Temporal Clustering of Time Series Via Threshold Autoregressive Models: Application To Commodity Prices

Abstract

The primary aim in this study is grouping time series according to the similarity between their data generating mechanisms (DGMs) rather than comparing pattern similarities in the time series trajectories. The approximation to the DGM of each series is accomplished by fitting the linear autoregressive and the non-linear threshold autoregressive models, and outputs of the estimates are used for feature extraction. Threshold autoregressive models are recognized for their ability to represent nonlinear features in time series, such as abrupt changes, time-irreversibility and regime-shifting behavior. The proposed clustering approach is mainly based on feature vectors derived from above-mentioned models estimates. Through the use of the proposed approach, one can determine and monitor the set of co-moving time series variables across the time. The efficiency of the proposed approach is demonstrated through a simulation study and the results are compared with other proposed time series clustering methods. An illustration of the proposed clustering approach is given by application to several commodity prices. It is expected that the process of determining the commodity groups that are time-dependent will advance the current knowledge about temporal behavior and the dynamics of co-moving and coherent prices, and can serve as a basis for multivariate time series analyses. Furthermore, generating a time varying commodity prices index and sub-indexes can become possible. Findings suggested that clusters of the prices series have been affected with the global financial crisis in 2008 and the data generating mechanisms of prices and so the clusters of prices might not be the same across the entire time-period of the analysis.