Fourier analysis

Information

• Fourier analysis is a mathematical technique used to represent a time series as a sum of sine and cosine functions with different frequencies.
• This technique allows us to decompose a complex signal into simpler components that can be easily analyzed and modeled.
• In time series forecasting, Fourier analysis is used to identify seasonal patterns or cycles in the data.
• The output of Fourier analysis is a set of Fourier coefficients that describe the amplitude and phase of each frequency component in the signal.
• The frequency components with higher amplitude represent the dominant cycles in the data, while the components with lower amplitude represent less important cycles.
• The dominant cycles can be used to create seasonal models that capture the seasonal patterns in the data and improve the accuracy of the forecasts.
• Fourier analysis can be applied to both stationary and non-stationary time series data.
• In non-stationary data, a modified version of Fourier analysis called the "wavelet transform" can be used to analyze signals with varying frequency content over time.