The Gaussian Process with a deep kernel is an extension of the classic GP regression model and this extended model usually constructs a new kernel function by deploying deep learning techniques like long short-term memory networks. A Gaussian Process with the kernel learned by LSTM, abbreviated as GP-LSTM, has the advantage of capturing the complex dependency of financial sequential data, while retaining the ability of probabilistic inference. However, the deep kernel Gaussian Process has not been applied to forecast the conditional returns and volatility in financial market to the best of our knowledge. In this paper, grid search algorithm, used for performing hyper-parameter optimization, is integrated with GP-LSTM to predict both the conditional mean and volatility of stock returns, which are then combined together to calculate the conditional Sharpe Ratio for constructing a long-short portfolio. The experiments are performed on a dataset covering all constituents of Shenzhen Stock Exchange Component Index. Based on empirical results, we find that the GP-LSTM model can provide more accurate forecasts in stock returns and volatility, which are jointly evaluated by the performance of constructed portfolios. Further sub-period analysis of the experiment results indicates that the superiority of GP-LSTM model over the benchmark models stems from better performance in highly volatile periods.
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