Our dataset is at the daily frequency, covering the indices of green bonds, clean energy stocks, Arca technology 100, S&P 500, Brent crude oil prices, S&P 500 composite index, and Eurostoxx 50. Price data are extracted from the DataStream of Refinitiv. The sample period is December 1, 2008—October 8, 2020, as depicted by data availability. All series are transformed to log-returns multiplied by 100, yielding 3,084 daily return observations for each index. The Appendix Figure 1 plots the time evolution of levels and log returns of the six indices.

The summary statistics of daily returns are shown in Table 1. Arca technology 100 index offers the highest average return, followed by the S&P 500. Crude oil returns exhibit a negative average return and the highest standard deviation. Conversely, green bonds have the lowest standard deviation. The returns of all indices are negatively skewed, except green bonds. There is evidence of excess kurtosis in all indices. The Jarque-Bera statistics show a departure from the Gaussian distribution for all return series. Evidence from the Augmented Dickey-Fuller (ADF) test (Dickey and Fuller, 1979) points toward the stationarity of all return series. Conditional heteroscedasticity is significant as indicated by the results of the ARCH-LM test. Pairwise correlations across the returns of the six indices (Table 2) are all positive, ranging between 0.1888 (green bonds and crude oil), and 0.9458 (Arca technology 100 and S&P 500). Notably, the correlations between green bonds and the other indices are the weakest.

The dynamic equicorrelation (DECO) model is used to study market integration among the various indices under study. This model proposed by Engle and Kelly (2012) is known for its efficiency in estimating covariance matrices without the numerical problems often encountered in other multivariate GARCH models (e.g., DCC and BEKK models).

Assume that r t is a 6 × 1 vector of asset returns such as: r t | I t − 1 ∼ N ( 0 , H t ) (1)

The conditional covariance matrix H t is decomposed in line with Engle (2002) as: H t = D t R t D t (2) ε t = H t 1 / 2 z t (3) R t = [ d i a g ( Q t ) − 1 / 2 ] Q t [ d i a g ( Q t ) − 1 / 2 ] (4) where the diagonal matrix ( D t ) contains the conditional standard deviations from the univariate GARCH model (See Eq. 5), R t denotes the time-varying conditional correlation matrix, ε t is a n × 1 vector of residuals conditional on the information set at time t-1, z t represents a n × 1 i.i.d. vector of standardized residuals, and Q t is the conditional correlation matrix of standardized residuals. We derive the elements of H t from the univariate GARCH (1,1) model: h i , t = ω i + α i ε i , t − 1 2 + β i h i , t − 1 (5) where h i , t is the conditional variance of the return series, ω i is a constant term, α i and β i measure the ARCH effect and the persistence of the volatility process, respectively. To make sure of the positivity and stability of the process of conditional variances, we set the following constraints: α i > 0 and α i + β i < 1 .

After estimating the univariate GARCH process in Eq. 5, we use the standardized residuals z t to estimate the conditional correlation parameters. We express the dynamics of Q in the DCC process as: Q t = ( 1 − θ 1 − θ 2 ) Q ¯ + θ 1 z t − 1 z t − 1 ′ + θ 2 Q t − 1 (6) where θ 1 , θ 2 and ϕ are parameter matrices, η t = I ( z t < 0 ) ∘ z t represents an indicator function that takes the value of 1 if the argument is true and 0 otherwise, and " ∘ " denotes the Hadamard product. Q ¯ j = E [ z t , z t ′ ] and N ¯ j = E [ η t , η t ′ ] are the unconditional correlation matrices of z t and η t , respectively. We express the time-varying correlation matrix as: R t = Q t ∗ − 1 Q t Q t ∗ − 1 (7) where Q t ∗ denotes a diagonal matrix with a square root of the i t h diagonal of Q t in its i t h diagonal position.

