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Nonlinear Autoregression with Positive Innovations
Author(s) -
Datta Somnath,
McCormick William P.,
Mathew George
Publication year - 1998
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/1467-842x.00026
Subject(s) - autoregressive model , mathematics , estimator , asymptotic distribution , nonlinear system , series (stratigraphy) , star model , vector autoregression , econometrics , conditional probability distribution , setar , time series , mathematical optimization , statistics , autoregressive integrated moving average , paleontology , physics , quantum mechanics , biology
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.