Predicting multi-scale positive and negative stock market bubbles in a panel of G7 countries: The role of oil price uncertainty

Van Eyden, Reneé; Gupta, Rangan; Sheng, Xin; Nielsen, Joshua Article Predicting multi-scale positive and negative stock market bubbles in a panel of G7 countries: The role of oil price uncertainty Economies Provided in Cooperation with: MDPI – Multidisciplinary Digital Publishing Institute, Basel Suggested Citation: Van Eyden, Reneé; Gupta, Rangan; Sheng, Xin; Nielsen, Joshua (2025) : Predicting multi-scale positive and negative stock market bubbles in a panel of G7 countries: The role of oil price uncertainty, Economies, ISSN 2227-7099, MDPI, Basel, Vol. 13, Iss. 2, pp. 1-25, https://doi.org/10.3390/economies13020024 This Version is available at: https://hdl.handle.net/10419/329304 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ Academic Editor: Robert Czudaj Received: 22 November 2024 Revised: 7 January 2025 Accepted: 15 January 2025 Published: 22 January 2025 Citation: van Eyden, R., Gupta, R., Sheng, X., & Nielsen, J. (2025). Predicting Multi-Scale Positive and Negative Stock Market Bubbles in a Panel of G7 Countries: The Role of Oil Price Uncertainty. Economies,13(2), 24. https://doi.org/10.3390/ economies13020024 Copyright: © 2025 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/ licenses/by/4.0/). Article Predicting Multi-Scale Positive and Negative Stock Market Bubbles in a Panel of G7 Countries: The Role of Oil Price Uncertainty Reneé van Eyden 1,* , Rangan Gupta 1, Xin Sheng 2and Joshua Nielsen 3 1Department of Economics, University of Pretoria, Private Bag X20, Hatfield 0028, South Africa; [email protected] 2Lord Ashcroft International Business School, Anglia Ruskin University, Chelmsford CM1 1SQ, UK; [email protected] 3 Boulder Investment Technologies, Limited Liability Company, 1942 Broadway Suite 314C, Boulder, CO 80302, USA; [email protected] *Correspondence: r[email protected] Abstract: While there is a large body of literature on oil uncertainty-equity prices and/or returns nexus, an associated important question of how oil market uncertainty affects stock market bubbles remains unanswered. In this paper, we first use the Multi-Scale Log-Periodic Power Law Singularity Confidence Indicator (MS-LPPLS-CI) approach to detect both positive and negative bubbles in the short-, mediumand long-term stock markets of the G7 countries. While detecting major crashes and booms in the seven stock markets over the monthly period of February 1973 to May 2020, we also observe similar timing of strong (positive and negative) LPPLS-CIs across the G7, suggesting synchronized boom-bust cycles. Given this, we next apply dynamic heterogeneous coefficients panel databased regressions to analyze the predictive impact of a model-free robust metric of oil price uncertainty on the bubbles indicators. After controlling for the impacts of output growth, inflation, and monetary policy, we find that oil price uncertainty predicts a decrease in all the time scales and countries of the positive bubbles and increases strongly in the medium term for five countries (and weakly the short-term) negative LPPLS-CIs. The aggregate findings continue to hold with the inclusion of investor sentiment indicators. Our results have important implications for both investors and policymakers, as the higher (lower) oil price uncertainty can lead to a crash (recovery) in a bullish (bearish) market. Keywords: multi-scale bubbles; oil price uncertainty; panel data regressions; G7 stock markets JEL Classification: C22; C32; C33; G15; Q02 1. Introduction As pointed out by (Bernanke,1983) and (Pindyck,1991), investment under uncertainty and real options implies that high oil price uncertainty creates cyclical fluctuations in investment by lowering the firms’ incentive for current investment. This, in turn, affects cash flows generated by a firm and the discount rate used to calculate stock prices and, hence, negatively impacts stock prices and/or stock returns (Swaray & Salisu,2018;Chen & Demirer,2022). Moreover, since stock prices are the sum of discounted cash flows, including dividends, oil price uncertainty can adversely affect stock prices by decreasing the overall profit that a firm generally uses to pay dividends, with this resulting from the fact that firms need to bear additional costs to avoid risk associated with oil price uncertainty Economies 2025,13, 24 https://doi.org/10.3390/economies13020024 Economies 2025,13, 24 2 of 25 (Demirer et al.,2015). The theoretical prediction that oil price uncertainty negatively drives international stock prices and or/returns via the investment and dividends channels has been widely empirically evaluated (see, for example, Sadorsky,1999;Basher & Sadorsky, 2006;Masih et al.,2011;Alsalman,2016;Diaz et al.,2016;Bass,2017;Benavides et al.,2019; Rahman,2021). While existing studies tend to agree that oil uncertainty would adversely impact equity prices and/or returns, an important question would be how it affects stock market bubbles, i.e., its boom-bust cycles. Intuitively, if stock prices are accelerating away from their fundamental value, higher (lower) oil uncertainty is likely to lead to a burst of the bubble (further growth) in the market. While the decline in stock prices would continue in the wake of higher oil uncertainty, a rally could be witnessed when oil price uncertainty declines. Moreover, (Zhang & Wong,2023) pointed out that oil price uncertainty negatively impacts stock liquidity, which, in turn, is central to the efficient functioning of trade and investor confidence in the financial markets. Naturally, deteriorating (improving) investment confidence following higher (lower) oil uncertainty could also lead to a collapse (recovery) of the stock market (see Scherbina & Schlusche,2014) for detailed discussions of the theoretical models based on investor disagreement, feedback trading, and biased selfattribution, used to relate investor sentiment or confidence to bubbles). Understandably, with tremendous fluctuations in oil prices witnessed since the Global Financial Crisis, what we propose to investigate in this paper is pertinent from the perspective of not only investors but also policymakers, as bubbles are known to historically not only impact economic activity (Reinhart & Rogoff,2009;Jordàet al.,2015) but impact welfare also (Narayan et al.,2016). Against this backdrop, we aim to analyze the effect of a robust metric of oil uncertainty on stock market bubbles of the G7 countries (i.e., Canada, France, Germany, Italy, Japan, the United Kingdom (UK), and the United