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Time series data abound and analysis of such data is challenging and potentially rewarding. One example is financial time series analysis. Most of the intelligent data analysis methods can be applied in principle, but evolutionary computing is becoming increasingly popular and powerful. In this paper we focus on one task of financial time series analysis - stock price forecasting based on historical data. The premise of this task is that the current price of a stock is dependent on the price of the same stock in the past. Here we consider an additional assumption, i.e., time dependency relevance, that the price in the nearer past is more relevant to the current price than that in the more distant past. This assumption appears intuitively sound, but needs formally validated. In this paper we set to test this assumption by introducing time weighting into similarity measures, as similarity is one of the key notions in time series analysis methods including evolutionary computing. We consider the generic neighborhood counting similarity as it can be specialized for various forms of data by defining the notion of neighborhood in a way that satisfies different requirements. We do so with a view to capturing time weights in time series. This results in a novel time weighted similarity for time series. A formula is also discovered for the similarity so that it can be computed efficiently. Experiments show that this similarity outperforms the standard Euclidean distance and a time weighted variant of it. We conclude that the time dependency relevance assumption is sound.