Gaussian Mixture Models for Time Series Modelling, Forecasting, and Interpolation

Abstract

Gaussian mixture models provide an appealing tool for time series modelling. By embedding the time series to a higher-dimensional space, the density of the points can be estimated by a mixture model. The model can directly be used for short-to-medium term forecasting and missing value imputation. The modelling setup introduces some restrictions on the mixture model, which when appropriately taken into account result in a more accurate model. Experiments on time series forecasting show that including the constraints in the training phase particularly reduces the risk of overfitting in challenging situations with missing values or a large number of Gaussian components.