Do all sectors respond to oil price shocks simultaneously?

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.