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 naive 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. 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.