States (US)) over the monthly period of February 1973 to May 2020 in a panel data setting. The choice of the G7 is not only driven by the availability of data that allows us to cover nearly five decades of extreme movements in the stock markets of these developed economies but also due to the fact that the G7 bloc accounts for nearly two-thirds of global net wealth and nearly half of world output, and hence, dynamics of bubbles in these stock markets are likely to have worldwide spillover effects and impact the sustainability of the global financial system (Das et al.,2019). At the same time, the decision to rely on panel data regressions is motivated by the high degree of synchronization of the indicators of the bubbles of these countries, which we discuss in detail below. But even though we conduct the estimation in a panel setting, we allow for heterogeneous responses of bubbles to oil uncertainty (and other controls) by utilizing the Random Coefficients (RC) approach of (Swamy,1970) to derive both overall and country-specific results. As far as detecting bubbles, we not only use the Log-Periodic Power Law Singularity (LPPLS) model, originally developed by (Johansen et al.,1999,2000;Sornette,2003) for both positive (upward accelerating price followed by a crash) and negative (downward accelerating price followed by a rally) bubbles, but we also apply the Multi-Scale LPPLS Confidence Indicators (MS-LPPLS-CI) of (Demirer et al.,2019) to characterize positive and negative bubbles at different time scales, i.e., short-, mediumand long-term, corresponding to estimation windows associated with trading activities over one to three months, three months to a year, and one year to two years, respectively. Note that the identification of both positive and negative multi-scale bubbles is not possible based on other existing wide array of statistical tests (see Balcilar et al.,2016;Sornette et al.,2018) for detailed reviews), which points to the suitability and added value of our applied methodology. In fact, we consider this as important because it would allow us to gauge the possible asymmetric Economies 2025,13, 24 3 of 25 effect of oil uncertainty on the equity market bubbles of the G7, given that crash and recovery at different horizons can carry different information for market participants as suggested by the Heterogeneous Market Hypothesis (HMH; Müller et al.,1997). To the best of our knowledge, this is the first paper to analyze the effect of oil uncertainty on six indicators of multi-scale positive and negative bubbles in the G7 countries based on a heterogeneous coefficients panel data model. In the process, we add to the literature on oil price uncertainty and stock returns by now considering the effect of the former on the boom-bust cycles of the latter. In addition, our paper also aims to provide a new predictor to an already large set of factors identified as drivers of bubbles (see Sornette et al.,2018) for a detailed review), with us also controlling for some of the prominent variables in our analyses. The remainder of the paper is organized as follows: Section 2 discusses the data and the basics of the econometric model. Section 3presents the empirical findings involving the detection of bubbles, as well as the effects of investor sentiment on the six LPPLS-CIs of bubbles in the panel of G7 countries. Finally, Section 4concludes the paper. 2. Data and Econometric Model 2.1. Data We first obtain weekly bubble indicators, derived based on the natural logarithmic values of the daily dividend-price ratio of the seven countries, using the dividend and the stock price index series in their local currencies, obtained from Refinitiv Datastream. Appendix Aof the paper outlines the mathematical details of how the MS-LPPLS-CIs are obtained and closely follows the presentation of Demirer et al. (2019). The generated bubbles indicators cover the weekly period of the first week of January 1973 to the fourth week of May 2020. Since our controls, following Caraiani et al. (2023), namely, the macroeconomic variables, besides the indicator of oil uncertainty, are at a monthly frequency, to obtain a monthly value for each of the multi-scale confidence indicators, we take the average for each of the scales weekly values that fall within a given month. The evolution of the MS-LPPLS-CIs can be used to detect crashes and rallies in realtime. To this end, we plot the short-, medium-, and long-term indicators (green, purple, and red lines) while we show the log price-to-dividend ratio as a black line in Figure 1a. A larger LPPLS-CI value for a particular scale shows that the LPPLS signature is present for many of the fitting windows to which we calibrated the model, making it a more reliable bubble indicator. The key message conveyed by Figure 1a is that there are many peaks in the LPPLS-CIs preceding substantial shifts in the log price-to-dividend ratio. We note that the bubble indicators across the G7 countries, in general, display peaks in the periods corresponding to crashes and recoveries before and around the collapse of the Bretton Woods system in 1973, the “Black Monday” episode in 1987, the Asian Financial Crisis of 1997, the Dot-com bubble burst from 2000 to 2002, the Global Financial Crisis of 2007 to 2008, the European sovereign debt crisis from 2009 to 2012, the “Brexit” in 2016, and to some extent during the COVID-19 episode. In other words, the MS-LPPLS-CIs are capable of providing leading information on all the major episodes of booms and busts witnessed globally from 1973 to 2020. In general, smaller crashes or rallies can best be recovered using shorter time scales, while longer time scales help to detect larger crashes or rallies, with the short-term LPPLSCIs preceding the medium-term ones and the latter leading the long-run indicators, i.e., maturation of the bubble heading towards instability is present across several distinct time-scales. More importantly, we observe a similar timing of the strong (positive as well as negative) MS-LPPLS-CI values in the cross-section of G7 countries, in line with the intuition that boom and bust cycles of the seven developed equity markets often occur in Economies 2025,13, 24 4 of 25 tandem, motivating the need to use a panel-based approach to analyze the impact of oil price uncertainty on stock market bubbles. Economies 2025, 13, x FOR PEER REVIEW 4 of 25 time-scales. More importantly, we observe a similar timing of the strong (positive as well as negative) MS-LPPLS-CI values in the cross-section of G7 countries, in line with the intuition that boom and bust cycles of the seven