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• Healthy and unhealthy infant cry signals are analyzed in by their respective cepstrums. • Approximate entropy and correlation dimension are estimated from cepstrums. • Statistical tests show evidence that approximate entropy and correlation dimension are different across healthy and unhealthy infant cry signals. • Approximate entropy and correlation dimension in cepstrum domain are promising biomarkers for pathology detection in infant cries. The analysis of infant cry signals is becoming an attractive field of research in biomedical physics and engineering for better understanding of the pathologies and appropriate medial diagnosis. The main purpose of the current study is to characterize infant normal and pathological cry signals by studying their respective oscillations by means of approximate entropy and correlation dimension estimated from their respective cepstrums. We analyzed two different sets. The first one is composed of 2638 expiration cry signals and the second set is composed of 1860 inspiration cry signals, both sets equally weighted. After estimating approximate entropy and correlation dimensions from cepstrums, three standard statistical tests are applied to them including the Student t -test, F -test, and two-sample Kolmogorov-Smirnov test. All statistical tests are performed at 5% statistical significance level. The empirical results follow. First, approximate entropy and correlation dimension measures exhibit different statistical characteristics across healthy and unhealthy infant cries from both expiration and inspiration sets. Second, the level of approximate entropy in cepstrums of healthy infant cries is statistically higher than that in cepstrums of unhealthy infant cries. Third, the level of correlation dimension in cepstrums of healthy infant cries is statistically higher than that in cepstrums of unhealthy infant cries. In other words, cepstrums of healthy infant cries show lower randomness and disorder compared to cepstrums of unhealthy infant cries. It is concluded that cepstrum-based approximate entropy and correlation dimension discriminate healthy from pathological infant cry signals and can be employed as effective biomarkers for biomedical diagnosis of cry records in clinical milieu. [ABSTRACT FROM AUTHOR]

• Via Renyi entropy we analyze the multiscale entropy measurement of global markets. • By estimating mutual information we expose the dependencies and information flow. • Randomness and disorder are more observed in low probability events. • The information sharing network among markets was modified during COVID-19 pandemic. • We offer a valuable insight of the impact of COVID-19 pandemic upon expectations and investor fear. The COVID-19 pandemic has seriously affected world economies. In this regard, it is expected that information level and sharing between equity, digital currency, and energy markets has been altered due to the pandemic outbreak. Specifically, the resulting twisted risk among markets is presumed to rise during the abnormal state of world economy. The purpose of the current study is twofold. First, by using Renyi entropy, we analyze the multiscale entropy function in the return time series of Bitcoin, S&P500, WTI, Brent, Gas, Gold, Silver, and investor fear index represented by VIX. Second, by estimating mutual information, we analyze the information sharing between these markets. The analyses are conducted before and during the COVID-19 pandemic. The empirical results from Renyi entropy indicate that for all market indices, randomness and disorder are more concentrated in less probable events. The empirical results from mutual information showed that the information sharing network between markets has changed during the COVID-19 pandemic. From a managerial perspective, we conclude that during the pandemic (i) portfolios composed of Bitcoin and Silver, Bitcoin and WTI, Bitcoin and Gold, Bitcoin and Brent, or Bitcoin and S&P500 could be risky, (ii) diversification opportunities exist by investing in portfolios composed of Gas and Silver, Gold and Silver, Gold and Gas, Brent and Silver, Brent and Gold, or Bitcoin and Gas, and that (iii) the VIX exhibited the lowest level of information disorder at all scales before and during the pandemic. Thus, it seems that the pandemic has not influenced the expectations of investors. Our results provide an insight of the response of stocks, cryptocurrencies, energy, precious metal markets, to expectations of investors in the aftermath of the COVID-19 pandemic in terms of information ordering and sharing. [ABSTRACT FROM AUTHOR]

• 45 cryptocurrency and 16 international stock markets are analyzed • A Big Data set is investigated before and during the COVID-19 pandemic period • We estimate stability and regularity metrics to infer on the predictability of price fluctuations • We find that cryptocurrencies embed higher instability and irregularity • Investing in digital assets during big crises could be considered riskier compared to equities We explore the evolution of the informational efficiency in 45 cryptocurrency markets and 16 international stock markets before and during COVID-19 pandemic. The measures of Largest Lyapunov Exponent (LLE) based on the Rosenstein's method and Approximate Entropy (ApEn), which are robust to small samples, are applied to price time series in order to estimate degrees of stability and irregularity in cryptocurrency and international stock markets. The amount of regularity infers on the unpredictability of fluctuations. The t -test and F -test are performed on estimated LLE and ApEn. In total, 36 statistical tests are performed to check for differences between time periods (pre- versus during COVID-19 pandemic samples) on the one hand, as well as check for differences between markets (cryptocurrencies versus stocks), on the other hand. During the COVID-19 pandemic period it was found that (a) the level of stability in cryptocurrency markets has significantly diminished while the irregularity level significantly augmented, (b) the level of stability in international equity markets has not changed but gained more irregularity, (c) cryptocurrencies became more volatile, (d) the variability in stability and irregularity in equities has not been affected, (e) cryptocurrency and stock markets exhibit a similar degree of stability in price dynamics, whilst finally (f) cryptocurrency exhibit a low level of regularity compared to international equity markets. We find that cryptos showed more instability and more irregularity during the COVID-19 pandemic compared to international stock markets. Thus, from an informational efficiency perspective, investing in digital assets during big crises as the COVID-19 pandemic, could be considered riskier as opposed to equities. [ABSTRACT FROM AUTHOR]

