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November, 1978 Estimation of Parameters in the ARMA Model When the Characteristic Polynomial of the MA Operator Has a Unit Zero
Tuan Pham-Dinh
Ann. Statist. 6(6): 1369-1389 (November, 1978). DOI: 10.1214/aos/1176344382

Abstract

We consider the estimation of parameters in the time series model $X(t) = \sum^q_{j = 1}a_jX(t - j) + \varepsilon(t) - \varepsilon(t - j) - \sum^p_{j = 1} c_j\{\varepsilon(t - j) - \varepsilon(t - j - 1)\}$ where the $\varepsilon(t)$ are independently identically distributed random variables with zero mean and variance $\sigma^2$. We compute the exact $\log$ likelihood of the model, propose and justify an asymptotic approximation of it. The latter will be used to derive estimates of the parameters which are shown to be asymptotically normal and efficient.

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Tuan Pham-Dinh. "Estimation of Parameters in the ARMA Model When the Characteristic Polynomial of the MA Operator Has a Unit Zero." Ann. Statist. 6 (6) 1369 - 1389, November, 1978. https://doi.org/10.1214/aos/1176344382

Information

Published: November, 1978
First available in Project Euclid: 12 April 2007

zbMATH: 0402.62023
MathSciNet: MR523771
Digital Object Identifier: 10.1214/aos/1176344382

Subjects:
Primary: 62F20

Keywords: $L^p$ norm , asymptotic distribution , autoregressive-moving-average model , consistency , Cumulants , innovation , likelihood function

Rights: Copyright © 1978 Institute of Mathematical Statistics

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Vol.6 • No. 6 • November, 1978
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