Varying coefficient functional autoregressive model with application to the U.S. treasuries

The functional autoregressive (FAR) model belongs to an important class of models for dependent functional data analysis (FDA) and has been investigated intensively in many applications, especially for modeling the autoregressive dynamics of high-volume time series data. In this paper, we extend the classical FAR model to address the intrinsic local stationarity of a process through a varying-coefficient (VC) FAR model which characterizes nonconstant dependence between the functional predictors and the functional responses with a time-varying operator. We express the nonparametric models under sieves, whereas the time-varying operator is estimated by a local regression technique. The asymptotic properties of the estimated operator are established in this paper. Our simulation study points to a substantial gain from the VC-FAR modeling as the underlying smooth structural changes can be captured precisely. As an application, we consider the yield curves of the U.S. government bonds with different maturities. Our proposed model provides a reasonable interpretation of the dynamic transition consistent to the economic events triggering the evolution shifts, and performs more accurately on forecasting actual yield data at both short and long horizons, compared with various standard benchmark forecasts.