6 Fourier time—frequency analysis of risk
6.1 Introduction
As we discussed in Chapter 5, Fourier series are powerful tools for analyzing periodic variables, such as musical tones of instruments, or for determining the spectral lines of inorganic and organic chemical components. But very few practical problems of financial-economic analysis do involve such rigidly periodic variables. We need a form of Fourier analysis that can deal with aperiodic, but still “cyclical” variables and that can identify Mandelbrot's aperiodic cyclicity prevalent in the long memory financial return series. Therefore, we'll discuss a frequency representation of aperiodic variables by means of the Fourier Transform (FT), which analyzes the frequency contents ...
Get Financial Market Risk now with the O’Reilly learning platform.
O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.
