GPU Accelerated Modelling and Forecasting for Large Time Series

Modelling of large scale data series is of significant importance in fields such as astrophysics and finance. The continuous increase in available data requires new computational approaches such as the use of multicore processors and accelerators. Recently, a novel time series modelling and forecasting method was proposed, based on a recursively updated pseudoinverse matrix which enhances parsimony by enabling assessment of basis functions, before inclusion into the final model. Herewith, a novel GPU (Graphics Processing Unit) accelerated matrix based auto-regressive variant is presented, which utilizes lagged versions of a time series and interactions between them to form a model. The original approach is reviewed and a matrix multiplication based variant is proposed. The GPU accelerated and hybrid parallel versions are introduced, utilizing single and mixed precision arithmetic to increase GPU performance. Discussions around performance improvement and high order interactions are given. A block processing approach is also introduced to reduce memory requirements for the accelerator. Furthermore, the inclusion of constraints in the computation of weights, corresponding to the basis functions, with respect to the parallel implementation are discussed. The approach is assessed in a series of model problems and discussions are provided.