• We employ SVR, GRP, RT, kNN, FFNN, BRNN and RBFNN machine learning models. • We comparatively evaluate AI systems in forecasting high-frequency Bitcoin prices via diverse metrics. • An entropy analysis reveals long memory traits, stochasticity and topological complexity. • The BRNN shows outstanding accuracy while its convergence is remarkably fast. • ANNs efficiently emulate parallel processing in human decision-making under noisy, nonlinear input-output variable spaces. Due to the remarkable boost in cryptocurrency trading on digital blockchain platforms, the utilization of advanced machine learning systems for robust prediction of highly nonlinear and noisy data, gains further popularity by individual and institutional market agents. The purpose of our study is to comparatively evaluate a plethora of Artificial Intelligence systems in forecasting high frequency Bitcoin price series. We employ three different sets of models, i.e., statistical machine learning approaches including support vector regressions (SVR) and Gaussian Poisson regressions (GRP), algorithmic models such as regression trees (RT) and the k -nearest neighbours (kNN) and finally artificial neural network topologies such as feedforward (FFNN), Bayesian regularization (BRNN) and radial basis function networks (RBFNN). To the best of our knowledge, this is the first time an extensive empirical investigation of the comparative predictability of various machine learning models is implemented in high-frequency trading of Bitcoin. The entropy analysis of training and testing samples reveals long memory traits, high levels of stochasticity, and topological complexity. The presence of inherent nonlinear dynamics of Bitcoin time series fully rationalizes the use of advanced machines learning techniques. The optimal parameter values for SVR, GRP and kNN are found via Bayesian optimization. Based on diverse performance metrics, our results show that the BRNN renders an outstanding accuracy in forecasting, while its convergence is unhindered and remarkably fast. The overall superiority of artificial neural networks is due to parallel processing features that efficiently emulate human decision-making in the presence of underlying nonlinear input-output relationships in noisy signal environments. [ABSTRACT FROM AUTHOR]

• A time-scale multi-fractal approach is used to investigate high-frequency Bitcoin prices & volume. • Big data analysis reveals heterogeneous multi-fractal dynamics in [5 mn–90 mn] & [120 mn–720 mn] intervals. • Wavelet leaders algorithmic technique provides robust description of the singularity spectrum. • Profitable high-frequency trading strategies in crypto-currency markets can be devised. We employ a time-scale multi-fractal decomposition approach to investigate the properties of Bitcoin prices and volume at different sampling rates using high-frequency data. We provide evidence of multi-fractality at all rates. The big data-driven analysis combined with statistical testing shows evidence of dominant multi-fractal traits within the intervals of 5 mn–90 mn, and 120 mn up to 720 mn. Wavelet leaders comprise a promising algorithmic technique that provides a richer description of the singularity spectrum. In particular, we reveal the distinct heterogeneity of the three log-cumulants for prices and volume between the two distinctive high-frequency sampling intervals. Our findings may assist in devising profitable high-frequency trading strategies in crypto-currency markets. [ABSTRACT FROM AUTHOR]

• We introduce for the first time in the literature a fractional-calculus-based artificial macroeconomic model. • A new system of fractional difference-order equations is proposed for the Goodwin model. • Using bifurcation diagrams, phase portraits and Lyapunov exponents among other measures, the characteristics of the new system are depicted. • We implement extensive simulations via a new hardware laboratory realization set up. In this novel research, through dynamical analysis, we introduce for the first time a fractional-calculus based artificial macroeconomic model, actually implemented in the Laboratory via a new hardware set up. Firstly, we propose a new model of a discrete-time macroeconomic system where fractional derivatives are incorporated into the system of equations. Using well-known tools and methods, including bifurcation diagrams and Lyapunov exponents, the characteristics of the system are disclosed, and the importance of the fractional-order derivative in the modeling of the system is shown. After that, a laboratory hardware realization is also carried out for the proposed system that provides further insight and a better understanding of the properties of the system. For the hardware realization an Arduino Due™ is chosen in which possess two analog output pins. Experimental results conspicuously illustrate the chaotic behavior of the system. Through the results of the hardware realization, phase portraits and bifurcation diagram of the system are demonstrated, and the effects of the parameters and fractional derivatives are studied. We believe the presented study and its results pave the way for future studies on the incorporation of fractional calculus into macroeconomic models. [ABSTRACT FROM AUTHOR]