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An important investigation of time series involves searching for \movement" patterns, such as \going up" or \going down" or some combinations of them. Movement patterns can be in various scales: a large scale pattern may cover a long time period, while a small scale pattern usually covers a short time period. This paper considers such scale requirement. More speciically, a pattern is deened as a regular expression of letters, where each letter describes a movement direction and covers a speciied length of time (called pattern unit length). To nd if a time series (or a part of it) matches a pattern, the time series is rst partitioned into consecutive sub-series of the unit length, and for each sub-series, the direction of its best tting line is taken as the movement direction of the sub-series if the distance between the best tting line and the sub-series is within a speciied tolerance (tolerance requirement). A direct implementation of pattern search will undoubtedly yield poor performance if the number of time series or the length of them is large. This paper introduces a pre-computation and indexing method to facilitate fast evaluation of pattern queries in user-speciied scales. An eecient pre-computation algorithm is given to nd the movement directions for all the sub-series that satisfy the tolerance requirement. Bounding triangles are used to represent clusters of sub-series. Relational database is then used to store these bounding triangles and relational operations are employed to facilitate the evaluation of pattern queries. The paper also reports some experiments performed on a real-life data set to show the eeciency and the scalability of the algorithms. 1 Introduction Time series data are important for many application domains ranging from nancial to scientiic applications. For example, trading prices of a stock market can be interesting to a nancial application and temperatures of the Earth's atmosphere may be crucial in an Earth science application.

Supporting fast search in time series for movement patterns in multiple scales