To estimate the DCC process of Engle (2002), first we fit univariate GARCH models for each return series. Then, we compute conditional correlation dynamics. However, as the number of series under study increases, it becomes difficult to estimate Eq. 6. Therefore, Engle and Kelly (2012) suggest the DECO model that assumes that the correlation across all return series is the same at any given time but varies over time. In fact, the DECO model simplifies the estimation process by reducing it to two equicorrelation parameters, α and β. It follows that the unconditional correlation matrix is: R t = ( 1 ρ ¯ t ⋯ ρ ¯ t ρ ¯ t 1 ⋯ ⋮ ⋮ ⋮ ⋱ ρ ¯ t ρ ¯ t ⋯ ρ ¯ t 1 ) R t is given by: R t = ( 1 − ρ ¯ t ) I n + ρ ¯ t J n (8) where I n denotes the n-dimensional identity matrices, J n denotes the n × n matrices of ones, and ρ ¯ t   denotes the equicorrelation given by: ρ ¯ t = 2 n ( n − 1 ) ∑ i ≠ j ρ i j , t = 2 n ( n − 1 ) ∑ i ≠ j q i j , t q i i , t q j j , t (9)

We define the scalar DECO model as ¹ : Q t = ( 1 − α 2 − β 2 ) Q ¯ + α 2 e t − 1 e t − 1 ′ + β 2 Q t − 1 (10)

In this section, we examine the potential drivers of the DECO return equicorrelation. Once the return equicorrelation series is extracted from the DECO model as shown in Section 2.2, its driving factors are uncovered using OLS and quantile regressions to make inferences regarding the determinants of market integration among the six indices under study. The base (OLS) regression model is specified as: Δ DECO t   = b 0 + b 1 V I X t + b 2 O V X t + b 3 E P U t + b 4 Δ D X Y t + b 5 F S I t + b 6 Δ T E R M t + b 7 Δ E M V t + e t (11) where VIX, OVX, EPU, DXY, FSI, TERM, and EMV denote CBOE United States implied volatility index, CBOE oil implied volatility, United States economic policy uncertainty (Baker et al., 2016), United States dollar index, OFR financial stress index, term spread (difference spread between 10-Year and 3-months Treasury Constant Maturities, a proxy for recession probabilities), and infectious EMV index (Baker et al., 2019), respectively. All are extracted from the DataStream of Refnitiv, except for data on FSI and EMV which are downloaded from https://www.policyuncertainty.com/infectious_EMV.html and https://www.financialresearch.gov/financial-stress-index/, respectively.

The choice of the explanatory variables is motivated by previous findings (e.g., Batten et al., 2019; Saeed et al., 2020a; Gupta et al., 2021) and the following rationales. Firstly, we use the United States VIX because it is a proxy for the United States stock market uncertainty. High levels of the VIX are often associated with low levels in the S&P 500 index. Secondly, the OVX is used as a barometer of uncertainty in the crude oil market. For example, during the COVID-19 outbreak, the OVX reached unpreceded levels not seen before, exceeding those reported during the oil price crash of 2014–2016. Saeed et al. (2020a) has shown that the connectedness between clean and dirty energy investments is affected by the OVX. Thirdly, the United States EPU is used because it represents the only uncertainty metric available at the daily frequency by Baker et al. (2016). This is suitable as the United States economy is considered as the locomotive for the world economy. By using EPU, we add to the scare evidence on the role of EPU for market integration in general and the correlation dynamics of clean, dirty energy investments and stock market indices. Our motivation to use uncertainty measures (e.g. VIX and EPU) on correlations arises from the growing literature showing the uncertainty surrounding the decision and policies of economists during crisis periods such as the 2008 global financial crisis and the COVID-19 outbreak. Fourthly, the United States dollar index is used as a potential explanatory variable for market integration given its effect not only on crude oil prices and stock market indices, but also on the relationship between United States and European stock indices. Fifthly, EMV is a newspaper-based Infectious disease Equity Market Volatility Tracker, constructed by Baker et al. (2019). It has the particularity of accounting for infectious diseases including the recent COVID-19. Several studies have shown the power of this index in driving financial markets (e.g., Gupta et al., 2021). Sixthly, FSI is the OFR financial stress index that measures the degree of financial stress in financial markets. Seventhly, the term spread is the difference spread between 10-Year and 3-months Treasury Constant Maturities, a proxy for recession probabilities.

