On generalized additive models with dependent time series covariates

Abstract : The generalized additive model (GAM) is a standard statistical methodology and is frequently used in various fields of applied data analysis where the response variable is non-normal, e.g., integer-valued, and the explanatory variables are continuous, typically normally distributed. Standard assumptions of this model, among others, are that the explanatory variables are independent and identically distributed vectors which are not multicollinear. To handle the multicollinearity and serial dependence together a new hybrid model, called GAM-PCA-VAR model, was proposed in [17] (de Souza et al., J Roy Stat Soc C-Appl 2018) which is the combination of GAM with the principal component analysis (PCA) and the vector autoregressive (VAR) model. In this paper, some properties of the GAM-PCA-VAR model are discussed theoretically and verified by simulation. A real data set is also analyzed with the aim to describe the association between respiratory disease and air pollution concentrations.