Koherenssifunktio

A koherenssifunktio, in Finnish, translates to coherence function in English. It is a measure used in signal processing and statistics to quantify the relationship between two time series or stochastic processes. Specifically, it assesses how well the fluctuations or variations in one signal can be explained by the fluctuations in another signal at different frequencies.

The coherence function is typically a complex-valued function of frequency. Its magnitude, often referred to as the squared coherence, ranges from 0 to 1. A value of 1 at a particular frequency indicates perfect linear coherence between the two signals at that frequency, meaning one signal can be perfectly predicted from the other. A value of 0 suggests no linear relationship between the signals at that frequency. The phase component of the coherence function provides information about the time lag or phase shift between the two signals at each frequency.

In practice, the coherence function is estimated from observed data. It is widely used in various fields, including econometrics for analyzing the relationship between economic indicators, neuroscience for studying brain activity, and mechanical engineering for identifying vibrations and resonances. By examining the coherence function, researchers can gain insights into causal relationships, identify common underlying factors, and understand the dynamic interactions between different systems.