developed equity markets often occur in tandem, motivating the need to use a panel-based approach to analyze the impact of oil price uncertainty on stock market bubbles. Economies 2025, 13, x FOR PEER REVIEW 4 of 25 time-scales. More importantly, we observe a similar timing of the strong (positive as well as negative) MS-LPPLS-CI values in the cross-section of G7 countries, in line with the intuition that boom and bust cycles of the seven developed equity markets often occur in tandem, motivating the need to use a panel-based approach to analyze the impact of oil price uncertainty on stock market bubbles. Figure 1. Cont. Economies 2025,13, 24 5 of 25 Economies 2025, 13, x FOR PEER REVIEW 5 of 25 Figure 1. Cont. Economies 2025,13, 24 6 of 25 Economies 2025, 13, x FOR PEER REVIEW 6 of 25 Figure 1. Cont. Economies 2025,13, 24 7 of 25 Economies 2025, 13, x FOR PEER REVIEW 7 of 25 (a) (b) Figure 1. (a) Monthly Multi-Scale LPPLS-CIs of the G7 Countries; (b) Model-Free Estimate of Oil Price Uncertainty. Next, we turn our attention to the main predictor, i.e., oil price uncertainty, depicted in Figure 1b. One must realize that uncertainty is a latent variable and needs to be measured. Given this, the majority of the studies mentioned in the introduction rely on univariate or bivariate Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models applied to the oil price returns to derive metrics of oil price uncertainty to relate to stock price and/or returns. In other words, GARCH-based oil price uncertainty is fully determined by changes in the level of oil price, and as a result, it is impossible to disentangle uncertainty about the oil price and changes in the oil price level (Jo, 2014). Given this, (Rahman, 2021) proposes a new measure of oil price uncertainty by utilizing Stochastic Volatility (SV) in a Structural Vector Autoregressive (SVAR) model (involving oil and stock prices and a monetary policy instrument). In this model, oil price uncertainty 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 1975 1980 1985 1990 1995 2000 2005 2010 2015 2020 Oil price uncertainty (opu) Figure 1. (a) Monthly Multi-Scale LPPLS-CIs of the G7 Countries; (b) Model-Free Estimate of Oil Price Uncertainty. Next, we turn our attention to the main predictor, i.e., oil price uncertainty, depicted in Figure 1b. One must realize that uncertainty is a latent variable and needs to be measured. Given this, the majority of the studies mentioned in the introduction rely on univariate or bivariate Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models applied to the oil price returns to derive metrics of oil price uncertainty to relate to stock price and/or returns. In other words, GARCH-based oil price uncertainty is fully determined by Economies 2025,13, 24 8 of 25 changes in the level of oil price, and as a result, it is impossible to disentangle uncertainty about the oil price and changes in the oil price level (Jo,2014). Given this, (Rahman,2021) proposes a new measure of oil price uncertainty by utilizing Stochastic Volatility (SV) in a Structural Vector Autoregressive (SVAR) model (involving oil and stock prices and a monetary policy instrument). In this model, oil price uncertainty is the conditional variance of the oil price change forecast error, and thus, it evolves independently of any change in the oil price level. 1 Despite the innovativeness of this approach over GARCH-based models in measuring oil price uncertainty, the metric is not free from the structure of any specific theoretical model. Given these empirical issues in constructing an appropriate metric of oil price uncertainty, (Nguyen et al.,2021) have proposed a novel construction of the oil price uncertainty index that is unconditional on a model. 2 These authors develop a measure of oil price uncertainty as the one-period-ahead forecast error variance of a forecasting regression with SV in the residual terms. The novelty of this construction approach lies in its flexibility in including a large number of additional information that is important in explaining fluctuations in oil prices, namely, exchange rate, oil production, global economic condition, and co-movement in the fuel market. In this sense, the index is able to capture uncertainty in oil prices rather than volatility as measured by both GARCH and SV models. According to Figure 1b, heightened oil price uncertainty coincides with the first and second oil crises of 1973 and 1979. These events are also associated with substantial positive and negative stock market bubbles across all G7 countries, as evident from Figure 1a. Following the oil crises of the 1970s, oil uncertainty peaked again during the first half of 1986, coinciding with a prolonged period of positive stock market bubbles across all G7 countries and at shortmediumand long-term time scales. A strong bull market overdue for a correction since 1982, exacerbated by heightened oil uncertainty, culminated in the Black Monday stock market crash of October 1987. Iraq’s invasion of Kuwait in 1990 had significant ramifications for global stock markets, leading to increased uncertainty and bearish sentiment. The invasion led to a sharp spike in oil prices and consequently increased inflation and reduced economic growth, typically negative for stock market performance. As with many geopolitical crises, investors pull out riskier assets like equities and move towards safer assets such as gold and government bonds. This effect shows up as positive asset bubbles, most notably in Germany and the US. The next episode of heightened oil market uncertainty started towards the end of 1998, with substantial positive stock market bubbles across all countries, but most pronounced for the US. The positive bubble indicators for the US remained high up to 2002, reflecting both the impact of the East-Asian crisis and the Dot-Com Bubble on global stock markets. Our model-free estimate of oil price uncertainty indicates another spike towards the end of 2008, further negatively contributing to the Global Financial Crisis. As is further evident from Figure 1b, the COVID-19 pandemic, which emerged at the end of 2019 and became a global health crisis in 2020, had profound effects on the global economy and various industries, with the oil and gas industries most severely impacted through a collapse in demand, storage issues and a price war between major oil producers in the OPEC+ group. The pandemic also accelerated discussions about the future of oil and the potential for a more rapid transition to renewable energy sources—leading to a significant increase of uncertainty in the oil