Frequency Domain Clustering: An Application to Time Series with Time-Varying Parameters

Time series distribution parameters, such as mean and variance, are usually used as features for clustering. In this paper, starting from the hypothesis that the distributional features of the time series are time-varying, a frequency domain clustering approach based on time-varying parameters is applied. Under a specified probability distribution, we estimate the time-varying parameters with the Generalized Autoregressive Score (GAS) model and cluster time series data according to a distance based on the obtained parameters’ frequency domain representation. Previous studies showed that frequency domain approaches are particularly useful for clustering financial time series data. Considering both simulated and real time series data, we compare the performances of the frequency domain clustering on time-varying parameters with those obtained with time-domain benchmark procedures.