Tjøstheim, Dag; Auestad, Bjørn H. Nonparametric identification of nonlinear time series: Projections. (English) Zbl 0813.62036 J. Am. Stat. Assoc. 89, No. 428, 1398-1409 (1994). Summary: We study the possibility of identifying general linear and nonlinear time series models using nonparametric methods. The kernel estimators of the conditional mean and variance are used as a basis, and the properties of these quantities as model indicators are briefly discussed. Some drawbacks are pointed out, and motivated by these we introduce projections as tools of identification. The projections are especially useful for additive modeling. Expressions for the asymptotic bias and variance are obtained. The projection of the conditional variance is suggested as a tool for identifying heteroscedastic time series. The results are illustrated by simulations for both the estimators of the projections and the estimators of the conditional mean and variance. Cited in 69 Documents MSC: 62G07 Density estimation 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) Keywords:linear time series; nonlinear time series; kernel estimation; conditional mean; projections; identification; additive modeling; asymptotic bias; conditional variance; heteroscedastic time series PDFBibTeX XMLCite \textit{D. Tjøstheim} and \textit{B. H. Auestad}, J. Am. Stat. Assoc. 89, No. 428, 1398--1409 (1994; Zbl 0813.62036) Full Text: DOI