Financial market prediction attracts immense interest among researchers nowadays due to rapid increase in the investments of financial markets in the last few decades. The stock market is one of the leading financial markets due to importance and interest of many stakeholders. With the development of machine learning techniques, the financial industry thrived with the enhancement of the forecasting ability. Probabilistic neural network (PNN) is a promising machine learning technique which can be used to forecast financial markets with a higher accuracy. A major limitation of PNN is the assumption of Gaussian distribution as the distribution of input variables which is violated with respect to financial data. The main objective of this study is to improve the standard PNN by incorporating a proper multivariate distribution as the joint distribution of input variables and addressing the multi-class imbalanced problem persisting in the directional prediction of the stock market. This model building process is illustrated and tested with daily close prices of three stock market indices: AORD, GSPC and ASPI and related financial market indices. Results proved that scaled t distribution with location, scale and shape parameters can be used as more suitable distribution for financial return series. Global optimization methods are more appropriate to estimate better parameters of multivariate distributions. The global optimization technique used in this study is capable of estimating parameters with considerably high dimensional multivariate distributions. The proposed PNN model, which considers multivariate scaled t distribution as the joint distribution of input variables, exhibits better performance than the standard PNN model. The ensemble technique: multi-class undersampling based bagging (MCUB) was introduced to handle class imbalanced problem in PNNs is capable enough to resolve multi-class imbalanced problem persisting in both standard and proposed PNNs. Final model proposed in the study with proposed PNN and proposed MCUB technique is competent in forecasting the direction of a given stock market index with higher accuracy, which helps stakeholders of stock markets make accurate decisions.
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