Comparative analysis of AR-GARCH and p-adic methods of the prediction of the financial market volatility

Correct modeling and useful prediction of the volatility of the return rate of financial instruments play an essential role for making decisions on the financial market. Due to several trends the modern financial market is characterized by an increase volatility of prices of financial instruments that determines difficulties in the selection of an investment instrument. Under these circumstances investment decision making should be based on the Fractal Market Hypothesis and should be applicable to data that have distribution with heavy tails. The main idea of the study is to present the p-adic method as a useful addition to well-known methods of financial market research. The purpose of the study is to implement a comparative analysis of two methods of prediction of financial time series (GARCH-method and p-adic method) in the case study of modern financial instruments. The novelty of the work is that the p-adic method has been applied to the problem of the investment portfolio composition. Herewith both shares prices and the prices of financial instruments have been analyzed. Besides, the latter is characterized by high volatility of the return rate (e.g. currencies and cryptocurrencies). Therefore, the p-adic method of modeling and prediction has been refined on necessary procedures: the objective function of modeling problem has been optimized with respect to two parameters, and the value of a significant lag that is given on the determinate significance level, of the partial autocorrelation function (PACF) has been used for receiving of the predictive p-adic function. In this paper, information criterion and numerical characteristics have been chosen as criteria for comparing models; mean absolute error (MAE), numerical characteristics, correlation coefficients have been chosen as criteria for comparing predictions. Based on these criteria analysis, the following results have been obtained: 1) the p-adic method provides a more statistically precise way of modeling of a random variable that has a distribution with heavy tails than the GARCH-method; 2) the p-adic method enables predictions of jumps in dynamics of the rate of return, whereas GARCH-method serves for predictions of trend; 3) the p-adic method allows to reveal the simulated and predicted volatility of the rate of return of financial instruments more statistically exactly than the GARCH-method. Further studies will be devoted to the comparative analysis of the p-adic and fractal methods in the investigation of financial series and the determination of the accuracy of the p-adic prediction and the limits of confidence interval.