One-step prediction of financial time series

This paper examines the one-step prediction of financial time series from a binary decision theory perspective. Under the assumption that the decision statistic of the binary hypothesis testing problem is a Gaussian random variable, bounds for the forecasting efficiency of the hypothesis testing problem are derived. When the criterion for forecasting performance is the total return over the investment period, an optimisation problem is formulated to compute an optimally weighted decision statistic for the binary hypothesis testing problem. Numerical results are illustrated using weekly time series of excess return between two US dollar bond portfolios having six months duration difference. In particular, it is shown that, on average, a 27 basis point excess return per annum is possible against a given benchmark by carrying out active duration management.