Searching for Additive Outliers in Nonstationary Time Series*

Abstract

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.

Real exchange rate adjustment in European transition countries

“…Related, Franses and Haldrup (1994) and Perron and Rodríguez (2003) show failure to account for outliers biases tests against rejection of the unit-root null. Beyond these size and power issues, this paper addresses the fact that the specification must be appropriate to the data to reduce bias in key parameter estimates -in this paper, the real exchange rate's speed of adjustment.…”

“…As noted above, because of changes in exchange-rate regimes, financial or political crises, and the large structural changes they have had to make, some transition-country time series appear to show such shifts. Second, the sharp disturbances that have rocked many transition countries suggest using the model proposed by Perron and Rodríguez (2003) to test for unit-root in the presence of additive outliers; Zivot and Andrews (1992) models for unit-root tests are modified to allow for outliers detected by the Perron and Rodríguez (2003) procedure. Third, for comparison to panel tests on developed countries' real exchange rates, and in some cases developing countries real rates, this paper also uses panel unit-root tests based on SUR techniques.…”

A Note on the Vogelsang Test for Additive Outliers

“…Recently, Vogelsang (1999) suggested an iterative procedure for the detection of multiple additive outliers in integrated time series. However, the procedure appears to suffer from serious size distortions towards the finding of too many outliers as has been shown by Perron and Rodriguez (2003). In this note we prove the inconsistency of the test in each step of the iterative procedure and hence alternative routes need to be taken to detect outliers in nonstationary time series.…”

Why is Chinese provincial output diverging?

“…A t-value is calculated for an outlier at each time period and the maximum is taken. This value is then compared with a critical value to decide whether or not an outlier is present, see Perron and Rodríguez (2003) for a discussion.…”