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The Multiple Outlier Problem in Time Series Analysis
Author(s) -
Schmid Wolfgang
Publication year - 1986
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1986.tb00711.x
Subject(s) - outlier , series (stratigraphy) , autoregressive model , estimator , mathematics , statistic , asymptotic distribution , time series , test statistic , asymptotic analysis , statistics , autoregressive integrated moving average , econometrics , statistical hypothesis testing , paleontology , biology
Summary In this paper we consider the multiple outlier problem in time series analysis. The underlying undisturbed time series is assumed to be an autoregressive process. The location of the suspicious values is supposed to be known. We introduce conditional least squares estimators for the parameters. The estimates are shown to be strongly consistent. Using similar arguments as in the theory of linear models, we get a test statistic for the general linear hypothesis. Its asymptotic distribution is derived.