Nonlinear Autoregression with Positive Innovations

Abstract

Use of nonlinear models in analyzing time series data is becoming increasingly popular. This paper considers a broad class of nonlinear autoregressive models where the autoregressive part is additive and the terms are nonlinear functions of the past data. Also, the innovation distribution is supported on the non‐negative reals and satisfies a tail regularity condition. The linear parameters of the autoregression are estimated using a linear programming recipe which yields much more accurate estimates than traditional methods such as conditional least squares. Limiting distribution of the linear programming estimators is obtained. Simulation studies validate the asymptotic results and reveal excellent small sample properties of the LPE estimator.

Department(s)

Mathematics

Document Type

Article

DOI

https://doi.org/10.1111/1467-842x.00026

Keywords

nonlinear time series, linear programming estimators, regular variation

Publication Date

1998

Journal Title

Australian & New Zealand Journal of Statistics

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