Global kernel estimator and test of varying-coefficient autoregressive model

We propose a varying-coefficient autoregressive model that contains additive models, varying- coefficient models, partially linear models and low-dimensional interaction models as special cases. A global kernel backfitting method is proposed for the estimation and inference of parameters and unknown functions in this model. Key large-sample results are established, including estimation consistency, asymptotic normality and the generalized likelihood ratio test for parameters and non-parametric functions. The proposed methodology is examined by simulation studies and applied to examine the relationship between suicide news reports in the three leading newspapers and the daily number of suicides in Taiwan. The relationship between the media reporting and suicide incidence has been established and explored. The Canadian Journal of Statistics 47: 487-519; 2019 (c) 2019 Statistical Society of Canada