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] 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 analysed with the aim to describe the association between respiratory disease and air pollution concentrations.

Association between respiratory hospital admissions and air quality in Portugal: A count time series approach

“…One example of such models are the INteger Generalised AutoRegressive Conditional Heteroskedastic (INGARCH) models which exhibit an ARMA-like structure, although the data generating mechanism is analogous to that of a GARCH model in the sense that, the conditional mean recursively depends on past conditional means and on past observations [19,20]. The INGARCH formulation incorporates link/transformation functions [21], to deal with negative serial correlation [22] and, time-varying covariates [23,24]. Moreover, the INGARCH class is able to capture seasonality and serial dependence through the regression on past observations and the autoregression on past conditional means.…”