Evaluation of Regression Models with Regularization on Financial Time Series Using an Adaptive Complex Metric

Abstract

The article proposes an approach to forecasting financial time series, the main tool of which is a comprehensive (composite) forecast quality metric ARL (Adaptive Risk Loss). The object of the study is the process of forecasting financial time series using adaptive mathematical models. The problem addressed is the inability of traditional symmetric metrics (MSE) to adequately evaluate models in real trading conditions, as they ignore the direction of price movement and risk asymmetry, penalizing profitable and unprofitable errors equally. The essence of the results obtained lies in the development of a methodology for selecting and adjusting regression models (Lasso, Elastic Net), where the ARL loss function integrates three dimensions: approximation accuracy, trend prediction quality (Directional Accuracy), and asymmetric risk (pinball-loss, q=0.05). A distinctive feature of the proposed approach is the use of fuzzy logic elements for dynamic weighting of metric components depending on the current market situation. The adaptability of the system is ensured by automatically changing optimization priorities based on the analysis of sliding statistical characteristics of time series, in particular volatility, asymmetry, excess, and autocorrelation. During periods of increased market turbulence, the influence of the risk-oriented component increases, which allows reducing the depth of potential declines, while in stable phases, the requirement for forecast accuracy dominates. The practical value of the results obtained lies in the possibility of applying the proposed approach together with walk-forward validation to build robust forecasting and risk management models in markets such as cryptocurrency, the gold commodity market, and the US stock market.

Experimental verification of forecasting was performed for seven financial assets (VIX Index, Brent Oil, USD/CHF, Bitcoin, Nasdaq, Gold, S&P 500) with step-by-step testing, in which the available history was used for training at each step and a forecast for the next period was formed. The validation confirmed the robustness of the effect for most assets, but it also revealed a limitation in the case of VIX, where ARL deteriorates by 4.86 % despite a 0.52 % improvement in MSE. According to the ARL criterion, the choice of regularization type depends on the asset; in particular, L1 regularization yields the best result for Bitcoin, while Elastic Net performs better for Brent Oil.