Sector stock indices respond to oil price fluctuations with temporal heterogeneities based on their oil dependence and multiple transmission mechanisms. Additionally, such heterogeneities may not persist across time scales due to their inherent multiscale features. Aiming to explore the lead-lag effects among oil-stock nexuses at sectoral level and further identify the transmission path of oil price shocks to different stock sectors chronologically across time scales, we propose an integrated research framework combining the wavelet transform, cross correlation coefficients and the network analysis together. We take the Brent oil price and Morgan Stanley Capital International (MSCI) world sector stock indices (Materials, Industrials, Consumer Discretionary, Consumer Staples, Health Care, Financials, Telecommunications, Utilities, Transportation and Metals & Mining) from January 2000 to January 2016 as data samples. We find that the number of oil-stock nexuses involved in lead-lag effects and the maximum time lags grow as the length of the time horizon. Each sector may lead or lag behind other sectors in different frequencies to move with an oil price shock, but Transportation, Utilities and Consumer Discretionary are sectors have higher probability to lag behind other sectors, while Materials and Telecommunications are the sectors with higher possibility to lead other sectors. In addition, The oil-stock nexuses of Utilities, Telecommunication and Consumer Staples work as key points in the frequencies of 8, 64, and 128 days, whereas the Brent-Transportation nexus control more information in the frequency of 256 days. Finally, we infer that the complexity of the interaction between oil price and the stock market is triggered by different causes across time scales. In the short term, such complexity is caused by high fluctuations of the oil-stock nexuses happening simultaneously because there are fewer lead-lag relationships among nexuses. In the long term, the relationships of oil-stock nexuses are more stable, but the time lags among nexuses become longer, which could overlap the impacts of oil price from different time points.

部门股票指数基于其对石油的依赖和多种传导机制，对石油价格的波动具有时间异质性的响应。另外，由于其固有的多尺度特征，此类异质性可能不会在时间尺度上持续存在。为了探索部门层面石油库存关系之间的超前滞后效应，并进一步确定油价冲击在不同时间范围内按时间顺序传递给不同股票部门的路径，我们提出了一个综合的研究框架，该模型将小波变换，互相关系数和网络分析在一起。我们采用布伦特原油价格和摩根士丹利资本国际（MSCI）世界各行业的股票指数（材料，工业，全权委托消费者，主食，医疗保健，金融，电信，公用事业，数据样本为2000年1月至2016年1月的运输和金属与采矿）。我们发现，与铅滞后效应有关的石油库存关系的数量和最大时滞随着时间跨度的增加而增长。每个部门可能会以不同的频率领先或滞后于其他部门，以随石油价格的波动而变化，但是运输，公用事业和非必需消费品部门有较高的可能性落后于其他部门，而材料和电信是具有较高领导可能性的部门其他部门。此外，公用事业，电信和消费必需品的石油库存纽带在8天，64天和128天的频率中是关键点，而布伦特运输关系在256天的频率中控制着更多的信息。最后，我们推断，油价与股市之间相互作用的复杂性是由跨时间尺度的不同原因触发的。在短期内，这种复杂性是由同时发生的石油库存关系的高波动引起的，因为关系之间的超前-滞后关系较少。从长远来看，石油库存关系的关系更加稳定，但是关系之间的时间滞后变得更长，这可能与不同时间点的油价影响重叠。