Statistical inference of locally stationary functional coefficient models

In this paper, we propose a novel functional coefficient model, useful for direct modeling of nonstationary time series data without needing to detrend the original data. The proposed model could reveal the underlying dynamics and evolutionary nature of the data, and is easy to interpret. Through the local polynomial technique we investigate an estimation procedure for the proposed model and establish the asymptotic properties of the resulting estimator. In addition, we develop a test statistic to check time-invariance and derive the asymptotic distribution of the test statistic. An extensive simulation study is conducted to assess the finite-sample performances, and the proposed procedures work well and suggest the feasibleness and effectiveness. Two real time series applications in finance and epidemiology are provided.