Previous studies prove that the oil price driven by different factors could exert diverse impacts on the stock market. Moreover, the oil price and stock indices as well as their interaction are characterized by the multiscale features since there are multiple stakeholders associating with different objectives rooting in various time horizons. However, existing studies consider the impacts of different oil prices on the stock market only in the holistic time horizon, which only could offer a limited picture concerning the interaction between the international oil market and the global stock market. Therefore, in this paper the impact of the oil price shocks driven by the oil supply and demand under various time horizons is explored. A combined research framework involving the wavelet transform and the Vector Auto-regress model is proposed. Brent oil price is chosen to represent changes of the international oil market since that 50% of the world oil trade is based it, when the Morgan Stanley Capital International world index is used to reflect the changes of the global stock market. The global oil production and the oil consumption of the OECD (Organization for Economic Co-operation and Development) countries are taken as proxies for the oil supply and demand. All data sets are sampled from February 1998 to December 2015 in monthly frequency. During the empirical processes, the Brent oil price and the world stock index are decomposed into 6 time scales, then the oil price changes driven by the oil supply and demand at each time scale are identified based on their dynamic correlation obtained through the wavelet coherence, and whether different oil prices could influence the global stock market or not and the features of the impact of oil prices in terms of the direction, amplitude, and duration are examined. The results show that both oil price changes driven by the supply and demand could exert significant influence on the stock market in short, medium and long time horizons, but the oil price driven by the demand could not cause the changes of the stock market in ultra-short and ultra-long time scales. Concerning the influence direction of the oil prices, the stock market responds to both types of oil price changes with random direction in short and medium terms, while the stock market has positive changes in the long term. When it comes to the duration of the impact of the oil prices, it is found that the lasting time become longer from 20 months in the short term to over 60 months in the long term with the increase of the time scales. In term of the amplitude of the influences of oil prices, the amplitudes in the short and medium terms are at least 60% stronger than that in the long term. According to above results, it is infered that the influences of the oil price changes transmit to the stock market with different channels. In the short term, the information spilling over between the oil market and the stock market relates two markets. In the medium term, the oil price changes could change the cost or benefit of the production entities and further change their performance in the stock market. In the long term, the oil price changes could redistribute the international wealth and lead more capital into the stock market, which may boom the stock market. Hence, it is necessary for the policy makers and investors to make specific decision refer to different time horizons and stock market shocks caused by different oil price types. In this paper, the multiscale features of the financial time series and the differences caused by different oil price shock types are considered simultaneously. The impacts of the oil price driven by the oil supply and demand are compared in 6 time scales. There are obvious differences and similarities across different time scales, which offer more detailed observation and forward one more step concerning the interaction between the oil market and the stock market.
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