Multivariate Time Series Forecasting With GARCH Models on Graphs

Modern-data provide us various challenges. They are multivariate where different variables relate to each other in an irregular way. Modern-data is also non-stationary, examples including wireless signals over time-varying channels, social networks data, brain signals, etc. Graph Signal Processing methods have gained important success over the last decade for multivariate data analysis. Various digital signal processing methods have been extended to the graph formulation such as filtering, sampling, followed by the development of the graph versions classical adaptive signal processing methods such as Graph-LMS and Graph-Sign algorithm. The time is mature now for the development of statistical graph-signal processing which models graph signals as stochastic processes. There has already been works in the literature on Graph-Vector AR and Graph- Vector ARMA processes which paved the way for stochastic graph models. Various network data, such as brain connectivity, gene expression networks, wireless communication networks and meteorological networks, change over time and space. To capture this non-stationary characteristics, our presenter will present a family of new graph stochastic models which extend the one-dimensional Generalised Autoregressive Conditional Heteroschedasticity (GARCH) which have been popular in financial data analysis. He will demonstrate the success of the new models on wind-energy forecasting. He hopes that this webinar will initiate discussions on the applications of non-stationary stochastic models various new fields such as neurological signal processing and financial data analysis.