Fourier Analysis - Definition
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Fourier analysis Academic Research on Fourier Analysis Option valuation using the fastFouriertransform, Carr, P., & Madan, D. (1999). Journal of computational finance,2(4), 61-73. This paper shows how the fast Fourier Transform may be used to value options when the characteristic function of the return is known analytically. Fourier analysisfor demand forecasting in a fashion company, Fumi, A., Pepe, A., Scarabotti, L., & Schiraldi, M. M. (2013). International Journal of Engineering Business Management,5(Godite 2013), 5-30. Given the strong seasonal nature of the products that characterize the fashion sector, this paper aims to highlight how the Fourier method can represent an easy and more effective forecasting method compared to other widespread heuristics normally used. For this purpose, a comparison between the fast Fourier transform algorithm and another two techniques based on moving average and exponential smoothing was carried out on a set of 4- year historical sales data of a 60+ million turnover medium- to large-sized Italian fashion company. Transformanalysisand asset pricing for affine jumpdiffusions, Duffie, D., Pan, J., & Singleton, K. (2000). Econometrica,68(6), 1343-1376. In the setting of affine jumpdiffusion state processes, this paper provides an analytical treatment of a class of transforms, including various Laplace and Fourier transforms as special cases, that allow an analytical treatment of a range of valuation and econometric problems. ApproximateFourier analysisof distribution functions, Bohman, H. (1961). Arkiv fr matematik,4(2-3), 99-157. Analysisof sectoral credit default cycle dependency with wavelet networks: Evidence from Turkey, Cifter, A., Yilmazer, S., & Cifter, E. (2009). Economic Modelling,26(6), 1382-1388. This paper investigates the relationship between industrial production and sectoral credit defaults (non-performing loans ratio) cycle by wavelet network analysis in Turkey over the period January 2001November 2007. A theory of entropy inFourier analysis, Fefferman, R. A. (1978).Advances in Mathematics,30(3), 171-201. This thesis deals with a certain set function called entropy and its pplications to some problems in classical Fourier analysis. Mode-locking'and internationalbusinesscycle transmission, Selover, D. D., & Jensen, R. V. (1999). Journal of Economic Dynamics and Control,23(4), 591-618. This study investigates international business cycle synchronization. This study suggests that the world business cycle results from a `mode-locking' phenomenon, a nonlinear process by which weak coupling between oscillating systems tends to synchronize oscillations in the systems. Measuring comovement in the timefrequency space, Rua, A. (2010). Journal of Macroeconomics,32(2), 685-691. A spectralanalysisof New Zealand output gaps usingFourierand wavelet techniques, Conway, P., & Frame, D. (2000). Reserve Bank of New Zealand. This paper uses frequency domain techniques to illustrate the properties of various measures of New Zealands output gap. Measures of the output gap are estimated using a number of different methods: a Structural VAR model, a multivariate unobserved components model, the Hodrick-Prescott filter, a multivariate time series filter, and a linear time trend filter. Fouriertransform, Weisstein, E. W. (2004). Privatization, foreign bank entry and bank efficiency in Croatia: aFourier-flexible function stochastic cost frontieranalysis, Kraft, E., Hofler, R., & Payne, J. (2006). Applied Economics,38(17), 2075-2088. Using bank balance sheet data for Croatia for 1994 to 2000, this study estimates a Fourier-flexible frontier cost function.