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RECURSIVE GENERALIZED M ESTIMATES FOR AUTOREGRESSIVE MOVING‐AVERAGE MODELS
Author(s) -
Allende Hector,
Heiler Siegfried
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.tb00091.x
Subject(s) - mathematics , autoregressive model , autocovariance , outlier , residual , robustness (evolution) , statistics , autoregressive–moving average model , series (stratigraphy) , monte carlo method , econometrics , algorithm , mathematical analysis , paleontology , biochemistry , chemistry , fourier transform , biology , gene
. Outliers in time series seriously affect conventional parameter estimates. In this paper a robust recursive estimation procedure for the parameters of auto‐regressve moving‐average models with additive outliers is proposed. Using ‘cleaned’ residuals from an initial robust fit of an autoregression of high order as input, bounded influence regression is applied recursively. The proposal follows certain ideas of Hannan and Rissanen, who suggested a three‐stage procedure for order and parameter estimation in a conventional setting. A Monte Carlo study is performed to investigate the robustness properties of the proposed class of estimates and to compare them with various other suggestions, including least squares, M estimates, residual autocovariance and truncated residual autocovariance estimates. The results show that the recursive generalized M estimates compare favourably with them. Finally, possible modifications to master even vigourous situations are suggested.