market, driven by not only immediate demandside shocks but also longer-term considerations about the future of energy consumption. Although most countries in the sample register some positive bubble effects, positive bubbles are most noticeable in the case of the US. Regarding the macroeconomic control variables included in the analysis, we use month-on-month growth of industrial production, month-on-month Consumer Price Index (CPI)-based inflation rate, and change in the interest rate, with all transformations to the Economies 2025,13, 24 15 of 25 With oil price uncertainty showing up as having strong negative effects on positive bubbles compared to other traditional macroeconomic and financial indicators, it is recommended that investors and policymakers should be careful when the level of oil uncertainty tends to rise at the time the stock markets are booming because this could imply an imminent crash. At the same time, when stock prices are facing relatively less severe bearish regimes, higher oil price uncertainty can lead to deep equity market downturns. Accordingly, policymakers should monitor rising oil price uncertainty closely and implement expansionary monetary and fiscal policies to ensure the revival of the equity market (André et al.,2023), as directly controlling oil price uncertainty is likely to be difficult due to it being driven by oil market-specific shocks and geopolitical events (Qian et al.,2022). As part of future research, in light of the large literature on the relationship between oil price or returns and stock price or returns (see Degiannakis et al.,2018), and (Smyth & Narayan,2018) for comprehensive reviews), it would be interesting to consider the effect of oil prices on stock market bubbles. But realizing that oil prices are driven by various shocks namely, oil-supply, global economic activity, oil-specific consumption demand and inventory demand (Kilian,2009;Baumeister & Hamilton,2019), having different directional impacts on stock prices (Kilian & Park,2009), we will need to decompose oil price movements due to these innovations to detect the impact on bubbles in possibly a time series-based structural SVAR model, which will also allow us to distinguish between opposing effects of higher oil prices on stock markets for oil-exporting and importing countries (Wang et al.,2013). 10 At the same time, our current analysis can also be extended to emerging economies.11 Author Contributions: Panel data analysis and write-up of panel results, R.v.E.; Conceptualization of the research idea, write-up of background, theoretical background, and literature review, R.G.; Panel data analysis, X.S.; Estimation of bubbles indicators and write-up of relevant segments associated with bubbles estimations, J.N. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Informed Consent Statement: Not applicable. Data Availability Statement: Data will be made available upon request from the authors, as underlying data has been obtained from a subscription-based source. Computer codes are available at https://pypi.org/project/lppls/ (accessed on 17 September 2023). Conflicts of Interest: The authors declare that they have no competing interests. Appendix A. Estimating the Multi-Scale Log-Periodic Power Law Singularity (LPPLS) Model (Filimonov & Sornette,2013) developed a stable and robust calibration scheme for the following LPPLS model given by: ln E[p(t)] =A+B(tc−t)m+C(tc−t)mcosωln(tc−t)m−ϕ(A1) where parameter tc represents the critical time (the date of the termination of the bubble); A is the expected log value of the observed time series, i.e., the stock price-dividend ratio, at time tc ; B is the amplitude of the power law acceleration; and C is the relative magnitude of the log-periodic oscillations. The exponent of the power law growth is given by m , while ω and ϕrepresent the frequency of the log-periodic oscillations and a phase shift parameter, respectively We make use of this stable and robust calibration scheme, and following Filimonov and Sornette (2013), reformulate Equation (A1) to reduce the complexity of the calibration Economies 2025,13, 24 16 of 25 process by eliminating the nonlinear parameter ϕ and expanding the linear parameter C to C1=Ccos ϕand C2=Ccos ϕ. The new formulation can be written as ln E[p(t)] =A+B(f)+C1(g)+C2(h)(A2) where f=(tc−t)m g=(tc−t)mcos[ωln (tC−t)] h=(tc−t)msin[ωln(tc−t)] To estimate the three nonlinear parameters: {tc,m,ω} , and 4 linear parameters: {A,B,C1,C2} , we fit Equation (A2) to the log of the price-dividend ratio. This is done by using L2norm to obtain the following sum of squared residuals: F(tc,m,ω,A,B,C1,C2)= N ∑ i=1hln p(τi)−A−B(fi)−C1(gi)−C2(hi)i2(A3) Since the estimation of the three nonlinear parameters depends on the four linear parameters, we obtain the following cost function: F(tc,m,ω)=min A,B,C1,C2 F(tc,m,ω,A,B,C1,C2)=Ftc,m,ω,ˆ A,ˆ B,ˆ C1,ˆ C2(A4) Solving the optimization problem allows for the estimation of the four linear parameters: {ˆ A,ˆ B,ˆ C1,ˆ C2}=arg min A,B,C1,C2 F(tc,m,ω,A,B,C1,C2)(A5) which can be done analytically by solving the following matrix equation:      N∑fi∑gi∑hi ∑fi∑f2 i∑figi∑fihi ∑gi∑figi∑g2 i∑gihi ∑hi∑fihi∑gihi∑h2 i           ˆ A ˆ B ˆ C1 ˆ C2      =      ∑ln pi ∑filnpi ∑gilnpi ∑hilnpi      (A6) Next, the three nonlinear parameters can be determined by solving the following nonlinear optimization problem: {ˆ tc,ˆ m,ˆ ω}=arg min tc,m,ωF(tc,m,ω)(A7) We use the Sequential Least Squares Programming (SLSQP) search algorithm (Kraft, 1988) to find the best estimation of the three nonlinear parameters {tc,m,ω}. The LPPLS confidence indicator, introduced by Sornette et al. (2015), is used to measure the sensitivity of bubble patterns in each country’s log price-dividend ratio time series. The larger the LPPLS confidence indicator (CI), the more reliable the LPPLS bubble pattern and vice versa. It is calculated by calibrating the LPPLS model to shrinking time windows by shifting the initial observation t1 forward in time toward the final observation t2 with a step dt . For each LPPLS model fit, the estimated parameters are filtered against established thresholds, and the qualified fits are taken as a fraction of the total number of positive or negative fits. A positive fit has estimated B< 0, and a negative fit has estimated B>0. Economies 2025,13, 24 17 of 25 Following the work of (Demirer et al.,2019), we incorporate bubbles of varying multiple time scales into this analysis. We sample the time series in steps of 5 trading days. We create the nested windows [ t1 , t2 ] and iterate through each window in steps of 2 trading days. In this manner, we