The Time–Frequency Relationship between Oil Price, Stock Returns and Exchange Rate

The concept of time scales is essential for modeling financial decisions. This paper investigates time–frequency relationships across time scales between stock market returns, crude oil prices and exchange rates by applying wavelet analysis technique over the period 1999 to 2021. We find evidence of several strong co-movements between oil price and stock market and between oil price and foreign exchange rate in India. Each of these associations is linked with some important macroeconomic events. This implies economic shocks in developed market have a spillover effect on Indian market. The phase relationships indicate stock returns are in phase with oil prices and exchange rates are in out of phase with oil prices. We find that the impact of volatility at lower scale has a short term effect on the variables. Further, the wavelet coherency at high scale has slower changes with long term effect on the relationship between the variables of our interest. These results are useful for investors aiming specific time horizon of their investment and preferences, for portfolio managers and in risk assessment. Understanding the leading and lagging relationships will also help in business cycle based investing by detecting the subsequent business cycle fluctuations and forecasting the trend.