Research on application of fractional calculus in signal real-time analysis and processing in stock financial market

In this paper, the author proposes a new stock financial market stochastic volatility and stock pricing model based on the Taylor formula, by embedding the strictly increasing harmonic steady-state process as a time variable into the Brownian motion with drift terms. The use of variance gamma and normal inverse high-lower distribution are special forms of NTS distribution, combined with principal component analysis (PCA) and artificial neural network (ANN) methods, for nonlinear and multi-scale complex financial time series in financial markets. The model is constructed and predicted, and the forecast and calculation of stock market index and foreign exchange rate are realized. Through calculation and research, the model can fill the blank of complex time series model research in financial market. The stock signal analysis based on fractional calculus equation proposed in the thesis is based on the idea of decomposition-reconstruction-integration, which can improve the prediction accuracy of the model for the time series combined financial model. The Shanghai and Shenzhen 300 Index and foreign exchange rates selected by the paper are taken from the market real data, and the skeleton prediction model is established. It can predict the short-term trend after the stock market closes, confirming the nonlinear, multi-scale and non-stationary the prediction accuracy of the sequential decomposition prediction method of financial time series is effectively improved, and the principal component and artificial neural network method are used to compress redundant data and shorten the prediction time.