obtain a weekly resolution from which we construct the following indicators: • Short-term bubble: A number ∈[0, 1] which denotes the fraction of qualified fits for estimation windows of length dt : =t2−t1∈[30 : 90] trading days per t2 . This indicator comprises of (90 −30)/2 =30 fits. • Medium-term bubble: A number ∈[0, 1] which denotes the fraction of qualified fits for estimation windows of length dt : =t2−t1∈[30 : 90] trading days per t2 . This indicator comprises of (300 −90)/2 =105 fits. • Long-term bubble: A number ∈ [0, 1] which denotes the fraction of qualified fits for estimation windows of length dt : =t2−t1∈[30 : 90] trading days per t2 . This indicator comprises of (745 −300)/2 =223 fits. • Filter conditions: After calibrating the model, the following filter conditions are applied to determine which fits are qualified: m∈[0.01, 0.99] ω∈[2, 15] tc∈[max(t2−60, t2−0.5(t2−t1)),min(252, t2+0.5(t2−t1))] O>2.5 D>0.5 where, O=ω 2πlntc−t1 tc−t2 is the number of oscillations, and D=m|B| ω|C| captures the damping parameter required to ensure that the crash hazard rate, h(t), is non-negative. Appendix B. Random Coefficients (RC) Estimation Traditional fixedand random-effects models incorporate panel-specific heterogeneity by including a set of nuisance parameters that provide each panel with its own constant term. However, in these models, all panels share common slope parameters – a restriction that is often less desirable as changes in independent variables may exert a heterogeneous impact on the dependent variable in question. Random—coefficients (RC) models (Swamy, 1970) are more general, allowing each panel to have a vector of randomly drawn slopes from a distribution common to all panels. According to Poi (2003), the implementation of the RC estimator ensures the best linear unbiased predictors of the panel-specific draws from this distribution. Consider a general random-coefficients model, with y being the dependent variable and X being the predictor, of the form: yi=Xiβi+εi(A8) In the case of RC, each panel-specific βi is related to an underlying common parameter vector β: βi=β+vi(A9) where E{vi}= 0, Eviv′ i=Σ , Enviv′ jo= 0 for j=i , and Enviϵ′ jo= 0 for all i and j . Equations (A8) and (A9) may be combined to get: yi=Xi(β+vi)+εi=Xiβ+ui Economies 2025,13, 24 18 of 25 with ui≡Xivi+εi. Furthermore: Euiu′ i=En(Xivi+εi)(Xivi+εi)′o=XiΣX′ i+σii I≡Πi The Ppanels can be represented in stack format: y=Xβ+u(A10) where: Π≡Euiu′ i=       Π10 0Π2 · · · 0 · · · 0 . . .. . . 0 0 .... . . · · · ΠP       Estimating the parameters in Equation (A9) is a standard problem, which can be solved with generalized least squares (GLS): ˆ β=X′Π−1X−1X′Π−1y=∑iX′ iΠ−1 iXi−1∑iX′ iΠ−1 iyi=∑iWibi(A11) where Wi is the Generalized Least Squares (GLS) weight and bi=X′ iXi−1X′ iy . The resulting ˆ β for the overall (national) result is, therefore, a weighted average of the statespecific OLS estimates. For more details on ˆ β variance specification and GLS weight, refer to Poi (2003). To obtain the state-specific ˆ βi vectors, Judge et al. (1985) suggest that if attention is restricted to the class of estimators β* i for which Eβ* i βi=βi , then the state-specific OLS estimator bi is appropriate. Following Greene’s (1997) suggested method of obtaining the variance of ˆ βi , it follows that ˆ β is both consistent and efficient, and although inefficient, biis also a consistent estimator of β. Poi (2003) also suggests a test to determine whether the country-specific βi s are significantly different from one another. The null hypothesis is stated as: H0:β1=β2=· · · =βP(A12) and the test statistic is defined as: T≡∑P t=1bi−β†′nˆ σ−1 ii (XiXi)obi−β†(A13) where β†=n∑P t=1ˆ σ−1 ii (XiXi)o−1∑P t=1ˆ σ−1 ii (XiXi)bi. The test statistic Tis distributed as χ2with k(P−1)degrees of freedom. Economies 2025,13, 24 19 of 25 Appendix C. Additional Results Economies 2025, 13, x FOR PEER REVIEW 19 of 25 Appendix C. Additional Results Figure A1. Impulse response functions from a panel vector autoregressive model for negative and positive equity bubbles due to a one-unit shock to the model-free estimate of oil price uncertainty identified using Cholesky decomposition: February 1975 to May 2020. Note: The PVAR models of the G7 comprise of the variables in the following order: Oil price uncertainty (opu); industrial production growth (ip_growth); consumer price index inflation (infl); interest rate difference (ir_diff); long-term negative bubble (lt_neg) or medium-term negative bubble (mt_neg) or short-term negative bubble (st_neg) or long-term positive bubble (lt_pos) or medium-term positive bubble (mt_pos) or short-term positive bubble (st_pos), with the blue line showing the mean responses to a one unit shock to opu, along with the 95% confidence bands (red dotted lines). Table A1. Random coefficient estimation of contemporaneous effects for negative and positive equity bubbles due to a model-free estimate of oil price uncertainty: February 1975 to May 2020. (1) (2) (3) (4) (5) (6) lt_neg mt_neg st_neg lt_pos mt_pos st_pos l.lt_neg 0.678 *** (20.54) l.mt_neg 0.413 *** (14.79) Figure A1. Impulse response functions from a panel vector autoregressive model for negative and positive equity bubbles due to a one-unit shock to the model-free estimate of oil price uncertainty identified using Cholesky decomposition: February 1975 to May 2020. Note: The PVAR models of the G7 comprise of the variables in the following order: Oil price uncertainty (opu); industrial production growth (ip_growth); consumer price index inflation (infl); interest rate difference (ir_diff); long-term negative bubble (lt_neg) or medium-term negative bubble (mt_neg) or short-term negative bubble (st_neg) or long-term positive bubble (lt_pos) or medium-term positive bubble (mt_pos) or short-term positive bubble (st_pos), with the blue line showing the mean responses to a one unit shock to opu, along with the 95% confidence bands (red dotted lines). Economies 2025,13, 24 20 of 25 Table A1. Random coefficient estimation of contemporaneous effects for negative and positive equity bubbles due to a model-free estimate of oil price uncertainty: February 1975 to May 2020. (1) (2) (3) (4) (5) (6) lt_neg mt_neg st_neg lt_pos mt_pos st_pos l.lt_neg 0.678 *** (20.54) l.mt_neg 0.413 *** (14.79) l.st_neg 0.248 *** (8.42) l.lt_pos 0.775 *** (46.19) l.mt_pos 0.582 *** (17.55) l.st_pos 0.323 *** (16.82) oilunc 0.00549 0.00847 *** 0.00246 * −0.0140 *** −0.0106 *** −0.00514 *** (1.46) (4.08) (1.84) (−7.05) (−7.25) (−3.69) ip_growth −0.244 ** −0.164 *** 0.0436 −0.0445 0.122 *** 0.141 * (−2.42) (−8.29) (1.61) (−0.42) (3.26) (1.89) infl 