Cross-Correlation Multifractal Analysis of Technological Innovation, Financial Market and Real Economy Indices

Technological innovation, the financial market, and the real economy are mutually promoting and restricting. Considering the interference of market-noise information, this paper applies the wavelet-denoising method of the soft- and hard-threshold compromise functions to process the original information so as to eliminate the noise information, and combines multifractal detrended cross-correlation analysis with the sliding-window approach, focusing on the change in the Hurst index and the parameter change in the multifractal spectrum to explore the interaction in between. The research results show that there is a certain cross-correlation among technological-innovation, financial-market, and real-economy indices. Firstly, the cross-correlation among them has significant multifractal characteristics rather than single-fractal characteristics. Secondly, the fractal characteristics reveal the long memory of the interaction among the three indices. Thirdly, there are also obvious differences in the degree of local chaos and volatility of the interaction. Fourthly, the cross-correlation among technological-innovation, financial-market, and real-economy indices has significant multifractal characteristics rather than single-fractal characteristics. In comparison, the cross-correlation multifractal characteristics among technological innovation, the financial market, and the real economy are time-varying, and the cross-correlation multifractal characteristics between the technological-innovation index and the real-economy index are the most obvious.