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Dynamic time warping (DTW) is the most widely used method to evaluate the similarity between time series. However, the DTW distance only takes into account the difference in amplitude, but does not reflect the time distortion information between them. In this paper, we propose a novel time similarity metric, called the time distortion coefficient, based on the DTW warping path to quantify the time distortion between time series. It is able to characterize the type and degree of time distortion between two time series at each point. By summing the absolute values of the time distortion coefficients, the overall time distortion is introduced to quantify time distortion between two time series. For the Nearest Neighbor (NN) based time series classification, a fusional similarity measure combining the DTW distance and the overall time distortion measure is proposed, which is able to evaluate the similarity in both amplitude and time domains. The experimental results conducted on the UCR time series classification archive datasets demonstrate that the proposed fusional similarity measure can significantly improve the classification accuracy of the 1-NN classifier with only a small amount of additional computational cost compared to the DTW distance and other metrics. [ABSTRACT FROM AUTHOR]