Finding Patterns in Time Series

Abstract

Large datasets are often time series data, and such datasets present challenging problems that arise from the passage of time reflected in the datasets. A problem of current interest is clustering and classification of multiple time series. When various time series are fitted to models, the different time series can be grouped into clusters based on the fitted models. If there are different identifiable classes of time series, the fitted models can be used to classify new time series.

For massive time series datasets, any assumption of stationarity is not likely to be met. Any useful time series model that extends over a lengthy time period must either be very weak, that is, a model in which the signal-to-noise ratio is relatively small, or else must be very complex with many parameters. Hence, a common approach to model building in time series is to break the series into separate regimes and to identify an adequate local model within each regime. In this case, the problem of clustering or classification can be addressed by use of sequential patterns of the models for the separate regimes.

In this chapter, we discuss methods for identifying changepoints in a univariate time series. We will emphasize a technique called alternate trends smoothing.

After identification of changepoints, we briefly discuss the problem of defining patterns. The objectives of defining and identifying patterns are twofold: to cluster and/or to classify sets of time series, and to predict future values or trends in a time series.