Abstract
In this paper, we employ the generalized autoregressive conditional heteroscedasticity-mixed data sampling (GARCH-MIDAS) framework to forecast the daily volatility of state-level stock returns in the United States (US) based on structurally decomposed four monthly oil shocks associated with oil supply, global economic activity, oil consumption and oil inventory. We find that over the daily period of (February) 1994 to (December) 2022 and various forecast horizons, in 46 out of the 50 states, the GARCH-MIDAS model with at least one oil shock can outperform the benchmark, i.e., the GARCH-MIDAS-Realized Volatility (RV), with 24 states depicting the importance of all the four shocks. In general, oil market-specific shocks, whether supply or demand, tend to matter more than a global economic impact driving the oil market in forecasting volatility of regional stock returns across with better forecasting performances related to states with higher CO2 emissions based on underlying energy consumption data. Our findings have important implications for investors and policymakers, with the observations for the former group depicted by an analysis of economic significance, i.e., utility gains.
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For instance, Dai and Tang (2024) recently show that the impact of oil supply shock on the systemic risk of stock markets is insignificant, while it is significant for demand shock. This is also reinforced by Hanif et al. (2024), where demand-related shocks have the most significant spillover effects on stock markets. However, Castro and Jiménez-Rodríguez (2024) highlight the role of an intervening variable, such as oil inventories, as a modifier of oil-specific demand shocks. The latter evidence further validates the consideration of additional oil shock variants in our paper beyond oil supply and demand shocks.
The corresponding results for the BRICS countries, i.e., Brazil, Russia, India, China and South Africa, as obtained by Salisu and Gupta (2021), were quite heterogeneous.
There exists a large literature involving the utilization of variants of the GARCH-MIDAS models to predict daily aggregate and industry-level stock returns volatility in the US (and internationally as well), and the reader is referred to Salisu et al. (2022, forthcoming) and Segnon et al. (2023) for detailed reviews. Some other studies (see, for example, Conrad et al. (2018), Borup and Jakobsen (2019), Conrad and Kleen (2020), and Yu et al. (2023) among others) provide empirical use of the multiplicative GARCH-MIDAS model.
Ghysels et al. (2019) compare the GARCH and realized volatility methodologies by producing multi-period-ahead forecasts and conclude that the MIDAS-based model yields the most precise forecasts of in-and out-of-sample volatility.
Oil Supply Shocks \(\left({u}_{oss}={q}_{t}-{\alpha }_{qp}{p}_{t}-{b}_{1}{\prime}{x}_{t-1}\right)\) measures the distortions/changes in the supply of oil; Economic Activity Shock \(\left({u}_{eas}={y}_{t}-{\alpha }_{yp}{p}_{t}-{b}_{2}{\prime}{x}_{t-1}\right)\) measures the distortions/changes in economic performance; Oil Consumption Demand Shock \(\left({u}_{\text{ocds}}={q}_{t}-{\beta }_{qy}{y}_{t}-{\beta }_{qp}{p}_{t}-\Delta {i}_{t}^{*}-{b}_{3}{\prime}{x}_{t-1}\right)\) measures the distortions/changes in the quantity of oil demanded for specific purpose(s)—consumption; and Oil Inventory Demand Shock \(\left({u}_{\text{oids}}=\Delta {i}_{t}^{*}-{\psi }_{1}^{*}{q}_{t}-{\psi }_{2}^{*}{y}_{t}-{\psi }_{3}^{*}{p}_{t}-{b}_{4}{\prime}{x}_{t-1}\right)\) measures the distortions/changes in the produced oil that is returned to inventory; where \({q}_{t}=100ln\left({Q}_{t}/{Q}_{t-1}\right)\) denotes the growth rate of oil production; \(\Delta {i}_{t}^{*}=100\left(\Delta {I}_{t}^{*}/{Q}_{t-1}\right)\) is the approximation of growth in consumption demand, where \(\Delta {I}_{t}^{*}={Q}_{t}^{S}-{Q}_{t}^{D}\), with \({Q}_{t}^{S}\) and \({Q}_{t}^{D}\) representing quantity supplied and demanded, respectively; \({y}_{t}\) is the cost of international ship** deflated by the US Consumer Price Index (CPI) and reported in deviations from a linear trend; \({p}_{t}\) is the log difference between the refiner acquisition cost of crude oil imports and the US CPI; \({x}_{t-1}\) are the lagged values of all the variables over the preceding two years (see, Baumeister and Hamilton (2019) for full details).
The data is downloadable from the internet page of Professor Christiane Baumeister at: https://sites.google.com/site/cjsbaumeister/research.
