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In this paper, we explore the (in)efficiency of the continuum Bitcoin-USD market in the period ranging from mid 2010 to early 2019. To deal with, we dynamically analyse the evolution of the self-similarity exponent of Bitcoin-USD daily returns via accurate FD4 approach by a 512 day sliding window with overlapping data. Further, we define the memory indicator by the difference between the self-similarity exponent of Bitcoin-USD series and the self-similarity index of its shuffled series. We also carry out additional analyses via FD4 approach by sliding windows of sizes equal to 64, 128, 256, and 1024 days, and also via FD algorithm for values of q equal to 1 and 2 (and sliding windows equal to 512 days). Moreover, we explored the evolution of the self-similarity exponent of actual S&P500 series via FD4 algorithm by sliding windows of sizes equal to 256 and 512 days. In all the cases, the obtained results were found to be similar to our first analysis. We conclude that the self-similarity exponent of the BTC-USD (resp., S&P500) series stands above 0.5. However, this is not due to the presence of significant memory in the series but to its underlying distribution. In fact, it holds that the self-similarity exponent of BTC-USD (resp., S&P500) series is similar or lower than the self-similarity index of a random series with the same distribution. As such, several periods with significant antipersistent memory in BTC-USD (resp., S&P500) series are distinguished.

The objective of this study is to contribute to the existing debate of green economic growth by empirically investigating the role of cleaner energy production, green innovation, and green trade in green economic growth in the context of South Asian countries. For this purpose, the study collects the data of South Asian Economies for 2000–2018 from different sources such as world development indicators (WDI), International Energy Statistics (IES), and Organization for Economic Co-operation and Development (OECD) statistics. The study applied Pesaran’s ( 2007 ) second-generation unit root test to test the stationarity of the data. Wasteland’s (2007) test of cointegration was applied to examine the long-run association among modeled variables. The study confirmed the long-run association among modeled variables that turn to be stationary at the first differences. Moreover, the study applied fully modified least square (FMOLS) and dynamic least square (DOLS) to estimate the empirical results of the study. Results of the study show that the production of clean energy, green innovation, and green trade positively contributes to the green economic growth of South Asian Economies

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Abstract. In this paper, three new algorithms are introduced in order to explore long memory in financial time series. They are based on a new concept of fractal dimension of a curve. A mathematical support is provided for each algorithm and its accuracy is tested for different length time series by Monte Carlo simulations. In particular, in the case of short length series, the introduced algorithms perform much better than the classical methods. Finally, an empirical application for some stock market indexes as well as some individual stocks is presented.

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