A note on predicting returns using bilinear ARMA models

In this note, a bilinear ARMA model is compared with the standard AR and ARMA models for forecasting power using monthly spot Sterling exchange rate. Evidence presented here suggests that the bilinear models might be useful in explaining a statistically significant, but often ignored, covariance structure between lagged variables in financial time series. The models assume that if there is a relationship between two or more random variables (for instance between two or more assets in a portfolio) then their covariance structure may be important in the prediction of expected returns. This implies that if there is any significant correlation between the variables, the coefficient associated with those particular variables will capture the relationship. Also, like the ARMA class of models, the bilinear models are very easy to apply to accounting and finance data.