This is obtained from the two-parameter beta weighting scheme \({\phi }_{k}\left({\omega }_{1},{\omega }_{2}\right)={\left[k/\left(K+1\right)\right]}^{{\omega }_{1}-1}\times {\left[1-k/\left(K+1\right)\right]}^{{\omega }_{2}-1}/{\sum }_{j=1}^{K}{\left[j/\left(K+1\right)\right]}^{{\omega }_{1}-1}\times {\left[1-j/\left(K+1\right)\right]}^{{\omega }_{2}-1}\) by constraining \({\omega }_{1}\) to 1 and setting \(\omega ={\omega }_{2}\).
The economic conditions indexes (ECIs) of the 50 US states are based on the work of Baumeister et al. (2022). These authors derive the indexes from mixed-frequency Dynamic Factor Models (DFMs) with weekly, monthly, and quarterly variables that cover multiple dimensions of the aggregate and the state economies. Specifically, Baumeister et al. (2022) group variables into six broad categories: mobility measures, labor market indicators, real economic activity, expectations measures, financial indicators, and household indicators. Table 1 in their paper summarize the state-level data that they use in the construction of the ECIs, and also include information on the frequency, source, transformation, seasonal adjustment, and the start date of each underlying data series utilized in the construction of the indexes. While the same for the aggregate US, i.e., for the national ECI, can be found in Table 4 in the Appendix of the paper of Baumeister et al. (2022). The indexes are scaled to 4-quarter growth rates of US real GDP and normalized such that a value of zero indicates national long-run growth. Note that these indexes are weekly, but as we combine them with the monthly oil shocks, we conver them to monthly by taking weekly averages over a particular month. The data is available for download from: https://sites.google.com/view/weeklystateindexes/dashboard.
Our paper recognizes the concern that value-weighted portfolios, which are typical for constructing indices, might disproportionately reflect the performance of large, nationally operating firms, thereby potentially capturing national rather than local shocks. However, this approach is adopted not to overlook the influence of large firms but to ensure that our analysis mirrors the actual investment landscape where these firms play a significant role. It is important to acknowledge that even though large companies may operate nationally or even globally, their economic activities—including investment, employment, and production—can have pronounced impacts on the states where they are headquartered. These activities can influence local economies and, by extension, the state-level stock market indices. Hence, while national shocks undoubtedly affect these indices, the impacts of such shocks can still provide valuable insights into state-level market dynamics, particularly how local economies and stock markets respond to changes in the national economic environment.
In fact, we created five metrics of entropy-based networks of the long-term volatilities across the US states, with one each corresponding to the GARCH-MIDAS-RV and the GARCH-MIDAS with the four oil shocks. Based on the correlation matrices, we perform a singular value decomposition and compute the entropy as in Caraiani (2018). The computation is done using a sliding window with a size of one year such that we can obtain a time series of the networks. When we related the five networks to the daily Aruoba-Diebold-Scotti (ADS; Arouba et al. 2009) business conditions index (designed to track real business conditions at high observation frequency), using ordinary least square (OLS) regressions (over March 1995 to December 2022), with heteroskedasticity and autocorrelation corrected (HAC) standard errors (Newey and West 1987), we found that the responses (with p-values), due to RV, OSS, EAS, OCDS, OIDS-based network of volatility respectively, were: 0.2495 (0.1515), 0.4670 (0.0066), 0.7637 (0.0109), 0.3534 (0.1881), -0.3206 (0.0157). In other words, volatility networks due to positive supply and global economic activity shocks, resulting in an oil price increase, can be considered good news and increase the ADS, while an oil price rise due to an oil-inventory demand shock is bad news. Therefore, the associated volatility network reduces the ADS. Interestingly, the volatility network of oil-specific consumption demand shock has an insignificant impact, just like that of the RV, with the latter finding being in line with superior forecasting performances of the oil shocks-based GARCH-MIDAS models relative to the GARCH-MIDAs-RV. Note the ADS index is available for download from https://www.philadelphiafed.org/surveys-and-data/real-time-data-research/ads. Complete details of these results are available upon request from the authors.
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Acknowledgements
We would like to thank two anonymous referees for many helpful comments. However, any remaining errors are solely ours. The last author of the paper also thanks the support provided by a grant from the Ministry of Research, Innovation and Digitization, CNCS—UEFISCDI, Romania, project number PN-III-P1-1.1-TE-2021-1339, within PNCDI III.
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Salisu, A.A., Gupta, R., Cepni, O. et al. Oil shocks and state-level stock market volatility of the United States: a GARCH-MIDAS approach. Rev Quant Finan Acc (2024). https://doi.org/10.1007/s11156-024-01295-z
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DOI: https://doi.org/10.1007/s11156-024-01295-z