The Analysis of Statistical and Financial modeling based on Fourier Transform
DOI:
https://doi.org/10.61173/csc0ss27Keywords:
Fourier Transform, Autoregressive Model, Statistical analysis, Financial ModelsAbstract
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.
References
[1] Stephen D.S.G Pollock, eng”Statistical Fourier analysis: Clarifications and interpretations,” Journal of Time Series Econometrics 1, 1– (2009).
[2] Bart Taub, eng. “Economic and financial modeling techniques in the frequency domain,” Economic Theory Bulletin 7, 1–17 (2019).
[3] Sajib Barua, Ruppa K. Thulasiram, and Parimala Thulasiraman, “High-performance computing for a financial application using fast Fourier transform,” in EURO-PAR 2005 Dean&Francis PARALLEL PROCESSING, PROCEEDINGS, Vol. 3648 (Springer Berlin Heidelberg, Berlin, Heidelberg, 2005) pp. 1246–1253.
[4] Bruno Ebner, Bernhard Klar, and Simos G. Meintanis, eng. “Fourier inference for stochastic volatility models with heavytailed innovations,” Statistical papers (Berlin, Germany) 59, 1043–1060 (2018).
[5] Gerasimos G Rigatos, eng”Validation of financial options models using neural networks with invariance to fourier transform,” in engState-Space Approaches for Modelling and Control in Financial Engineering, Intelligent Systems Reference Library, Vol. 125 (Springer International Publishing AG, Switzerland, 2017) pp. 167–181.
[6] Muhammad Noaman Zahid, Rashid Ali, and Muhammad Shakeel Afzal, eng“Acquisition and analysis of multi-global navigation satellite system signals based on fast fourier transform,” Journal of communications technology electronics 64, 1288–1297 (2019).
[7] Ramamurti. Shankar, eng“Principles of quantum mechanics,” engPrinciples of quantum mechanics, (1980).
[8] C.S Burrus, eng“Fast fourier transform and convolution algorithms,” Signal processing 12, 106–107 (1987).
[9] Peter J. Brockwell and Richard A. Davis, eng. “Introduction to time series and forecasting,” Springer Texts in Statistics (2016).
[10] Robert H. Shumway and David S. Stoffer, eng“Time series analysis and its applications with r examples,” engTime series analysis and its applications with R examples, Springer texts in statistics (2010).
[11] Stanley Krasner, Examining Applications of Fourier Transforms to Financial Data and Covariance Estimation, Ph.D. thesis, Carnegie Mellon University (2015).
[12] Iacopo Giampaoli, Wing Ng, and Nick Constantinou, “Analysis of ultra-high-frequency financial data using advanced fourier transforms,” Finance Research Letters 6, 47–53 (2009).
[13] Thomas A. Gallagher, Alexander J. Nemeth, and Lotfi Hacein-Bey, “An introduction to the fourier transform: Relationship to mri,” American Journal of Roentgenology 190, 1396–1405 (2008), pMID: 18430861, https://doi.org/10.2214/ AJR.07.2874.
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