Journal of Data Science

Abstract: Additive model is widely recognized as an effective tool for di mension reduction. Existing methods for estimation of additive regression function, including backfitting, marginal integration, projection and spline methods, do not provide any level of uniform confidence. In this paper a sim ple construction of confidence band is proposed for the additive regression function based on polynomial spline estimation and wild bootstrap. Monte Carlo results show three desirable properties of the proposed band: excellent coverage of the true function, width rapidly shrinking to zero with increasing sample size, and minimal computing time. These properties make he pro cedure is highly recommended for nonparametric regression with confidence when additive modelling is appropriate.

Abstract: A seasonal additive nonlinear vector autoregression (SANVAR) model is proposed for multivariate seasonal time series to explore the possible interaction among the various univariate series. Significant lagged variables are selected and additive autoregression functions estimated based on the selected variables using spline smoothing method. Conservative confidence bands are constructed for the additive autoregression function. The model is fitted to two sets of bivariate quarterly unemployment rate data with comparisons made to the linear periodic vector autoregression model. It is found that when the data does not significantly deviate from linearity, the periodic model is preferred. In cases of strong nonlinearity, however, the additive model is more parsimonious and has much higher out-of-sample prediction power. In addition, interactions among various univariate series are automatically detected.