Finding Outliers in Linear and Nonlinear Time Series [chapter]

Pedro Galeano, Daniel Peña
2013 Robustness and Complex Data Structures  
Outliers, or discordant observations, can have a strong effect on the model building process for a given time series. First, outliers introduce bias in the model parameter estimates, and then, distort the power of statistical tests based on biased estimates. Second, outliers may increase the confidence intervals for the model parameters. Third, as a consequence of the previous points, outliers strongly influence predictions. There are two main alternatives to analyze and treat outliers in time
more » ... eries. First, robust procedures can be applied to obtain parameter estimates not affected by the presence of outliers. These robust estimates are then used to identify outliers by using the residuals of the fit. Second, diagnostic methods are useful to detect the presence of outliers by analyzing the residuals of the model fit through iterative testing procedures. Once the outliers have been found, their effects are jointly estimated with the model parameters, obtaining, as a by-product, robust model parameter estimates. In this paper we focus on diagnostic methods and refer to Chap. 8 of Maronna et al. (2006) for a detailed review of robust procedures for ARMA models and Muler and Yohai (2008) and Muler et al. (2009) for two recent references. For linear models, Fox (1972) introduced additive outliers (AO), which affect a single observation, and innovative outliers (IO), which affect a single innovation, and proposed the use of likelihood ratio test statistics for testing for outliers in autoregressive models. Tsay (1986) proposed an iterative procedure to identify outliers, to remove their effects, and to specify a tentative model for the underlying process. Chang et al. (1988) derived likelihood ratio criteria for testing the existence of outliers of both types and criteria for distinguishing between them and proposed
doi:10.1007/978-3-642-35494-6_15 fatcat:326o4gghmvbhzbz2fdex7s6pmm