Research on the application of improved MCMC algorithm in the measurement of high-dimensional financial data

In the face of high-dimensional financial data econometric analysis, numerous algorithms inevitably face problems such as difficult model identification, too slow convergence, and too long iteration time. Therefore, the study combines wavelet theory, multiresolution analysis and parallelized sampling to propose. A parallelized Markov chain Monte Carlo algorithm based on wavelet transform is developed to effectively reduce the difficulty of multivariate stochastic fluctuation modeling and Bayesian inference by decomposing the original data with high frequency and filtering noise reduction based on the wavelet theory; secondly, an adaptive process and a multi-chain parallel sampling method are introduced to adjust the sample generating mechanism of the multivariate stochastic fluctuation model. In the empirical experiments, the estimation error of the fluctuation parameters of the improved algorithm is only 0.0018; the estimation error of the noise variance is only 0.0011; the annealing time is 342 s; and the iteration time is 364 s. The research outcomes denote that the improved algorithm proposed by the study can effectively increase the speed of iterative sampling and simulated annealing operation, and solve the long time-consuming and inefficient of the traditional algorithm. Moreover, it can significantly improve the computational efficiency and save the computational cost when dealing with financial time series containing high-frequency data.