Nonparametric Identification of Nonlinear Time Series: Projections

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 po...

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Bibliographic Details
Published in:Journal of the American Statistical Association 1994-12, Vol.89 (428), p.1398-1409
Main Authors: Tjøstheim, Dag, Auestad, Bjørn H.
Format: Article
Language:English
Subjects:
Additive
Asymptotic bias
Autoregressive models
Conditional mean
Conditional variance
Consistent estimators
Estimators
Estimators for the mean
Exact sciences and technology
Forecasts
Inference from stochastic processes
time series analysis
Kernel estimation
Linear models
Mathematics
Non-linear models
Parametric models
Probability and statistics
Sciences and techniques of general use
Statistical variance
Statistics
Theory and Methods
Time series
Time series models
Weighting functions
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Description
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.
ISSN:0162-1459
1537-274X
DOI:10.1080/01621459.1994.10476879