Nonparametric and semiparametric outlier detection and quality control in seasonal time series data
LE3 .A278 2016
Master of Science
Mathematics and Statistics
Mathematics & Statistics
Outliers in time series data can indicate a wide variety of issues or interesting features. Most types of outlier have been well discussed in the statistics literature, however collective outliers or discords tend to have been overlooked. Collective outliers only occur in periodic data where there is a repeating or \seasonal" pattern. They are characterized by an abnormal pattern for a particular period or periods. Often in these cases, the individual observations in the anomalous data are not unusual on their own and thus may not be detectable using traditional outlier detection methods, however their unusual seasonal pattern may still be of concern. Existing discord detection algorithms have primarily come from the data mining literature, and have involved searching for the most unusual sequence/period within the data, for example using distance measures. One issue with these methods is that they don't allow for inference. In this thesis we introduce a method of testing for a discord, which doesn't rely on assumptions about the distribution of the data. Furthermore, we use the quality control framework to show how collective outliers can be detected in real-time, using sieve bootstrap sampling.
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