Abstract: We propose a functional threshold autoregressive model for flexible functional time series modeling. In particular, the behavior of a function at a given time point can be described by different autoregressive mechanisms, depending on the values of a threshold variable at a past time point. Sufficient conditions for the strict stationarity and ergodicity of the functional threshold autoregressive process are investigated. We develop a novel criterion-based method simultaneously conducting dimension reduction and estimating the thresholds, autoregressive orders, and model parameters. We also establish the consistency and asymptotic distributions of the estimators of both thresholds and the underlying autoregressive models. Simulation studies and an application to U.S. Treasury zero-coupon yield rates are provided to illustrate the effectiveness and usefulness of the proposed methodology.

Key words and phrases: Functional time series, minimum description length principle, multiple thresholds.