Clustering Locally Stationary Time Series Using Quantile Autocorrelations

Locally stationary time series frequently arise in various fields such as environmental science, economics, and seismology. However, statistical methods for analyzing such data remain underdeveloped. This work presents a clustering approach for locally stationary time series that employs a dissimilarity measure based on local estimates of the quantile autocorrelation function at each time point. This distance is then used in combination with a K-medoids-type minimization problem which includes a penalty term that accounts for the size of the neighborhood used in the local estimation. To solve this problem, we propose an iterative procedure that guarantees a decrease in the objective function at each step. Several simulations demonstrate that the method generally outperforms natural benchmarks in terms of clustering accuracy. The effectiveness of the approach is further illustrated through an application to real-world particulate matter time series data from Saudi Arabia.