ANALYSIS AND FORECASTING OF THE RETURN OF MICROSOFT AND PFIZER SHARES USING ARIMA-GARCH MODELS

Abstract

Shares are one of the most common objects for investment. Individual investors both invest directly in the securities of a certain company and invest in various funds created from the shares of public companies according to different structures. For a significant share of the population of highly developed countries with a developed financial infrastructure, income from investments is an important source of passive income that increases the financial security of households in case of temporary loss of work, illness, or other adverse circumstances. Therefore, the analysis of securities quotes to select assets for further investment is an extremely important task. When studying the dynamics of stock quotes, due to the significant role of risk, volatility is an essential component. To correctly respond to possible spikes in volatility caused by certain events, and forecasting their duration, it is important to use analysis. Econometric analysis with the help of time series research models is selected as the optimal option for the study of the dynamics of stock quotations. Due to the high quality, the most common is the simulation of securities quotations using a combination of ARIMA-GARCH models. Various modifications of this method were implemented in this work using the R programming language. Data on the daily returns of Microsoft and Pfizer shares were used for the analysis. At the first stage of the modeling process, a transition to log- returns was made, graphs of the initial time series, autocorrelation functions were constructed, time series were checked for stationarity according to the Dickey-Fuller test, and the optimal specification of the ARIMA model was obtained for both indices. At the same time, when checking the residuals of the models for autocorrelation and the ARCH effect, positive results were obtained, which indicates the inadequacy of using only the ARIMA model and the need for GARCH. As a result of sorting through various GARCH specifications, optimal ones were chosen for two stocks, both of which take into account the asymmetric impact of disturbances depending on their signs. The resulting models were tested by the Leung-Box test, the ARCH LM test, and the Pearson test for specification optimality. Based on the obtained models, a forecast was built using the sliding window method and compared with the actual time series data. The quality of the forecasts of the optimal models and other specifications was also correlated to check that the minimum forecast error was obtained using the selected models. All results confirmed the correctness of the built models, which allows them to be used for analysis and forecasting already for further periods.