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This paper mainly studies the market nonlinearity and the prediction model based on the intrinsic generation mechanism (chaos) of Bitcoin's daily return's volatility from June 27, 2013 to November 7, 2019 with an econophysics perspective, so as to avoid the forecasting model misspecification. Firstly, this paper studies the multifractal and chaotic nonlinear characteristics of Bitcoin volatility by using multifractal detrended fluctuation analysis (MFDFA) and largest Lyapunov exponent (LLE) methods. Then, from the perspective of nonlinearity, the measured values of multifractal and chaos show that the volatility of Bitcoin has short-term predictability. The study of chaos and multifractal dynamics in nonlinear systems is very important in terms of their predictability. The chaos signals may have short-term predictability, while multifractals and self-similarity can increase the likelihood of accurately predicting future sequences of these signals. Finally, we constructed a number of chaotic artificial neural network models to forecast the Bitcoin return's volatility avoiding the model misspecification. The results show that chaotic artificial neural network models have good prediction effect by comparing these models with the existing Artificial Neural Network (ANN) models. This is because the chaotic artificial neural network models can extract hidden patterns and accurately model time series from potential signals, while the benchmark ANN models are based on Gaussian kernel local approximation of non-stationary signals, so they cannot approach the global model with chaotic characteristics. At the same time, the multifractal parameters are further mined to obtain more market information to guide financial practice. These above findings matter for investors (especially for investors in quantitative trading) as well as effective supervision of financial institutions by government.

Numerous nonlinear phenomena that exhibit discontinuous jumps in behavior have been modeled with catastrophe theory. Cobb's Cusp Surface Analysis Program (CUSP) provides a way to empirically estimate and test a nonlinear cusp catastrophe model. A model of emotion during problem solving is used to introduce catastrophe theory modeling and is discussed in conjunction with how to run CUSP, how to interpret the output, and how to improve CUSP's performance. Comparisons are made between linear regression and catastrophe theory models and between catastrophe theory gradient dynamics and Cobb's static statistical cusp model.

In this study, a two-step procedure for the analysis of pretest-posttest data is developed and illustrated. In the first step, a nonlinear canonical correlation analysis was conducted on data from a pretest-posttest control group design. This technique transforms the measure of the pretests (including the scores on the treatment variable) and the posttests in such a way that they become interrelated linearly and possible deviations from the linear model due to nonlinearity have been minimized. In the second step, the resulting optimally scaled set of pretest and posttest measures were analyzed using covariance procedures to assess program effects. The resultant variance appeared to be increased substantially, either by a better prediction of posttest scores from pretest scores, by a better estimation of the effect of the treatment, or by both. It is concluded that the two-step procedure indeed has important advantages.

Using annual data for India, we examine the impact of taxation and government expenditure on income inequality by endogenizing GDP, urbanization, economic globalization, remittances inflows and net FDI flows. For the empirical analysis, we use the nonlinear autoregressive distributed lag model, which indicates a long‐run interplay between government expenditure and taxation on income inequality. Further, the results show that a rise in taxation increases the income inequality, while government expenditure reduces the income inequality in the long‐run. Contrastingly, the findings reveal that GDP, urbanization and economic globalization worsen and remittance inflows and net FDI flows exacerbate income inequality. Therefore, the study suggests that the active policy makers in India can curb rising income inequality by looking at both government expenditure and the sources of taxation before framing any policies related to income distribution. Our results also underscore the close interlinkages between development strategies pursued by India and the wealth gap, which have facilitated the redistribution of gains among those already enjoying high income levels.