Combining parametric and nonparametric approaches for more efficient time series prediction

Keywords: ARMA representation, noisy data, Nonparametric regression, optimal prediction

Abstract: We introduce a two-step procedure for more efficient nonparametric prediction of a strictly stationary process admitting an ARMA representation. The procedure is based on the estimation of the ARMA representation, followed by a nonparametric regression where the ARMA residuals are used as explanatory variables. Compared to standard nonparametric regression methods, the number of explanatory variables can be reduced because our approach exploits the linear dependence of the process. We establish consistency and asymptotic normality results for our estimator. A Monte Carlo study and an empirical application on stock market indices suggest that significant gains can be achieved with our approach.

MPRA working paper

Journal of the American Statistical Association , 105, 1554--1565, 2010.

R code used to obtain Figures 3 and 4 , Table 1 , Table 2 , Table 3 , Figures 4, 5, 6 and 7 , Figures 8, 9 and 10

Stock indices data sets used for the illustrations : zip file of the series of the daily returns (obtained from yahoo).