0.418 ** −0.285 *** 0.0369 −0.861 * −0.696 *** −0.0167 (2.16) (−4.19) (0.36) (−1.86) (−3.35) (−0.09) ir_diff 0.000924 −0.000903 0.000470 0.000316 −0.000104 −0.00355 *** (0.91) (−0.73) (0.64) (0.32) (−0.06) (−3.09) constant −0.00155 −0.00161 0.00290 *** 0.0164 *** 0.0162 *** 0.0123 *** (−0.61) (−1.21) (3.08) (6.39) (11.16) (11.29) # observations 3808 3808 3808 3808 3808 3808 # groups 7 7 7 7 7 7 Test for par constancy,χ2112.70 60.96 54.60 44.60 66.14 35.38 d.o.f 36 36 36 36 36 36 Prob. 0.0000 0.0058 0.0241 0.1538 0.0016 0.4978 Note: l(one-month lag); Oil price uncertainty (opu); industrial production growth (ip_growth); consumer price index inflation (infl); interest rate difference (ir_diff); long-term negative bubble (lt_neg); medium-term negative bubble (mt_neg); short-term negative bubble (st_neg); long-term positive bubble (lt_pos); medium-term positive bubble (mt_pos); short-term positive bubble (st_pos); t-statistics (based on bootstrapped robust standard errors) in parentheses; * p< 0.10, ** p< 0.05, *** p< 0.01. Table A2. Random coefficient estimation predictive results for negative and positive equity bubbles due to nominal oil price returns: February 1973 to May 2020. (1) (2) (3) (4) (5) (6) lt_neg mt_neg st_neg lt_pos mt_pos st_pos l.lt_neg 0.658 *** (21.21) l.mt_neg 0.463 *** (13.80) l.st_neg 0.244 *** (8.41) l.lt_pos 0.779 *** (47.09) l.mt_pos 0.582 *** (17.40) l.st_pos 0.321 *** (16.47) Economies 2025,13, 24 21 of 25 Table A2. Cont. (1) (2) (3) (4) (5) (6) l.oil_returns −0.000106 −0.0000317 −0.00000734 −0.0000668 −0.00000533 −0.0000428 (−1.62) (−1.09) (−0.28) (−1.49) (−0.12) (−0.76) l.ip_growth −0.179 ** −0.0234 −0.0655 0.172 *** 0.167 ** 0.0565 (−2.08) (−0.37) (−1.04) (3.16) (2.40) (1.58) l.cpi_growth 0.371 0.226 0.387 *** −0.178 −0.951 *** −0.522 *** (1.19) (1.05) (4.53) (−0.42) (−2.94) (−3.85) l.ir_diff 0.00151 0.000351 0.00224 *** −0.00156 −0.00213 −0.00265 ** (1.13) (0.93) (5.63) (−1.31) (−1.44) (−2.24) constant 0.00257 *** 0.00398 *** 0.00454 *** 0.00555 *** 0.00893 *** 0.00934 *** (4.40) (7.44) (13.25) (4.71) (9.84) (26.01) # observations 3997 3997 3997 3997 3997 3997 # groups 777777 Test for par constancy,χ2102.76 70.23 533.72 40.66 76.26 35.94 d.o.f 36 36 36 36 36 36 Prob. 0.0000 0.0006 0.0290 0.2727 0.0001 0.4716 Note: l(one-month lag); Oil price returns (oil_returns); industrial production growth (ip_growth); consumer price index inflation (infl); interest rate difference (ir_diff); long-term negative bubble (lt_neg); medium-term negative bubble (mt_neg); short-term negative bubble (st_neg); long-term positive bubble (lt_pos); medium-term positive bubble (mt_pos); short-term positive bubble (st_pos)t-statistics (based on bootstrapped robust standard errors) in parentheses; ** p< 0.05, *** p< 0.01. Table A3. BRICS sample: Random coefficient estimation predictive results for negative and positive equity bubbles due to a model-free estimate of oil price uncertainty: February 1999 to May 2020. (1) (2) (3) (4) (5) (6) lt_neg mt_neg st_neg lt_pos mt_pos st_pos l.lt_neg 0.521 *** (7.75) l.mt_neg 0.450 *** (9.18) l.st_neg 0.230 *** (5.56) l.lt_pos 0.702 *** (23.08) l.mt_pos 0.502 *** (15.96) l.st_pos 0.245 *** (4.95) l.oilunc 0.0000485 0.00224 0.00158 −0.00280 −0.00145 −0.00165 (0.01) (0.82) (0.67) (−1.04) (−0.46) (−0.40) l.ip_growth −0.00940 0.0155 −0.0799 ** 0.0531 0.0433 0.0973 ** (−0.78) (0.73) (−2.06) (1.35) (1.05) (2.25) l.infl 0.0426 −0.108 −0.0883 0.0438 −0.231 −0.0682 (0.37) (−0.75) (−0.64) (0.27) (−0.71) (−0.42) l.ir_diff −0.00398 0.00134 * 0.00180 * 0.00570 0.00241 0.00177 (−1.27) (1.67) (1.69) (0.94) (0.97) (1.01) constant 0.00155 0.00206 0.00472 * 0.00616 ** 0.0105 *** 0.0108 *** (0.42) (0.74) (1.81) (2.37) (3.17) (2.73) # observations 1264 1264 1264 1264 1264 1264 # groups 555555 Test for par constancy 55.74 38.12 31.15 32.97 25.21 27.61 d.o.f 24 24 24 24 24 24 Prob. 0.0002 0.0337 0.1494 0.1047 0.3943 0.2767 Note: l(one-month lag); Oil price uncertainty (opu); industrial production growth (ip_growth); consumer price index inflation (infl); interest rate difference (ir_diff); long-term negative bubble (lt_neg); medium-term negative bubble (mt_neg); short-term negative bubble (st_neg); long-term positive bubble (lt_pos); medium-term positive bubble (mt_pos); short-term positive bubble (st_pos)t-statistics (based on bootstrapped robust standard errors) in parentheses; * p< 0.10, ** p< 0.05, *** p< 0.01. Economies 2025,13, 24 22 of 25 Table A4. BRICS sample: Random coefficient estimation predictive results for the country-specific impact of a model-free estimate of oil price uncertainty on negative and positive equity market bubbles: February 1999 to May 2020. (1) (2) (3) (4) (5) (6) lt_neg mt_neg st_neg lt_pos mt_pos st_pos Brazil l.opu 0.0023 0.0042 −0.0005 −0.0085 0.0037 −0.0023 (0.59) (0.66) (−0.09) (−0.80) (0.18) (−0.30) Russia l.opu −0.0028 0.0031 0.0016 0.0033 0.0020 −0.0088 (−0.60) (0.47) (0.31) (0.60) (0.18) (−1.19) India l.opu −0.0014 0.0008 0.0036 −0.00006 −0.0047 −0.0023 (−0.26) (0.09) (0.68) (−0.01) (−0.31) (−0.30) China l.opu −0.0093 * −0.0099 −0.0003 −0.0015 0.0035 0.0082 (−1.90) (−0.99) (−0.06) (−0.12) (0.25) (1.12) South Africa l.opu 0.0108 ** 0.0078 * 0.0040 −0.0154 −0.0129 −0.0032 (2.49) (1.63) (0.77) (−0.82) (−0.90) (−0.44) Note: l(one-month lag); Oil price uncertainty (opu); long-term negative bubble (lt_neg); medium-term negative bubble (mt_neg); short-term negative bubble (st_neg); long-term positive bubble (lt_pos); medium-term positive bubble (mt_pos); short-term positive bubble (st_pos)t-statistics in parentheses; * p< 0.10, ** p< 0.05. Notes 1 Using this framework, Rahman (2021) provides evidence that increased oil price uncertainty has a negative effect on (real) stock returns of the US. 2 The data for the oil uncertainty index can be obtained from the website of Dr. Bao H. Nguyen at: https://sites.google.com/site/ nguyenhoaibao/datasets/oil-market-uncertainty?authuser=0 (accessed on 23 August 2023). 3https://www.oecd.org/sdd/oecdmaineconomicindicatorsmei.htm (accessed on 23 August 2023). 