Probability distributions, trading strategies and leverage: an application of Gaussian mixture models

The purpose of this paper is twofold. Firstly, to assess the merit of estimating probability density functions rather than level or classification estimations on a one-day-ahead forecasting task of the EUR|USD time series. This is implemented using a Gaussian mixture model neural network, benchmarking the results against standard forecasting models, namely a naïve model, a moving average convergence divergence technical model (MACD), an autoregressive moving average model (ARMA), a logistic regression model (LOGIT) and a multi-layer perceptron network (MLP). Secondly, to examine the possibilities of improving the trading performance of those models with confirmation filters and leverage. <P>While the benchmark models perform best without confirmation filters and leverage, the Gaussian mixture model outperforms all of the benchmarks when taking advantage of the possibilities offered by a combination of more sophisticated trading strategies and leverage. This might be due to the ability of the Gaussian mixture model to identify successfully trades with a high Sharpe ratio. Copyright © 2004 John Wiley & Sons, Ltd.