The development of algorithmic trading has been one of the most prominent trends in finance and its applications. Hidden Markov Models (HMMs) help enhance the predictive power of statistical models and improve trading strategies for data scientists and algorithmic traders. In recent years there has been growing interest in investigating the pairs trading and multiple trading based on robust Kalman filtering (KF) using data-driven innovation volatility forecasts (DDIVF). KF algorithms were successfully applied in pairs trading with two cointegrated assets using DDIVF as a method for forecasting non-normal innovation volatility. In this paper a novel combined pairwise trading strategy is proposed by combining HMM and DDIVF to further optimize trading signals in different market regimes. The results of the numerical experiments on two cointegrated stocks show that the proposed profitable trading strategy using DDIVF-HMM outperforms the recently studied robust trading strategy using DDIVF alone.

There has been a growing interest in studying risk forecasting using data-driven exponential weighted moving average (DD-EWMA) volatility models as well as nonlinear neuro volatility models based on Neural network (NN). However, the recently proposed volatility forecasting models have not been used to study portfolio optimization. Large kurtosis of the portfolio return sequence shows that it follows a heavy-tailed t distribution. Significant sample autocorrelations of the absolute portfolio returns and squared portfolio returns suggest that time-varying volatility models are more appropriate to model the volatility. In this paper, a DD-EWMA portfolio volatility forecasting model is used to study the generalized portfolio optimization using the intelligent probabilistic risk forecasts based on data-driven t distribution of the portfolio returns. Optimal portfolio weights are obtained by minimizing the corresponding risk forecasts of portfolio volatility, mean absolute deviation (MAD), Value-at-Risk (VaR), and conditional Value-at-Risk (CVaR) for minimum risk forecast portfolios. Moreover the portfolio weights of the generalized tangency portfolios with different risk measures are obtained by maximizing the corresponding portfolio Sharpe ratio (PSR) forecasts. Experiments are conducted to show that the DD-EWMA volatility forecasting model is most computationally efficient (less computing time), whereas neuro volatility model takes longer time to obtain one-step ahead portfolio volatility forecasts. Moreover, the superiority of the portfolio selection based on data-driven volatility forecasts over the portfolio selection based on volatility estimates is demonstrated through numerical experiments using ten frequently traded stocks.