Rule Discovery from Time Series

We consider the problem of finding rules relating patterns in a time series to other patterns in that series, or patterns in one series to patterns in another series. A simple example is a rule such as "a period of low telephone call activity is usually followed by a sharp rise in call volume". Examples of rules relating two or more time series are "if the Microsoft stock price goes up and Intel falls, then IBM goes up the next day," and "if Microsoft goes up strongly for one day, then declines strongly on the next day, and on the same days Intel stays about level, then IBM stays about level." Our emphasis is in the discovery of local patterns in multivariate time series, in contrast to traditional time series analysis which largely focuses on global models. Thus, we search for rules whose conditions refer to patterns in time series. However, we do not want to define beforehand which patterns are to be used; rather, we want the patterns to be formed from the data in the context of rule discovery. We describe adaptive methods for finding rules of the above type from time-series data. The methods are based on discretizing the sequence by methods resembling vector quantization. We first form subsequences by sliding a window through the time series, and then cluster these subsequences by using a suitable measure of time-series similarity. The discretized version of the time series is obtained by taking the cluster identifiers corresponding to the subsequence. Once the time-series is discretized, we use simple rule finding methods to obtain rules from the sequence. We present empirical results on the behavior of the method.