Time Series Forecasting Using Distribution Enhanced Linear Regression

Amongst the wealth of available machine learning algorithms for forecasting time series, linear regression has remained one of the most important and widely used methods, due to its simplicity and interpretability. A disadvantage, however, is that a linear regression model may often have higher error than models that are produced by more sophisticated techniques. In this paper, we investigate the use of a grouping based quadratic mean loss function for improving the performance of linear regression. In particular, we propose segmenting the input time series into groups and simultaneously optimizing both the average loss of each group and the variance of the loss between groups, over the entire series. This aims to produce a linear model that has low overall error, is less sensitive to distribution changes in the time series and is more robust to outliers. We experimentally investigate the performance of our method and find that it can build models which are different from those produced by standard linear regression, whilst achieving significant reductions in prediction errors.