  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.
