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SEARCHING FOR ADDITIVE OUTLIERS IN NONSTATIONARY TIME SERIES*
Author(s) -
Perron Pierre,
Rodríguez Gabriel
Publication year - 2003
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 - 10.1111/1467-9892.00303
Subject(s) - outlier , unit root , robustness (evolution) , mathematics , series (stratigraphy) , null hypothesis , statistical hypothesis testing , anomaly detection , statistics , sample size determination , time series , iterative method , econometrics , algorithm , computer science , data mining , paleontology , biochemistry , chemistry , biology , gene
. Recently, Vogelsang (1999) proposed a method to detect outliers which explicitly imposes the null hypothesis of a unit root. It works in an iterative fashion to select multiple outlier in a given series. We show, via simulations, that, under the null hypothesis of no outliers, it has the right size in finite samples to detect a single outlier but, when applied in an iterative fashion to select multiple outliers, it exhibits severe size distortions towards finding an excessive number of outliers. We show that his iterative method is incorrect and derive the appropriate limiting distribution of the test at each step of the search. Whether corrected or not, we also show that the outliers need to be very large for the method to have any decent power. We propose an alternative method based on first‐differenced data that has considerably more power. We also show that our method to identify outliers leads to unit root tests with more accurate finite sample size and robustness to departures from a unit root. The issues are illustrated using two US/Finland real‐exchange rate series.