Essays on outlier and break detection

Thesis

The study of outliers and structural breaks in econometric models is crucial because of their potential to distort statistical inference, model selection, and forecasting. This thesis investigates algorithms that are used in applied research to detect outliers and structural breaks in econometric models. It is organised into two parts.

The first part considers outlier detection algorithms in two-stage least squares regression models for cross-sectional data. These algorithms classify observations with standardised residuals beyond a certain cut-off value as outliers and re-estimate the model using the remaining observations. Chapter 1 analyses the false outlier detection rate of these algorithms under the null hypothesis of no outliers in the data, providing an asymptotic theory for the share and number of falsely detected outliers in the sample. These theoretical insights provide guidance on how to set the cut-off value.

Chapter 2 builds on the results of Chapter 1 by proposing statistical tests for the presence of outliers in the sample, whose asymptotic distribution is derived under the additional assumption of normally distributed errors for the non-outlying observations. Monte Carlo simulations assess and compare the performance of the different tests, showing that the size can be well controlled and that the power of the tests increases both in the outlier frequency and outlier magnitude. The methods and tests analysed in Chapters 1 and 2 are implemented in the R package robust2sls, providing a useful tool for empirical researchers.

The second part shifts focus to time series regression models estimated by ordinary least squares, examining the performance of super saturation, a method that is used to detect both outliers and location shifts. Chapter 3 uses Monte Carlo simulations to assess the performance of this method, offering recommendations for setting its tuning parameters to reach high detection rates of outliers and location shifts while limiting the risk of spurious discoveries.

Overall, this thesis advances the field by providing new theoretical and practical insights into outlier and break detection, both for cross-sectional and time series econometric models.

Authors: Kurle, JK

• DOI: 10.5287/ora-2nxp8rn7r
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: outlier robustness; two-stage least-squares; structural break; Monte Carlo simulation; outlier; outlier testing; super saturation; location shift; indicator saturation; instrumental variables regression
• Subjects: Econometrics; Econometrics--Computer programs; Econometrics--Asymptotic theory; Economics