Gaussian Process Regression And Extensions For Stock Market Prediction And Comparative Analysis

Forecasting financial time series is an attractive topic for investors and scholars since a financial market is a complicated dynamic system with a huge volume of time series data.An effective prediction can help investors generate excess profits.While Gaussian process regression(GPR)is a kernel-based nonparametric method that has been proved to be effective and powerful in many areas,including time series prediction.In this thesis,we focus on the framework of Bayesian non-parametric Gaussian process regression and its extensions,including Gaussian process regression with Student-t likelihood(GPRT)and Student-t process regression(TPR).By applying all these models to stock markets,GPR and its extensions show the powerful ability and usefulness in financial time series prediction.Firstly,we introduce Gaussian process regression from weight-space view and function-space view in details,including all the assumptions and derivations.In addition,extra attention is paid to the several important parts of GPR,including model structure,kernel,mean function,and parameters estimation.The kernel contains our presumptions about the function we wish to learn and define the closeness and similarity between data points while mean function dominates the predictions in the region far from training data.When it comes to parameter estimation,it is essential that the predictive mean and variances can be obtained only if all the undetermined parameters are learned from the data.At last,several model evaluation approaches are introduced.Secondly,we investigate the influences of various prior distributions of the initial hyper-parameters in GPR models to the parameter estimation and the predictability of the models when numerical optimization of likelihood function was utilized.The numerical results show that the sensitivity of the hyper-parameter estimation depends on the choice of kernels,and the prior distributions have a huge impact on the estimates of the parameters.However,it is noteworthy that the GPR models always perform well in terms of predictability,despite the poor estimates of the hyper-parameters in some cases.Particularly the performances of the GPR models using various priors are little worse than that of the true time series model in terms of prediction.Overall,the prior distributions of the hyperparameters have little impact on the performance of GPR models.Finally,we introduce GPR and its extensions,including GPRT and TPR,with all the above models applied to predict 10 main equity indices from all over the world.By simple comparison,we have found that TPR completely outperforms GPR.And this conclusion is consistent when compared with the classical time series model ARMA.However,the conclusion is not so apparent in the more statistics-based experiments.After comparing GPR and TPR using LOO-CV and k-fold cross-validation,the performance of TPR is the same as GPR.Specifically,the performance of GPR and TPR is not good in terms of index prediction in LOO-CV,with even GPR and TPR not having better index prediction than a simple linear predictor.Specifically,they perform better in terms of log-return series,and TPR outperforms GPR.In LOO-CV,TPR performs as well as GPR,even outperforms in some cases.When our discussion considers sliding window analyses,the TPR model has a slightly better predictive performance than GPR,especially when making short-term predictions,e.g.a one-week-ahead prediction in specific markets.To conclude,GPR and TPR can make a considerable prediction of equity indices.