considers financial and economic time series in production, banking, and investment branches. Empirical research in the field of economics increasingly uses data at the individual or household level obtained from surveys. Some variables are difficult enough to measure that such problems arise even when estimating simple bivariate regressions; when panel data are used in ways that effectively distinguish much of the true change while adding to the noise. Results of analysis of real information give the reasons to suppose that the most adequate mathematic models of non-stationary financial time series are homoscedastic and heteroscedastic probabilistic models with partially unknown impact factors. We propose the auto regression and moving average (ARMA) models for analysis of homoscedastic series and auto regression and integrated moving average (ARIMA) models for analysis of heteroscedastic series. These models cover rather wide class of random processes, which are non-stationary in wide and narrow sense. Correct choice of model order allows getting the results with acceptable errors (discrepancy) using rather simple models. We showed the principal useless of tendency to non-critical enlarging of order of moving average and regression equations. Moreover, the model gets much more complicated, and the errors of extrapolation, corresponding with forecasting, grow very quickly. The article attempts a preliminary survey and analysis of time series data for the specification of a model of the interrelationship of variables. It should be recognized that the practical implementation of the above rules is not trivial. In particular, it is obvious that it is possible to obtain satisfactory estimates of the spectrum of financial and economic time series, but at the moment it is not clear how to quantitatively estimate volatility values, cooperation processes in conflict conditions, etc. Only further analysis, both theoretical and empirical, can provide answers to these questions.
References
Smith Adam, Cannan Edwin. The Wealth of Nations. Modern Library; Sixth Printing edition, 1994. Reprint of 1880 George Bell Publishers. – 1200 pp.
Smith Adam. The Theory of Moral Sentiments. 2011. Reprint of 1790 London Edition Gutenberg Publishers. 538 pp.
Tsay R.S., Analysis of Financial Time Series. 3rd ed. John Wiley & Sons, Inc., Hoboken, New Jersey, 2010. - 677 p.
Korolyuk, V., Limnios, N., Mishura, Y., Sakhno, L., & Shevchenko, G. (Eds.). (2014). Modern Stochastics and Applications. Springer Optimization and Its Applications. - Springer International Publishing Switzerland 2014. XVII, 349 p.
Papoulis A. Probability, Random Variables, and Stochastic Processes, 4th Ed. / Athanasios Papoulis, Unnikrishna Pillai. – McGraw-Hill, New York, NY, 2002. – 852 p.
Bendat J.S. Random Data: Analysis and Measurement Procedures, 4th Ed. Julius S. Bendat, Allan G. Piersol. - John Wiley & Sons, Inc., Hoboken, New Jersey, 2010. - 640 p.
George.E.P. Box, G.M. Jenkins, G.C. Reinsel, G.M. Ljung Time series analysis: forecasting and control, Fifth ed. John Wiley & Sons, Inc., Hoboken, New Jersey, 2016. - 669 pp.
Mosteller F., Tukey J. W. Data Analysis and Regression: A Second Course in Statistics. Pearson, 1977. 588 p.
Anderson T.W. The Statistical Analysis of Time Series. Wiley, Hoboken, 2011. 704 p.
Afifi A. A., Azen S. P. Statistical Analysis, Second Ed.: A Computer Oriented Approach 2nd Edition. Academic Press; 2nd ed., 1979. 442 pp.
