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NON‐NEGATIVE AUTOREGRESSIVE MODELS
Author(s) -
Hongzhi An
Publication year - 1992
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.1992.tb00108.x
Subject(s) - autoregressive model , mathematics , estimator , combinatorics , independent and identically distributed random variables , stationary process , statistics , random variable
. Consider a stationary non‐negative autoregressive (AR) model given x t = b 1 x t ‐1, +…+ b p x t‐p + e t , where the e t are independent identically distributed non‐negative variables and b 1 , …, b p are non‐negative parameters, and all the roots of the equation 1 – b 1 u –…– b p u p = 0 are outside the unit circle. The stationary solution of the above AR model is called a stationary non‐negative AR process. Let x 1 , x 2 , … x n be an example of a stationary non‐negative AR process. Under very general conditions strongly consistent estimators of the AR parameters b 1 , b 2 , …, b p have been studied. In this paper a new procedure is proposed to estimate not only b 1 , b 2 , …, b p but also b o which is the essential lower bound of the variable e t . We shall show that the new estimators obtained using the new procedure are consistent estimators of b o , b 1 , …, b p under the weakest condition which guarantees that the stationary non‐negative AR model has a stationary non‐degenerative solution.