Abstract
Through Monte Carlo simulations, we explore the size, power and probability of making a type II error for a linear model with an exogenous regressor and ARCH or GARCH volatility. We estimate and compare the results for OLS with OLS standard errors, OLS with White’s standard errors, and maximum-likelihood estimation (MLE). We find that for small samples, all estimation methods have higher frequencies of type II errors and lower power than the nominal test size suggests. In addition, we find that White’s standard errors are an improvement over OLS, but the improvement is much smaller than one might expect, especially when compared to MLE. Increasing the sample size decreases the frequency of type II errors for all methods, but the rate of convergence to the nominal test size is much faster for MLE than the other two methods. Using empirical data from Jan 1986 to November 2021, we show that researchers are more likely to find a statistically significant impact of changes in oil prices on U.S. stock returns if they account for time-varying volatility. Our results have important practical implications and will help in resolving previous inconsistencies in the literature.
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The datasets analyzed during the current study are available from the corresponding author on request
Notes
Smyth and Narayan (2018) provide a comprehensive survey of literature on studies using both linear and non-linear time-series models to explore the relationship between oil prices and stock prices.
It may be important to note that we are not making any judgements regarding these authors using robust standard errors, or claim that their findings are related to time-varying volatility. We are simply using their work to highlight the currently accepted use of White’s correction matrix, showing that the question raised in this paper is currently relevant.
We get very similar results when we set \(\beta _1=0\), although we do not report these results for brevity.
In a related paper, Saha (2022) examines the impact of changes in oil prices on stock prices using country and sectoral level data incorporating linear and non-linear models.
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The authors have no relevant financial or non-financial interests to disclose. The authors have no competing interests to declare that are relevant to the content of this article. However, the second author currently serves on the editorial board of the Journal of Economics and Finance. All authors certify that they have no affiliations with or involvement in any organization or entity with any financial interest or non-financial interest in the subject matter or materials discussed in this manuscript. The authors have no financial or proprietary interests in any material discussed in this article
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Herb, P., Malik, F. Re-examining the impact of oil prices on stock returns in the presence of time-varying volatility. J Econ Finan 47, 815–843 (2023). https://doi.org/10.1007/s12197-023-09638-7
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DOI: https://doi.org/10.1007/s12197-023-09638-7