Abstract
In terms of today, one may argue, throughout observations from energy literature papers, that (i) one of the main contributors of the global warming is carbon dioxide emissions, (ii) the fossil fuel energy usage greatly contributes to the carbon dioxide emissions, and (iii) the simulations from energy models attract the attention of policy makers to renewable energy as alternative energy source to mitigate the carbon dioxide emissions. Although there appears to be intensive renewable energy works in the related literature regarding renewables’ efficiency/impact on environmental quality, a researcher might still need to follow further studies to review the significance of renewables in the environment since (i) the existing seminal papers employ time series models and/or panel data models or some other statistical observation to detect the role of renewables in the environment and (ii) existing papers consider mostly aggregated renewable energy source rather than examining the major component(s) of aggregated renewables. This paper attempted to examine clearly the impact of biomass on carbon dioxide emissions in detail through time series and frequency analyses. Hence, the paper follows wavelet coherence analyses. The data covers the US monthly observations ranging from 1984:1 to 2015 for the variables of total energy carbon dioxide emissions, biomass energy consumption, coal consumption, petroleum consumption, and natural gas consumption. The paper thus, throughout wavelet coherence and wavelet partial coherence analyses, observes frequency properties as well as time series properties of relevant variables to reveal the possible significant influence of biomass usage on the emissions in the USA in both the short-term and the long-term cycles. The paper also reveals, finally, that the biomass consumption mitigates CO2 emissions in the long run cycles after the year 2005 in the USA.
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Notes
HFCs include HFC23, HFC134a, and HFC152a
If f(x) is a non-periodic function, its Fourier transform \( F(x):\mathbb{R}\mathbb{\to}\mathbb{C} \) returns a complex-valued function, which has complex weights for different frequency contributions under integral as a similar way to the coefficients in the periodic functions’ case.
There is an alternative representation of Fourier transformation analogous (identical) to Eq. 1. Since sines and cosines are 2π-periodic functions, w = 2πκ denotes radian frequency: \( H(w)={\int}_{-\mathit{\infty}}^{\mathit{\infty}}h(t){e}^{-iwt}dt={\int}_{-\mathit{\infty}}^{\mathit{\infty}}h(t)\left[ \cos (wt)-i \sin (wt)\right]dt \)
If a wavelet is square integrable \( \phi (t)\in {L}^2\left(\mathbb{R}\right) \), then it must satisfy \( {\int}_{-\mathit{\infty}}^{\mathit{\infty}}\mathit{\varnothing}{(t)}^2dt<\mathit{\infty} \) .
The conjugate of a complex number, c + di, is simply c − di. If the value is real rather than complex, its conjugate is itself. In economic applications complex wavelets are more popular, thus the conjugation becomes important.
Grinsted et al. (2004) provides an example of a derived smoothing parameter of the cross wavelet coherency generated from complex Morlet wavelet transformation.
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Bilgili, F., Öztürk, İ., Koçak, E. et al. The influence of biomass energy consumption on CO2 emissions: a wavelet coherence approach. Environ Sci Pollut Res 23, 19043–19061 (2016). https://doi.org/10.1007/s11356-016-7094-2
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DOI: https://doi.org/10.1007/s11356-016-7094-2