Executive Summary : | Estimation of stock returns/prices and parameters involved in portfolio optimization and financial models is one of the most important concerns for investors and portfolio managers. For instance, the out-sample performance from the mean-variance model is significantly depends on how well one has estimated the values for its model parameters, i.e. the mean and covariance matrices, when the accurate forecasts have the potential to generate high investment returns with low risks. Machine learning (ML) based models which have been explored in the area of finance, reported a stronger ability to deal with non-linear and non-stationary structure of financial time series problems than the statistical models. Therefore, we propose to apply Deep Gaussian Process Regression ML model integrating the topological data analysis (TDA) for the estimation of stocks return and hence aim to improve the performance of the portfolio optimization models. The proposed scheme is anticipated to predict the stock prices more accurately which is the most crucial topic in finance and investment to develop more informed and robust decision models yielding superior return-risk outputs with better hedging of downward risk. We aim to test the proposed scheme on the data available on https://www.bryankellyacademic.org/ which contains monthly total individual equity returns from CRSP for all firms listed in the NYSE, AMEX, and NASDAQ. The sample begins in March 1957 (the start date of the S\&P 500) and ends in December 2016, totaling 60 years. |