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This article focuses on a new characteristic quantity, "similarity distance", which is defined for a pair of time series data and reflects similarity between them. This characteristic quantity is defined with the help of a smooth approximating function, which is obtained by "WISAM (Wavelet Interpolation Method with Simulated Annealing)" developed by Mori (1999) and Mori and Misawa (2001). Afterwards, as an illustrated example of the usage of similarity distance together with WISAM, the classifications and similarity of the annual GDP data for ten regions in Japan are investigated.