Fourier analysis
The purpose of spectral density estimation is to measure the amplitude of a signal or a time series according to its frequency [3:4]. The spectral density is estimated by detecting periodicities in the dataset. A scientist can better understand a signal or time series by analyzing its harmonics.
Note
The spectral theory
Spectral analysis for time series should not be confused with spectral theory, a subset of linear algebra that studies Eigenfunctions on Hilbert and Banach spaces. Harmonic and Fourier analyses are regarded as a subset of spectral theory.
The fast Fourier transform (FFT) is the most commonly used frequency analysis algorithm [3:5]. Let's explore the concept behind the discrete Fourier series and the Fourier transform as well as their benefits as applied to financial markets. The Fourier analysis approximates any generic function as the sum of trigonometric functions, sine and cosine. The decomposition in a basic trigonometric function is known as a Fourier...
