Maximum likelihood estimation for arma models in the presence of ARMA errors |
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| Authors: | Jong Hyup Lee Dong Wan Shin |
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| Affiliation: | 1. Department of Statistics , Sungshin Women's University , Corporate Research and Development One Research Circle, Seoul, Korea;2. Department of Statistics , Ewha Womans University , Corporate Research and Development One Research Circle, Seoul, Korea |
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| Abstract: | An ARMA(p, q) process observed with an ARMA(c, d) error has an ARMA (p + c, k) representation with k = max(c + q, p + d) whose parameters satisfy some nonlinear constraints. Identification of the model is discussed. We develop Newton-Raphson estimators for the ARMA(p + c, k) process which take advantage of the information contained in the nonlinear restrictions. Explicit expressions for the derivatives of the restrictions are derived. |
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| Keywords: | ARMA error Identification Maximum likelihood estimation Newton-Raphson procedure |
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