Predicting Stock Returns with Batched AROW

Financial markets exhibit highly non-stationary behaviors, making it difficult to build predictive signals that do not decay too rapidly (see [SCSG13, Con01] for empirical studies of return time series). A standard method for capturing these changes in time series data consists in using a rolling regression, that is, a linear regression model trained on a rolling window and kept as static model during a prediction period. However, the size of historical training data as well as the duration of the prediction period have a direct impact on the performance of the resulting model: using too many training data would result in a model that does not react quickly enough to sudden changes while short training and prediction windows would make the model unstable (see for instance [IJR17]). Online learning algorithms are suited to situations where data arrives sequentially. New information is taken into account by updating the model parameters in a supervised fashion. More precisely, an online learning algorithm repeats the following steps indefinitely: receive a new instance x t, make a prediction ŷ t, receive the correct label y t for the instance and update the model accordingly. In the particular case of regression, online models are also good candidates to handle the non-stationarity inherent in financial time series while keeping a certain memory of what has been learnt from the beginning. The recursive least squares (RLS) algorithm is a well known approach to online linear regression problems (e.g.