4 The SSRs are derived from the website of Dr. Leo Krippner: https://www.ljkmfa.com/ (accessed on 23 August 2023) Note that the SSR estimates used in this paper are derived from the works of Krippner (2013,2015) due to their coverage involving the G7, besides being considered an improvement over those obtained by Wu and Xia (2016) (for the Euro area, the UK and the US), as discussed in detail by Krippner (2020). The SSR is based on models of the term structure, which essentially removes the effect that the option to invest in physical currency (at an interest rate of zero) has on yield curves, resulting in a hypothetical “shadow yield curve" that would exist if the physical currency were not available. The “shadow policy rate” generated in this manner, therefore, provides a measure of the monetary policy stance after the actual policy rate reaches zero. The main advantage of the SSR is that it is not constrained by the Zero Lower Bound (ZLB), and thus allows us to combine the data from the ZLB period with that of the non-ZLB era and, in turn to use it as the common metric of monetary policy stance across the conventional and unconventional monetary policy episodes. 5https://globalfinancialdata.com/ (accessed on 17 September 2023). 6 Note that the application of the Hausman (1978) test suggested that oil price uncertainty and the control variables are exogenous to the specification, with complete details of these results available upon request from negative and positive equity market bubbles across the three time scales presented in Table 1. The authors. Hence, in Table A1 in Appendix C, we depict the contemporaneous effects of all the predictors. 7 These results in terms of the sign are also confirmed, along with delayed significant effects, in Figure A1 in Appendix C, via impulse response functions, following an oil price uncertainty shock, identified using Cholesky decomposition, on six Panel VAR (PVAR) models with variables ordered as follows: opu, ip_growth, infl, ir_diff, and a specific MS-LPPLS-CI for the G7. 8These findings are consistent for contemporaneous opu, as reported in Table A1. 9All non-bootstrapped results are available from the authors upon request. 10 This line of reasoning is perhaps confirmed by our finding of insignificant predictive impacts of replacing oil price uncertainty in our model in Equation (1) with nominal WTI oil price returns on the MS-LPPLS-CIs, as reported in Table A2 in Appendix C. As initial analysis, we related the daily measure of crash risk, as given by the Chicago Board Options Exchange (CBOE)’s S&P 500 skewness index, with lagged oil-supply and demand as well as financial shocks based on a SVAR decomposition by Ready (2018), and found that skewness is only negatively impacted (with a coefficient of − 75.915) in a statistically significant manner (at the 5% level), i.e., the crash risk increases due to financial uncertainty over 2 January 1990 to 9 February 2024. This result was again confirmed when we used the lagged corporate earnings shock of Miescu and Mumtaz (2024), which is a proxy for positive financial shock, to obtain a statistically significant (at the 1% level) positive (with a coefficient of 0.311) relationship with skewness, i.e., increases in corporate earnings which signals reduction in financial uncertainty, reduces crash risk by increasing the skewness, over the period of 18 January 1990 to 16 October 2019. Economies 2025,13, 24 23 of 25 11 As a preliminary analysis, results are presented in Tables A3 and A4 in Appendix Cof the paper for the BRICS (Brazil, Russia, India, China and South Africa) countries. Table A3 contains the combined results, while Table A4 contains the country-specific results, focusing on the impact of lagged oil price uncertainty on positive and negative stock market bubbles at the shortmediumand long-term scales. As can be seen, unlike the case for the G7 countries, which presents with overall strong results for positive MS-LPPLS-CIs, we find no causal impact of oil price uncertainty on stock market bubbles in the short, medium or long term. Country-specific effects for the negative MS-LPPLS-CIs are also weak in the case of the BRICS countries, with only South Africa presenting a significant negative impact of lagged oil price uncertainty on negative stock market bubbles in the long and medium terms. The differences may be attributed to several economic, structural and institutional differences between the G7 and BRICS countries. BRICS countries, such as Russia and Brazil, are resource-dependent economies with a significant reliance on oil and commodity exports. This may make their stock markets more directly tied to oil price levels rather than uncertainty. Investors in these markets may have adjusted expectations to frequent oil price fluctuations, reducing the sensitivity of bubbles to uncertainty. G7 countries, on the other hand, are generally more diversified and less reliant on oil exports. Instead, oil price uncertainty acts as a broader economic risk factor, influencing investor behaviour and contributing to speculative bubbles in stock markets. Additionally, BRICS stock markets are less mature, while G7 markets are more institutionalized and more responsive to economic uncertainties. Oil price uncertainty can amplify risk aversion and speculation, fuelling bubbles. References Alsalman, Z. (2016). Oil price uncertainty and the U.S. stock market analysis based on a GARCH in mean VAR model. Energy Economics, 59, 251–260. [CrossRef] André, C., Caraiani, P., & Gupta, R. (2023). Fiscal policy and stock markets at the effective lower bound. Finance Research Letters,58, 104564. [CrossRef] Balcilar, M., Gupta, R., Jooste, C., & Wohar, M. E. (2016). Periodically collapsing bubbles in the South African stock market? Research in International Business and Finance,38, 191–201. [CrossRef] Basher, S. A., & Sadorsky, P. (2006). Oil price risk and emerging stock markets. Global Finance Journal,17(2), 224–251. [CrossRef] Bass, A. (2017). Does oil price uncertainty affect stock returns in Russia: A bivariate GARCH-in-mean approach. International Journal of Energy Economics and Policy,7(4), 224–230. Baumeister, C., & Hamilton, J. D. (2019). Structural interpretation of vector autoregressions with incomplete identification: Revisiting the role of oil supply and demand shocks. American Economic Review,109(5), 1873–1910. [CrossRef] Benavides, D. R., García, M. A. M., & Reyes, L. F. H. (2019). Uncertainty of the international oil price and stock returns in Mexico through an SVAR-MGARCH. Contaduría y Administración,64(3), 1–16. Bernanke, B. S. (1983). Irreversibility, uncertainty, and cyclical investment. Quarterly Journal of Economics,98(1), 85–106. [CrossRef] Caraiani, P., Gupta, R., Nel, J., & Nielsen, J. (2023). Monetary policy and bubbles in G7 economies using a panel VAR approach: Implications for sustainable development. Economic Analysis and Policy,78, 133–155. [CrossRef] Chen, C. -D., & Demirer, R. (2022). Oil beta uncertainty and global stock returns. Energy Economics,112, 106150. [CrossRef] Çepni, O., Gupta, R., & Ji, Q. (2023). Sentiment regimes and reaction of stock markets to conventional and unconventional