The oil price could exert asymmetric effects on the stock market. Does this effect persist in various time horizons? To answer this multiscale puzzle, we combine the wavelet transform and the vector auto-regression model to examine the dynamic relations between the oil price increase or decrease and stock returns at various time horizons. This paper finds evidence that for each time horizon, both the oil price increase and decrease have significant effects on the stock returns; in addition, the stock market has a reverse influence on the oil price. Further examination proves that the response amplitude of the stock market to the oil price changes ascends as the time horizon lengthens and the response direction varies across different time horizons. Moreover, compared with the exchange rate, the oil price changes could exert a greater effect on the stock market. Overall, based on the influence direction and the extent of the oil price increase and decrease vary with the time scale, there is no persistent asymmetric effect of the oil price on the stock market across time scales. However, the impacts in the longer time horizons deserve more attention from the policy-makers and investors. (C) 2015 Elsevier Ltd. All rights reserved.