Estimation of functional-coefficient autoregressive models with measurement error

The functional-coefficient autoregressive (FAR) models are flexible to fit nonlinear features in time series data with covariates. Cai et al. (2000) developed an effective local linear estimation procedure under the FAR framework. When the time series data are observed with measurement error, we first derive the asymptotic bias of the naive local linear estimator (LLE) by ignoring the measurement error. Then, we propose a bias-corrected local linear estimation procedure for both the functional coefficients and the autoregressive error variance. Through simulation study, we present that the naive LLE is biased while the proposed estimation method shows superior performance with much reduced bias under various choices of FAR model settings. Furthermore, sensitivity analysis shows the robustness of the proposed estimator under a chosen misspecified measurement error model. The asymptotic properties of the bias-corrected estimators are also established. At last, the proposed approach is applied to a cybersecurity real data example.