Bayesian Testing of Granger Causality in Functional Time Series

We develop a multivariate functional autoregressive model (MFAR), which captures the cross-correlation among multiple functional time series and thus improves forecast accuracy. We estimate the parameters under the Bayesian dynamic linear models (DLM) framework. In order to test for Granger causality from one FAR series to another we employ Bayes Factor. Motivated by the broad application of functional data in finance, we investigate the causality between the yield curves of USA and UK. Bayes factor values shows that no causal relation exists among the interest rates of these two countries. Furthermore, we illustrate a climatology example, suggesting that the meteorological factors Granger cause pollutant daily levels in Delhi. The Github repository https://www.Bayesian-Testing-Of-Granger-Causality-In-Functional-Time-Series contains the detailed study of simulation and real data applications.