Analysis of Financial Time Series, Third Edition

12.6 Missing Values and Outliers

In this section, we discuss MCMC methods for handling missing values and detecting additive outliers. Let be an observed time series. A data point yh is an additive outlier if

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where ω is the magnitude of the outlier and xt is an outlier-free time series. Examples of additive outliers include recording errors (e.g., typos and measurement errors). Outliers can seriously affect time series analysis because they may induce substantial biases in parameter estimation and lead to model misspecification.

Consider a time series xt and a fixed time index h. We can learn a lot about xh by treating it as a missing value. If the model of xt were known, then we could derive the conditional distribution of xh given the other values of the series. By comparing the observed value yh with the derived distribution of xh, we can determine whether yh can be classified as an additive outlier. Specifically, if yh is a value that is likely to occur under the derived distribution, then yh is not an additive outlier. However, if the chance to observe yh is very small under the derived distribution, then yh can be classified as an additive outlier. Therefore, detection of additive outliers and treatment of missing values in time series analysis are based on the same idea. ...