Application of the Automatic Relevance Determination Regression (ARD) for Short-term Forecasting and Analysis of Financial Time Series

Recently, Bayesian methods are becoming popular in many areas of science. The Bayesian approach provides a theoretical justification for such techniques as L1-, L2-regularization, and also has a wide range of tools to account for more complex a priori knowledge about the object under study. One of such tools is the Automatic Relevance Determination (ARD), which allows the selection of relevant features, which should prevent the overfitting of models. Using all the advantages of the ARD, it is theoretically possible to improve the quality of short-term forecasting of financial time series. The relevance of this study is due to the fact that previously this method was not used to predict financial time series, however, it is potentially a worthy competitor to the classic Box-Jenkins procedure. Based on the obtained results, it is possible to further develop the topic in terms of adapting the ARD to predict time series, taking into account the classical knowledge of the subject area. A class of false stationary time series with specific dynamics was identified, by the result that the Dickey-Fuller and KPSS tests in all specifications give an incorrect answer. According to the analysis of 1 000 time series in the form of logarithmic returns, the following characteristic features of the current implementation of the Automatic Relevance Determination (in Python) and the Box-Jenkins procedure (in R) were identified: 1) models are evaluated by the ARD approximately 1.5 times faster than ARIMA models with model selection based on the Akaike criterion (AIC); 2) in some cases, the quality of forecasting by the ARD (based on RMSE) is largely inferior to the classical Box-Jenkins approach due to the presence of single and exceeding a unit root of the estimated AR (p) polynomial; 3) the Box-Jenkins procedure is more conservative and often uses Gaussian White Noise as the optimal specification, while ARD rarely uses this specification; 4) the ARD model is more flexible and often the dynamics of the estimated mean of the process replicates the dynamics of the original series in the levels, which, however, may indicate overfitting; 5) both models are often mistaken at high and low values of logarithmic returns, have a high correlation of errors, as well as a smaller variance in the quality of forecasts (based on the Pearson correlation) over long (more than 5000 observations) time series.