Measuring and forecasting the volatility of USD/CNY exchange rate with multi-fractal theory

Exchange rate fluctuations continue to intensify because of global economic integration. Research on the characteristics of exchange rate volatility is particularly urgent and important. In this paper, the fractal theory is introduced. The function box counting method and the qth-order moment structure partition function method are applied to test the multi-fractal features of USD/CNY exchange rate. On this basis, the multi-fractal spectrum analysis is carried out. It is found that USD/CNY exchange rate has multi-fractal characteristics and there is a strong connection between the standard deviation of the scale index and volatility of USD/CNY exchange rate. By adjusting the standard deviation of scaling exponents, we construct the multi-fractal volatility index and build a dynamic model for testing and forecasting the volatility of USD/CNY exchange rate based on fractal theory. The model lnS¯α-ARMA(1,1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ln \bar{{S}}_\alpha -\hbox {ARMA} (1,1) $$\end{document} for measuring and forecasting volatility proposed in our paper is demonstrated to be a good fit to the exchange rate data, which provides sound methodological reference for exchange rate volatility measurement.