On Generalized Additive Models with Dependent Time Series Covariates
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  (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.
KeywordsAir pollution Generalized additive model Multicollinearity Principal component analysis Time series Vector autoregressive model
The authors thank the following agencies for their support: the National Council for Scientific and Technological Development (Conselho Nacional de Desenvolvimento Científico e Tecnológico—CNPq), the Brazilian Federal Agency for the Support and Evaluation of Graduate Education (Coordenação de Aperfeiçoamento de Pessoal de Nível Superior—CAPES), Espírito Santo State Research Foundation (Fundação de Amparo à Pesquisa do Espírito Santo—FAPES) and Minas Gerais State Research Foundation (Fundação de Amparo à Pesquisa do estado de Minas Gerais—FAPEMIG). Márton Ispány was supported by the EFOP-3.6.1-16-2016-00022 project. The project is co-financed by the European Union and the European Social Fund. Pascal Bondon thanks to the Institute for Control and Decision of the Université Paris-Saclay.
- 13.Nascimento, A.P., Santos, J.M., Mil, J.G., de Souza, J.B., Reis Júnior, N.C., Reisen, V.A.: Association between the concentration of fine particles in the atmosphere and acute respiratory diseases in children. Rev. Saude Publ. 51, 3 (2017)Google Scholar
- 17.de Souza, J.B., Reisen, V.A., Franco, G.C., Ispány, M., Bondon, P., Santos, J.M.: Generalized additive models with principal component analysis: an application to time series of respiratory disease and air pollution data. J. Roy. Stat. Soc. C-Appl. 67(2), 453–480 (2018)Google Scholar
- 20.Wood, S.N.: Generalized Additive Models: An Introduction with R. 2nd edn. Chapman and Hall/CRC (2017)Google Scholar
- 21.Zamprogno, B.: PCA in time series with short and long-memory time series. Ph.D. Thesis at the Programa de Pós-Graduação em Engenharia Ambiental do Centro Tecnológico, UFES, Vitória, Brazil (2013)Google Scholar