To save space, we do not provide the summary statistics and unit root tests of the explanatory variables in Eq. 11. Instead, we indicate here that the results of Augmented Dicky Fuller and Phillips-Perron tests indicate that VIX, OVX, EPU, and FSI are stationary at levels, therefore we use the level of these variables in the regression models. In contrast, DXY, term spread, and EMV are non-stationary and therefore we use the first-difference of these variables.

Besides applying an OLS model to Eq. 11, we consider a quantile regression that allows to uncover the drivers of the various states (high and low) of the return equicorrelation. The benefits of using a quantile regression are well recognized in academia, which includes its ability to move beyond the mean function into low and high quantile functions of the conditional distribution of the dependent variable (Koenker and Bassett, 1978; Koenker, 2005). The quantile regression has been recently applied in various papers covering the fields of finance, economics, and energy (e.g., Bouri et al., 2019; Dawar et al., 2021).

The quantile version of Eq. 11 involving the τ t h conditional quantile of the ΔDECO distribution has the following general form: Q Δ D E C O t | X t ( τ ) = X t β ( τ ) (12) where D E C O t represents the time-varying equicorrelation extracted from the DECO model; Q Δ D E C O t | X t ( τ ) denotes the τ t h conditional quantile, X _t represents a (k+1) × 1 vector of regressors discussed at the beginning of this section, as well as the constant 1 for the intercept. In Eq. 12, the parameters are estimated for every quantile τ by minimizing the weighted absolute deviation: β ( τ ) = arg min β ∈ ℝ k ∑ t = 1 T ρ τ ( Δ D E C O t − X t β ( τ ) ) (13) where ρ τ ( u ) = u ( τ − I ( u < 0 ) ) , 0 < τ < 1 , and I (   ) denotes the indication function. To address the minimization problem in Eq. 13, we follow Koenker and d’Orey (1987). To obtain the standards errors, we use the pair bootstrap method of Buchinsky (1995).

Besides applying the baseline regression model in Eq. 11, we examine the COVID-19 effect on the drivers of equicorrelation. To this end, we add the COVID-19 interaction terms, by multiplying the COVID-19 dummy variable with each regressor. Therefore, we estimate the following augmented model: Δ DECO t   = b 0 + b 1 V I X t + b 2 O V X t + b 3 E P U t + b 4 Δ D X Y t + b 5 F S I t + b 6 Δ T E R M t + b 7 Δ E M V t + b 8 V I X t D C O V I D + b 9 O V X t D C O V I D + b 10 E P U t D C O V I D + b 11 Δ D X Y t D C O V I D + b 12 S F I t D C O V I D + b 13 Δ T E R M t D C O V I D + e t (14) where DCOVID is a dummy variable representing the COVID-19 outbreak. It takes the value of 1 from February 2020 till the end of the sample period (October 8, 2020) and 0 otherwise.

Our first results involve the DECO model (Table 3). The parameter β (0.9825) is high and significant, suggesting a persistence in the association among the six indices under study. The parameter α (0.0134) is significant. Notably, α + β is near unity, suggesting integrated equicorrelation. Regarding the ARCH and GARCH parameters estimated in the first stage, they are both significant at the 1% level for all return series ² . Notably, the GARCH term ranges between 0.8147 for the S&P 500 to 0.9268 for the Green Bond Index.

