Temporal Clustering of Time Series via Threshold Autoregressive Models: Application to Commodity Prices

This study aimed to find temporal clusters for several commodity prices using the threshold non-linear autoregressive model. It is expected that the process of determining the commodity groups that are time-dependent will advance the current knowledge about the dynamics of co-moving and coherent prices, and can serve as a basis for multivariate time series analyses. The clustering of commodity prices was examined using the proposed clustering approach based on time series models to incorporate the time varying properties of price series into the clustering scheme. Accordingly, the primary aim in this study was grouping time series according to the similarity between their Data Generating Mechanisms (DGMs) rather than comparing pattern similarities in the time series traces. The approximation to the DGM of each series was accomplished using threshold autoregressive models, which are recognized for their ability to represent nonlinear features in time series, such as abrupt changes, time-irreversibility and regime-shifting behavior. Through the use of the proposed approach, one can determine and monitor the set of co-moving time series variables across the time dimension. Furthermore, generating a time varying commodity price index and sub-indexes can become possible. Consequently, we conducted a simulation study to assess the effectiveness of the proposed clustering approach and the results are presented for both the simulated and real data sets.