Predicting Asset Dynamics with Hybrid Bivariate Kernel Density Estimate and Markov Model

There exists a variety of mathematical models for the prediction of asset dynamics. Some of them are based on special assumptions for the data, such as the normal distribution of logarithms of the total return rates, nonnegative asset values, etc. By using the term "asset", we refer to time-varying data such as currency exchange rates, stock prices, etc. In this work, we present a universal approach to the prediction of asset dynamics which does not require the normality assumption, i.e., the data may follow any type of probability distribution. The presented method employs the two-dimensional kernel density estimate for asset return rates. In this sense, the resulting bivariate random variable estimates the probability distribution of the asset return rates. The distribution is then used to directly simulate asset dynamics or acts as a tool to estimate the transition matrix for the proposed discrete hybrid model. The results show that the hybrid approach yields a smaller prediction error for shorter time horizons, i.e., spanning 1 month or less. The corresponding prediction error is below 1%. Should one need to simulate longer time periods, additional model tuning is required, mainly by testing transition matrices of bigger dimensions.