This paper suggests an approach for the identification of the structure of both linear and non-linear time series through semi-parametric estimation of the unknown curves in models of the type Yt=E(Yt| Xt ) +et , where Xt=(Yt-1,Yt-2,...,Yt-d), d=1,2,…. The conditional expectation is estimated either in a fully nonparametric fashion or via additive (semi-parametric) models. Specifically, the unknown function will be estimated by local linear regression, with kernel estimators. Under the proposed methodology, it was verified that the Lag Dependence Function (LDF) and the Partial Lag Dependence Function (PLDF) are capable of identifying non-linear structures in time series, generalizing the traditional autocorrelation and partial autocorrelation functions. The simulation studies were conducted to evaluate and compare the proposed methodology to traditional ones. The approach was illustrated with the study of the structure of a time series of prices of Petrobras PN’S shares.
time series; nonparametric regression; kernel smoothing
