Outlier Detection Algorithms for Least Squares Time Series Regression

40 Pages Posted: 16 Oct 2014

See all articles by Soren Johansen

Soren Johansen

University of Copenhagen - Department of Economics; Aarhus University - CREATES

Bent Nielsen

University of Oxford - Department of Economics

Date Written: September 8, 2014

Abstract

We review recent asymptotic results on some robust methods for multiple regression. The regressors include stationary and non-stationary time series as well as polynomial terms. The methods include the Huber-skip M-estimator, 1-step Huber-skip M-estimators, in particular the Impulse Indicator Saturation, iterated 1-step Huber-skip M-estimators and the Forward Search. These methods classify observations as outliers or not. From the asymptotic results we establish a new asymptotic theory for the gauge of these methods, which is the expected frequency of falsely detected outliers. The asymptotic theory involves normal distribution results and Poisson distribution results. The theory is applied to a time series data set.

Keywords: Huber-skip M-estimators, 1-step Huber-skip M-estimators, iteration, Forward Search, Impulse Indicator Saturation, Robustified Least Squares, weighted and marked empirical processes, iterated martingale inequality, gauge

JEL Classification: C22, C52

Suggested Citation

Johansen, Soren and Nielsen, Bent, Outlier Detection Algorithms for Least Squares Time Series Regression (September 8, 2014). Available at SSRN: https://ssrn.com/abstract=2510281 or http://dx.doi.org/10.2139/ssrn.2510281

Soren Johansen (Contact Author)

University of Copenhagen - Department of Economics ( email )

Ă˜ster Farimagsgade 5
Bygning 26
1353 Copenhagen K.
Denmark

Aarhus University - CREATES ( email )

Nordre Ringgade 1
Aarhus, DK-8000
Denmark

Bent Nielsen

University of Oxford - Department of Economics ( email )

Manor Road Building
Manor Road
Oxford, OX1 3BJ
United Kingdom

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