A parallel recursive framework for modelling time series

Time series modelling is of significance to several scientific fields. Several approaches based on statistics, machine learning or combinations have been utilized. In order to model and forecast time series a novel parallel framework based on recursive pseudoinverse matrices is proposed. This framework enables the design of arbitrary statistical and machine learning models, adaptively, from a set of potential basis functions. This unification enables compact definition of existing and new models as well as easy implementation for new massively parallel architectures. The choice of appropriate basis functions is analysed and the fitting accuracy, termination criteria and model update operations are presented. A block variant for multivariate time series is also proposed. Parallel GPU implementation and performance optimization of the framework are provided, based on mixed precision arithmetic and matrix operations. The use of different basis functions is showcased with respect to various model univariate and multivariate time series for applications such as regression, frequency estimation and automatic trend detection. Discussions on limitations and future directions of research are also provided.