Moving to the plot of equicorrelation (Figure 1), it shows clear evidence of variation in its time evolution. Notably, it varies between 0.25 and 0.66, with an average value of 0.42 shown by the solid line. The equicorrelation peaked at 0.64 in August 2010 and December 2011, which corresponds to temporary peaks in the levels of many indices such as green bonds, clean energy stocks, and crude oil prices. Conversely, a trough is noticed in late September 2017 and February 2020 just before the erupt of the COVID19 after which the level of the equicorrelation increased to 0.44, suggesting an increase in the level of market integration around the pandemic. During that period of increased uncertainty in financial markets, crude oil prices crashed, and equity indices declined sharply. Therefore, the indices under study appear to be more subject to contagious effects if one index such as crude oil experiences a price collapse. However, we notice various price behaviours in the relationship between the six indices under study and the average equicorrelation. In fact, from 2015 till late 2019, broad equity indices, the technology index, and to some extent, the crude oil market, experienced a long uptrend, whereas the rest of indices entered into a congestion (side-way) area. Accordingly, the equicorrelation reached its bottoms around Q3-2017. While all the indices experienced a major decline during the COVID-19 outbreak period, we notice a major long spike in the clean energy stock index which led this index to move to new all-time levels. During that time, the level of integration increased to 0.44, which generally concords with previous studies showing that the level of correlation among financial markets increases during times of stress (Longin and Solnik, 2001).

In this section, we consider the significance of the potential drivers of equicorrelation, as specified in Eqs. 11–13.

The estimated results based on the OLS regression specified in Eq. 11 are reported in Table 4. They show that VIX, EPU, FSI, and ΔEMV are significant drivers of the mean return equicorrelation. Specifically, the coefficients of VIX, EPU, and ΔEMV are positive and significant at the 1, 5, and 10% levels, respectively, whereas the coefficient of FSI is negative and significant at the 5% level. In terms of magnitude, the strongest effect is for VIX and FSI, followed by EMV and EPU, which indicates the closer relationship in mean between global market uncertainty measures and market integration among green, clean, dirty energy investments, technology stocks, and conventional stock indices.

Next, we move to the drivers of return equicorrelation across lower and upper quantiles based on a quantile regression (Eq. 12). The estimated results from Table 4 show some differences between the determinants of the return equicorrelation at lower and upper quantiles, which further motivates our decision to employ the quantile regression. In fact, at low levels of the equicorrelation (i.e., quantiles 0.10 and 0.20), only OVX is a significant driver of market integration, with a positive coefficient that is significant at the 1% level. However, at high levels of the equicorrelation (i.e., quantiles 0.80), more variables are significant drivers of market integration, which is highlighted in the increase of the Pseudo R ² and the probability value of the Quasi-LR stat. Notably, VIX, OVX, EPU, and FSI are significant drivers of market integration, with the coefficient of the VIX being positive while the coefficient of the rest is negative. At quantile 0.90, the coefficient of ΔEMV becomes significant, and the VIX coefficient intensifies in magnitude while remaining in positive territories. Therefore, at higher quantiles (80 and 90%), the positive VIX coefficients confirm, bolster and support the increase in the level of correlation among financial markets during times of stress as showed in previous studies (Longin and Solnik, 2001). This finding is reinforced by the well-acknowledged negative correlation between the market fear index and the S&P500.

Considering the results of the interactions terms, Table 5 shows that only the coefficients of interaction ΔDXY*DCOVID and ΔTERM*DCOVID are statistically significant. Both are positive, which implies that during the COVID-19 outbreak period the United States Dollar index and Term spread have significantly increased the equicorrelation of green, clean, dirty energy investments. The other interaction terms do not have any statistical significance, suggesting that other variables do not drive market integration during the pandemic.

Given that China has been playing an important role in clean and green investments, crude oil, and conventional stock indices covering technology stocks as the second largest economy, we consider the effect of its stock market index returns on market integration. To this end, we re-run Eq. 14 while adding the returns of the MSCI China stock index ³ as an additional explanatory variable. Furthermore, we also add an interaction term (China*DCOVID) given that China has went through pandemic ⁴ . The results are reported under the Model 2 in Table 5. They show that not only the Chinese stock market returns have a significant effect on the equicorrelation of green, clean, dirty energy investments but its interaction term with the COVID-19 dummy variable is also significant, with a positive value, suggesting it has significantly increased the market integration among the indices under study.

Overall ⁵ , the above-mentioned results improve our understanding of the factors affecting market integration in the universe of green, clean, dirty energy investments, technology stocks, and conventional stock indices. This adds to the existing literature such as Dutta et al. (2021) and Saeed et al. (2020b), which tends to study return spillovers without considering the time evolution of integration and the financial and economic factors that can affect it.