Introduction

Over the past several decades, researchers and practitioners have used various forecasting methods to study foreign exchange market time series events, thus implicitly challenging the concepts of informational and speculative efficiency. These forecasting methods largely stemmed from the fields of financial econometrics and machine learning. For example, the 1960s saw the development of a number of large macroeconometric models purporting to describe the economy using hundreds of macroeconomic variables and equations. It was found that although complicated linear models can track the data very well over the historical period, they often perform poorly for out-of-sample forecasting [287]. This has often been interpreted that the explanatory power of exchange rate models is extremely poor. Nelson [310] discovered that univariate autoregressive moving average (ARMA) models with small values for p and q produce more robust results than the big models. Box [58] developed the autoregressive integrated moving average (ARIMA) methodology for forecasting time series events. The basic idea of ARIMA modeling approaches is the assumption of linearity among the variables. However, there are many time series events for which the assumption of linearity may not hold. Clearly, ARIMA models cannot be effectively used to capture and explain nonlinear relationships. When ARIMA models are applied to processes that are nonlinear, forecasting errors often increase greatly as the forecasting horizon becomes longer. To improve forecasting nonlinear time series events, researchers have developed alternative modeling approaches. These include nonlinear regression models, the bilinear model [171], the threshold autoregressive model [392], and the autoregressive heteroskedastic model by [115]. Although these methods have shown improvement over linear models for some specific cases, they tend to be application specific, lack generality, and are often harder to implement [424].