Support Tensor Machine for Financial Forecasting

Past decades have witnessed excessive use of the Support Vector Machines (SVMs) in financial contexts. Despite their success, given the inherently multivariate nature of financial indices, the vector-based nature of SVM will inevitably lead to a loss of information, owing to its inability to fully exploit the available multi-way data structure. Motivated by the superior structural information content in tensors over vectors, we investigate the usefulness of the tensor extension of SVM, termed the Support Tensor Machine (STM), in the financial application of forecasting the daily direction of movement of price of the S&P 500 financial index. A computationally efficient least-squares formulation of STM (LS-STM) is considered, and the tensorized data includes the VIX, i.e. the implied index of volatility of the S&P 500, the GC1 gold commodity, and the S&P 500 itself. Next, a method to allow kernel usage in LS-STM is also introduced. The LS-STM based results are interpreted probabilistically via Platt scaling, while performance is evaluated comprehensively in terms of accuracy rate, annualized Sharpe ratio, and annualized volatility. All performance metrics conclusively demonstrate the superiority of LS-STM over standard SVM.