Abstract: Time series similarity search is of growing importance in many applications. Wavelet transforms are used as a dimensionality reduction technique to permit efficient similarity search over high-dimensional time series data. Proposed in this paper are the tight upper and lower bounds on the estimation distance using wavelet transform, and it is shown that the traditional distance estimation is only a part of the lower bound. According to the lower bound, more dissimilar time series can be excluded than the traditional method. And according to the upper bound, whether two time series are similar can be directily judged, and the number of time series to process in the original time domain can be further reduced. The experiments show that using the upper and lower tight bounds can significantly improve the filter efficiency and reduce the running time than the traditional method.