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The relationship between environmental degradation and economic growth has become a prominent topic in recent decades, increasing multidisciplinary approaches across a wide range of studies. Analyzing the economy-environment nexus is significant because most countries attempt to limit environmental deterioration while pursuing economic growth. This paper studies the non-linear cross-correlations between economic growth and environmental degradation on a sample of five developed European countries - France, Germany, Spain, Norway, and the United Kingdom. The study is performed using two approaches: multifractal detrended cross-correlation analysis and wavelet-based analysis. According to the empirical tests, there are non-linear cross-correlations between economic growth and environmental degradation in all five countries. For each country, multifractal metrics such as Hurst exponents, scaling exponents, and multifractal spectra are computed to show the significance of all time-series pairs. The strongest multifractal features have been observed in France, Norway, and Spain. Shuffling the series suggests that multifractality in the cross-correlations arises both from a broad probability density function and from different long-term correlations. Wavelets are applied to detrend all data sets before computing the cross-correlation. Moreover, the wavelet coherence is computed as a measure for analyzing interdependencies across time and frequencies. Except for France and Spain, Wavelet-detrended cross-correlation values are considerably lower than cross-correlation values of the raw data sets, which indicates that the interdependence between growth and environmental degradation is rather long-term. In terms of wavelet coherence, results vary among the countries, with France and Spain showing the highest and most persistent coherence values. [ABSTRACT FROM AUTHOR]

Abstract: This work aims at determining the factors affecting economic output in developed countries. However, the definition of development depends on the criteria by which different principles provide different criteria of level of development. Therefore, there exists uncertainty about choice of sample or real development country and if the selected samples are not representative of the underlying population of real developed countries then the ordinary least squares coefficients may be biased. This paper examines the determinants of economic output in the panel data of 22 developed countries from 1996 to 2008 utilizing econometric techniques that take into account the selective nature of the samples. In general, there are two approaches to estimate the sample selection model, namely the maximum likelihood method and the method proposed by Heckman (1979) [21]. Moreover, these two approaches require that the joint distribution to be known. In general the multivariate normal distribution is assumed. However, this assumption can often be seen as excessively restrictive and this lead to uncertainty about the structure or assumption of joint distribution. Smith (2003) [37] suggests applying the copula approach, especially the Archimedean copula to the sample selection model and the result also shows that the copula approach is well suited to apply to a model where the sample selection is biased, using cross-section data. In our work, we employ the copula approach to construct the sample selection model in the case of panel data, resulting in the identification of significant factors affecting economic output. [Copyright &y& Elsevier]

• We propose fractional permutation entropy and fractional Jensen–Shannon divergence to analyze financial time series. • Through establishing entropy plane, we can distinguish different time series and get an ideal result. • We expand the fractional entropy to multiscale and gain multiscale fractional permutation entropy and multiscale fractional Jensen–Shannon divergence. • We explore the relationship between multiscale entropy and find it is very regular under different scales. Permutation entropy (PE) has been proposed to reflect the complexity of time series in recent years, and it has a wide range of applications. In this paper, we extend PE to the fractional order through the parameter α , and then obtain fractional permutation entropy (FPE). FPE can increase the sensitivity of the complex system by adjusting the fractional order. We combine FPE with fractional Jensen–Shannon divergence (FJSD) to construct the entropy plane and discover that the entropy plane can classify various time series. In particular, it can distinguish the stock indices of developing countries and developed countries. We introduce FPE and FJSD to multiscale, and gain multiscale fractional permutation entropy (MFPE) and multiscale fractional Jensen–Shannon divergence (MFJSD). We employ simulated data and financial stock data to explore the relationship of MFPE and MFJSD under different scales, and the results show that some data are similar to direct proportion relationship and others data are sharply increasing curves, which portrays the internal mechanism of the stock market excellently. [ABSTRACT FROM AUTHOR]