monetary policies: Evidence from OECD countries. Journal of Behavioral Finance,24(3), 365–381. [CrossRef] Das, S., Demirer, R., Gupta, R., & Mangisa, S. (2019). The effect of global crises on stock market correlations: Evidence from scalar regressions via functional data analysis. Structural Change and Economic Dynamics,50(C), 132–147. [CrossRef] Degiannakis, S., Filis, G., & Arora, V. (2018). Oil prices and stock markets: A review of the theory and empirical evidence. The Energy Journal,39(5), 85–130. [CrossRef] Demirer, R., Demos, G., Gupta, R., & Sornette, D. (2019). On the predictability of stock market bubbles: Evidence from LPPLS confidence multi-scale indicators. Quantitative Finance,19(5), 843–858. [CrossRef] Demirer, R., Jategaonkar, S. P., & Khalifa, A. A. A. (2015). Oil price risk exposure and the cross-section of stock returns: The case of net exporting countries. Energy Economics,49, 132–140. [CrossRef] Diaz, E. M., Molero, J. C., & de Gracia, F. P. (2016). Oil price volatility and stock returns in the G7 economies. Energy Economics,54, 417–430. [CrossRef] Filimonov, V., & Sornette, D. (2013). A stable and robust calibration scheme of the log-periodic power law model. Physica A: Statistical Mechanics and Its Applications,392(17), 3698–3707. [CrossRef] Greene, W. H. (1997). Econometric analysis (3rd ed.). Prentice Hall. Hausman, J. A. (1978). Specification Tests in Econometrics. Econometrica,46(6), 1251–1271. [CrossRef] Im, K. S., Pesaran, M. H., & Shin, Y. (2003). Testing for unit roots in heterogeneous panels. Journal of Econometrics,115(1), 53–74. [CrossRef] Economies 2025,13, 24 24 of 25 Jo, S. (2014). The effects of oil price uncertainty on global real economic activity. Journal of Money, Credit and Banking,46(6), 1113–1135. [CrossRef] Johansen, A., Ledoit, O., & Sornette, D. (2000). Crashes as critical points. International Journal of Theoretical and Applied Finance,2, 219–255. [CrossRef] Johansen, A., Sornette, D., & Ledoit, O. (1999). Predicting financial crashes using discrete scale invariance. Journal of Risk,1(4), 5–32. [CrossRef] Jordà,Ò., Schularick, M., & Taylor, A. M. (2015). Leveraged bubbles. Journal of Monetary Economics,76, S1–S20. [CrossRef] Judge, G. G., Hill, R. C., Griffiths, W. E., Lütkepohl, H., & Lee, T. C. (1985). The theory and practice of econometrics (2nd ed.). John Wiley and Sons. Kilian, L. (2009). Not all oil price shocks are alike: Disentangling demand and supply shocks in the crude oil market. American Economic Review,99(3), 1053–1069. [CrossRef] Kilian, L., & Park, C. (2009). The impact of oil price shocks on the US stock market. International Economic Review,50(4), 1267–1287. [CrossRef] Kraft, D. (1988). A software package for sequential quadratic programming. Institut für Dynamik der Flugsysteme. Krippner, L. (2013). Measuring the stance of monetary policy in zero lower bound environments. Economics Letters,118, 135–138. [CrossRef] Krippner, L. (2015). Zero lower bound term structure modeling: A practitioner’s guide. Palgrave Macmillan. Krippner, L. (2020). A note of caution on shadow rate estimates. Journal of Money, Credit, and Banking,52(4), 951–962. [CrossRef] Masih, R., Peters, S., & de Mello, L. (2011). Oil price volatility and stock price fluctuations in an emerging market: Evidence from South Korea. Energy Economics,33(5), 975–986. [CrossRef] Miescu, M. S., & Mumtaz, H. (2024). Corporate earnings announcements and economic activity. International Economic Review,65(4), 1777–1793. [CrossRef] Müller, U. A., Dacorogna, M. M., Davé, R. D., Olsen, R. B., & Pictet, O. V. (1997). Volatilities of different time resolutions: Analyzing the dynamics of market components. Journal of Empirical Finance,4, 213–239. [CrossRef] Narayan, P. K., Sharma, S. S., & Phan, D. H. B. (2016). Asset price bubbles and economic welfare. International Review of Financial Analysis,44(C), 139–148. [CrossRef] Nguyen, B., Okimoto, T., & Tran, T. D. (2021). Uncertainty-dependent and sign-dependent effects of oil market shocks. Journal of Commodity Markets,26, 100207. [CrossRef] Pan, W. -F. (2020). Does sentiment drive stock market bubbles? Beware of excessive optimism! Journal of Behavioral Finance,21(1), 27–41. [CrossRef] Pindyck, R. (1991). Irreversibility, uncertainty, and investment. Journal of Economic Literature,29(3), 1110–1148. Poi, B. P. (2003). From the help desk: Swamy’s random coefficients model. The Stata Journal,3(3), 302–308. [CrossRef] Qian, L., Zeng, Q., & Li, T. (2022). Geopolitical risk and oil price volatility: Evidence from markov-switching model. International Review of Economics & Finance,81(C), 29–38. Rahman, S. (2021). Oil price volatility and the US stock market. Empirical Economics,61(3), 1461–1489. [CrossRef] Ready, R. C. (2018). Oil prices and the stock market. Review of Finance,22(1), 155–176. [CrossRef] Reinhart, C. M., & Rogoff, K. S. (2009). This time is different: Eight centuries of financial folly. Princeton University Press. Sadorsky, P. (1999). Oil price shocks and stock market activity. Energy Economics,21(5), 449–469. [CrossRef] Scherbina, A., & Schlusche, B. (2014). Asset price bubbles: A survey. Quantitative Finance,14(4), 589–604. [CrossRef] Smyth, R., & Narayan, P. K. (2018). What do we know about oil prices and stock returns? International Review of Financial Analysis, 57(C), 148–156. [CrossRef] Sornette, D. (2003). Why stock markets crash: Critical events in complex financial systems. Princeton University Press. Sornette, D., Cauwels, P., & Smilyanov, G. (2018). Can we use volatility to diagnose financial bubbles? Lessons from 40 historical bubbles. Quantitative Finance and Economics,2(1), 486–590. [CrossRef] Sornette, D., Demos, G., Zhang, Q., Cauwels, P., Filimonov, V., & Zhang, Q. (2015). Real-time prediction and post-mortem analysis of the Shanghai 2015 stock market bubble and crash. Journal of Investment Strategies,4, 77–95. [CrossRef] Swamy, P. A. V. (1970). Efficient inference in a random coefficient regression model. Econometrica,38, 311–323. [CrossRef] Swaray, R., & Salisu, A. A. (2018). A firm-level analysis of the upstream-downstream dichotomy in the oil-stock nexus. Global Finance Journal,37, 199–218. [CrossRef] Van Eyden, R., Gupta, R., Nielsen, J., & Bouri, E. (2023). Investor sentiment and multi-scale positive and negative stock market bubbles in a panel of G7 countries. Journal of Behavioral and Experimental Finance,38, 100804. [CrossRef] Wang, Y., Wu, C., & Yang, L. (2013). Oil price shocks and stock market activities: Evidence from oil-importing and oil-exporting countries. Journal of Comparative Economics,41(4), 1220–1239. [CrossRef]