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The foreign exchange (FX) market is long established as the largest and most important global financial market. While a large number of research papers focus on forecasting in the FX market, there are still gaps in the literature. First, very few papers focus on improving the parameter estimation process in the forecasting context. Second, artificial neural networks (ANN) with large sizes have not been applied to FX forecasting with the recently fast-developed GPU techniques. Third, forecasting for trading purposes in the FX market has been limited to either building forecasting models or analysing technical indicators. A combination of ANN forecasting models with technical indicators is rare in the existing literature. The use of more accurate parameter estimation algorithms and GPU techniques also makes the thesis unique in the methodological sense. The thesis uses three types of ANN models, namely GARCH-ANN, large Multilayer Perceptron (MLPNN) and Long Short Term Memory (LSTM), to forecast volatility, the direction of price movements and price patterns in the FX market. Research is conducted at three data frequencies, namely monthly, daily and hourly as the analysis goes from the macro-perspective to the micro-perspective. In the first empirical chapter, a Recursive Simulation Algorithm (RSGA) is proposed for estimating the parameters of a volatility forecasting model using GARCH-ANN. The proposed algorithm significantly improves the stability and accuracy of the estimation process by dealing with the local-optimum and convergence problems. The second empirical chapter utilises a large MLPNN model with GPU implementation to forecast the price direction of different FX pairs, with over 40 macro-economic indicators as input variables. Highly profitable out-of-sample results are observed for some of the currency pairs, which challenges the semi-strong form of the Efficient Market Hypothesis (EMH). Significant efficiency improvement is achieved with the GPU implementation. The third empirical chapter proposes the use of the Relative Strength Indicator (RSI) as a measure of the extent of trend-following and mean-reversion patterns of FX rates. A LSTM modelis utilised to forecast price movement patterns (measured by RSI). The trading strategy based on forecasting results of price movement patterns generates more stable profits than the benchmark Moving Average (MA) or RSI implemented on their own. However, the overall low profitability over time for the four currency pairs fails to challenge the weak-form EMH. Overall, with the novel methodologies and technologies implemented within different models, this thesis finds evidence on some extent of inefficiency of the FX market at lower trading frequency (e.g. monthly) and less inefficiency of the FX market at higher trading frequency (e.g. hourly). One possible explanation is that at higher frequencies, the large number of daily (or higher frequency) traders and high-frequency trading algorithms reduce both the number of mis-pricing opportunities and the length of time that any mis-pricing opportunity may last.