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In spite of the certain risk imposed by financial stress on the real economy, the relationship between financial stress and economic activity is complicated and underresearched, meaning that important gaps still remain in the authors’ understanding of this critical relationship. Therefore, the current study aims to answer the significant question regarding whether a stressful financial sector has predictive power on the real sector and vice versa. Hence, the study examines the causal interrelationship between financial stress index (FSI) and economic activity in Luxembourg as a sample country.

In this study, accompanying the time domain Granger causality framework of Hacker and Hatemi-J (2012), the authors utilize the spectral causality technique of Breitung and Candelon (2006), which is based on the study of Geweke (1982) and Hosoya (1991). This method enables the researcher to measure the degree of a particular variation in time series. Moreover, it allows considering the nonlinearities and causality cycles. The authors further apply the recent method of Farné and Montanari (2018) that is a bootstrap framework on Granger-causality spectra, which allows for disambiguation in causalities.

The time-domain approach finds evidence of bidirectional causation between the variables. However, the spectral causality results indicate the causal linkages between the series are only valid under the medium-run frequency. This study’s findings emphasize covering the frequency causality to deliver a more comprehensive picture of the interrelationship between the variables.

There are many studies in this area that examine the nexus between financial stress and economic activity. However, the authors believe this paper is the first study in the context of Luxemburg. The authors focus on this country since its financial sector is designated as the most important pillar for the economy. Thus, a careful and reliable examination of the relationship between the financial sector and economic activity is likely to be of considerable interest to policymakers and researchers in this field.

This paper aims to examine the stochastic convergence of the per capita CO₂ emissions among the top four crude oil exporter countries, namely, Canada, Iraq, Russia and Saudi Arabia, from 1960 to 2017. Assessing the stationarity and unit root properties of the environmental series in these countries is important as their large fossil fuel resources increases the potential for rising CO₂ emissions compared to other countries.

In addition to implementing the conventional unit root tests, the authors also benefit from the application of three nonlinear unit root tests, namely, wavelet unit root test, nonlinear unit root test of Güriş (2019) and the Fourier quantile unit root test. These methods are robust to the presence of possible structural breaks and other forms of nonlinearities, while the wavelet unit root test enables us to examine the stochastic behavior of the variables in both time and frequency domains. Hence, they all provide more reliable inferences on the convergences of the CO₂ emissions compared to their standard competitors.

The standard unit root test results show strong evidence in favor of non-stationarity in all countries. This conclusion supports the results of the other nonlinear unit root tests and the overall findings of the Fourier quantile unit root test. The wavelet unit root test provides a controversial finding. However, due to its limitations, its findings must be interpreted with caution. The details of the Fourier quantile unit root test indicate that per capita CO₂ emissions follow mean-reverting properties in middle quantile ranges for Canada, Russia and Iraq. This validates the asymmetric behaviors of per capita CO₂ emissions in these countries.

The novelty of the work can be stated in two ways. First, among the available studies, this is the first paper to emphasize the importance of examining the convergence of per capita CO₂ emissions among the top four oil exporters. Second, to the best of the knowledge, no study has yet been undertaken in which all these methods have been simultaneously applied. Sustainable environmental policies depend heavily on the CO₂ series’ properties. Thus, the findings can provide significant environmental and economic implications for policymakers to construct feasible and optimal policies in climate change mitigation.