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Mean reversion is an important property when constructing efficient contrarian strategies. Researchers observe that mean reversion has multiperiodical and asymmetric nature simultaneously in real market. To better utilize mean reversion and improve the existing online portfolio selection strategies, we propose a new online strategy named multiperiodical asymmetric mean reversion (MAMR). The MAMR strategy incorporates a multipiecewise loss function with the moving average method and then imitates the passive-aggressive algorithm. We further provide a solution via convex optimization. This strategy runs in linear time and thus is suitable for large-scale trading applications. Our empirical results testing six real market datasets show that this strategy can achieve better results in bearing higher transaction cost. [ABSTRACT FROM AUTHOR]