We consider the problem of nding 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 de ne beforehand which patterns are to be used; rather, we want the patterns to be formed from the data in the co...