Financial time series modelling with discounted least squares backpropagation

We propose a simple modification to the error backpropagation procedure which takes into account gradually changing input-output relations. The procedure is based on the principle of Discounted least squares whereby learning is biased towards more recent observations with long term effects experiencing exponential decay through time. This is particularly important in systems in which the structural relationship between input and response vectors changes gradually over time but certain elements of long term memory are still retained. The procedure is implemented by a simple modification of the least-squares cost function commonly used in error backpropagation. We compare the performance of the two cost functions using both a controlled simulation experiment and a non-trivial application in estimating stock returns on the basis of multiple factor exposures. We show that in both cases the DLS procedure gives significantly better results. Typically, there is an average improvement of above 30% (in MSE terms) for the stock return modelling problem.