The Analysis of Statistical and Financial modeling based on Fourier Transform

Abstract

In this manuscript, we mainly focus on the contribution of the Fourier transform in studies of economics and statistics and show how this mathematical technique helps analysts build various analytical models to understand complex data behavior. We focus on explaining how the application of the Fourier transform is used in time series analysis and regression analysis with examples and demonstrating why the Fourier transform contributes to these two analyses. First, modeling techniques without using Fourier transform omit information in time series analysis, especially when dealing with large data. Second, utilizing the Fourier Transform can sufficiently decrease the complexity of calculation and provide estimation, such as covariance estimation, in stochastic process and time series analysis.