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In this paper, an evolving least squares support vector machine (LSSVM) learning paradigm with a mixed kernel is proposed to explore stock market trends. In the proposed learning paradigm, a genetic algorithm (GA), one of the most popular evolutionary algorithms (EAs), is first used to select input features for LSSVM learning, i.e., evolution of input features. Then, another GA is used for parameters optimization of LSSVM, i.e., evolution of algorithmic parameters. Finally, the evolving LSSVM learning paradigm with best feature subset, optimal parameters, and a mixed kernel is used to predict stock market movement direction in terms of historical data series. For illustration and evaluation purposes, three important stock indices, S&P 500 Index, Dow Jones Industrial Average (DJIA) Index, and New York Stock Exchange (NYSE) Index, are used as testing targets. Experimental results obtained reveal that the proposed evolving LSSVM can produce some forecasting models that are easier to be interpreted by using a small number of predictive features and are more efficient than other parameter optimization methods. Furthermore, the produced forecasting model can significantly outperform other forecasting models listed in this paper in terms of the hit ratio. These findings imply that the proposed evolving LSSVM learning paradigm can be used as a promising approach to stock market tendency exploration.