Lag effect of market switching in oil price volatility forecasting

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Abstract
Stock market volatility is commonly used to study economic fluctuations, and volatility in the crude oil market is widely known to have significant effects on the stock market. Using the Standard & Poor's 500 (S&P 500) index and West Texas Intermediate (WTI) crude oil futures from 1990 to 2022, this study investigates the effect of stock market volatility on forecasts of oil market volatility. Moreover, we use a buffered autoregressive (BAR) model to capture the nonlinear threshold effect of stock market fluctuations and investigate the lag effect of market switching. The BAR model is shown to be superior to threshold autoregressive (TAR) and linear models in both in-sample and out-of-sample forecasting in the empirical analysis. This suggests that the threshold effect of the stock market is valuable for forecasting oil volatility and that the lag effect of market switching (the hysteresis effect) indeed exists in this real-world oil market. A likelihood ratio test for the hysteresis effect is proposed, and the asymptotic distribution of the test statistic is derived. We also demonstrate the stability of the BAR model by setting different lag orders. This study can help investors and institutions develop sound investment strategies and formulate effective policies.

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