Recent successes in both Artificial Neural Networks (ANN) and wavelets have placed these two methods in the spotlight of quantitative traders seeking the best tool to forecast financial time series. The Wavelet Neural Network (W-NN), a prediction model which combines wavelet-based denoising and ANN, has successfully combined the two strategies in order to make accurate predictions of financial time series. We explore how the most recent formulation of the W-NN model, with the Nonlinear Autoregressive Neural Network with Exogenous variables (NARX), is affected by the choice of wavelet thresholding technique when predicting daily returns of American index futures contracts. We explore how the choice of thresholding technique affects the profitability of two technical trading models based on daily return predictions from a NARX-based W-NN. The purpose of this research is twofold: it compares the effect of different wavelet thresholding techniques on a NARX-based W-NN’s forecasting ability on 1-day returns of American index futures contracts and offers two easy-to-implement trading strategies.

In the second part of the thesis, we formulate a hybrid NARX-based seasonal predictive model, Seasonal Nonlinear Autoregressive Neural Network with Exogenous Variables (S-NARX ), for end-of-day volume, where end-of-day volume is directly driven by the end of the day auctions. The S-NARX model will seek to take advantage of the information found in the data up until the auction time and high-frequency intraday trading volume’s diurnal seasonal pattern to predict end-of-day volume. Volume is well known to be a leading indicator of price changes and the two metrics are simultaneously positively correlated. Algorithmic traders rely on accurate volume predictions to deploy algorithmic trading algorithms, especially when utilizing a Volume Weighted Average Price (VWAP) algorithm, that allows the execution of large orders with minimal slippage. Fundamental and quantitative investors are also interested in trading volume because it is a measure of trading intensity and an indicator of market liquidity. The S-NARX augments the NARX with the feature set from a seasonal ARMA(P,Q)[s] and offers quantitative traders a flexible machine learning model for forecasting time series with both longer dependencies and seasonality.

Finally, we develop an R package that provides the traditional NARX network along with the novel seasonal version of the CoFES S-NARX that augments the NARX feature set with the features from an ARMA(P,0)[s]. The networks are built using the Keras framework in R and utilize the sequential model from this package.