  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 capture 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 two countries. Furthermore, we illustrate a climatology
example, examining whether the weather conditions Granger cause pollutant daily
levels in a city.
