This is an advance summary of a forthcoming article in the Oxford Research Encyclopedia of Economics and Finance. Please check back later for the full article.
Detection of outliers is an important explorative step in empirical analysis. Once detected, the investigator will have to decide how to model the outliers depending on the context. Indeed, the outliers may represent noisy observations that are best left out of the analysis or they may be very informative observations that would have a particularly important role in the analysis. For regression analysis in time series a number of outlier algorithms are available, including impulse indicator saturation and methods from robust statistics. The algorithms are complex and their statistical properties are not fully understood. Extensive simulation studies have been made, but the formal theory is lacking. Some progress has been made toward an asymptotic theory of the algorithms. A number of asymptotic results are already available building on empirical process theory.