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Modelling nonlinearities in commodity prices using smooth transition regression models with exogenous transition variables

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Abstract

This paper investigates the nonlinearities in commodity prices using smooth transition regression (STR) models. What distinguishes this paper from the majority of the studies in the smooth transition literature is its use of exogenous transition variables, in addition to the standard autoregressive lags of the dependent variable, in modelling the regime switching behavior of commodity prices. Two exogenous transition variables were found successful in capturing the regime switching behavior of commodity prices: inflation rate and oil price. Inflation rate was capable of capturing the early dynamics (between 1900 and 1950) of the commodity index whereas oil price captured the late ones (between 1970 and 2007). This result motivates the use of common exogenous threshold variables in regime switching models in general and, in particular, the use of inflation and oil price in the STR model when applied to an index of commodity prices. The paper also provides further insight on the issue of co-movement of commodity prices by classifying individual commodities into groups according to their border price (an issue that has been ignored in previous studies on commodity prices), and then trying to find the best common transition variable that can explain the dynamic behavior of each group. The results show that, for traded commodities, individual price series recorded on a free on board basis are driven by macroeconomic news in the exporting country. On the other hand, individual price series recorded on a cost and freight basis are driven by oil price and macroeconomic news variables in the importing country.

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Notes

  1. Border prices, also known as International Commercial Terms (Incoterms), are the terms of selling that define the obligations of the trading parties engaged in trading contracts. Among all border prices, two are used the most: Free on board (FOB) prices and cost insurance and freight (CIF) prices. A trading contract effected on a FOB basis implies that the exporter, also known as the shipper, bears all the risks and costs of transporting the cargo from the point of origin, e.g., the exporter’s factory, to the port of export in the country of origin, i.e., the exit point of the exporting country. The importer, also known as the consignee, bears all the risks and costs of the cargo from that point up to delivery to final destination. A CIF price, on the other hand, is a FOB price plus insurance cost plus ocean freight cost; that is, under a CIF contract, the exporter, in addition to the insurance, bears all risks and costs of transporting the cargo from the point of origin to the port of discharge, i.e., the entry point of the importing country.

  2. The MUV index is a trade-weighted index of the exports of the five major developed countries to developing countries. The five major developed countries are France, Germany, Japan, the United Kingdom, and the United States.

  3. The difference stationary (DS) model is an alternative to the TS model that was made popular in the 1970’s by the work of Box and Jenkins, where the first difference of the logarithm of a time series is regressed on a constant and an error term.

  4. See, for instance, Lin and Teräsvirta (1994).

  5. For more details on pure threshold models, see Tong (1990) and the references therein.

  6. For more details on the selection criterion for STR models, see Teräsvirta’s (1994) and the references therein.

  7. To facilitate the construction of an effective grid, I follow Teräsvirta’s (1998) suggestion to standardize the exponent of the transition function \(G(s_t ;\gamma ,{\varvec{c}})\) by dividing it by the \(k\mathrm{th}\) power of the sample standard deviation of the transition variable \({\hat{\sigma }}_s^k\). This is done mainly to render the parameter \(\gamma \) scale-free.

  8. For more details, see Eitrheim and Teräsvirta (1996).

  9. Fahmy (2011) showed that the cost of fuel represents roughly around 20–25 % of the recorded CIF price of any commodity traded on a CIF basis.

  10. Fahmy (2011) showed that oil price is indeed the best transition variable that was capable of explaining the observed nonlinear dynamics in all commodity prices recorded on a CIF basis in the GYCPI.

  11. I am indebted to Stephan Pfaffenzeller for supplying the recent update from 2003 to 2007.

  12. Testing the presence of ARCH up to order \(v=4\) is adequate here since we have annual data.

  13. The forecasts were made without re-estimating the models during the prediction period (from 2001 to 2007).

  14. The dynamic behavior of the time series \(y_t \) in both regimes when the transition variable is \({\Pi }_{t-1} \) is summarized in Table 3.

  15. The dynamic behavior of the time series \(y_t \) in both regimes when the transition variable is \(R_{t-1} \)is summarized in Table 5.

  16. Details regarding the classification, estimation, and the dynamic analysis of the limiting processes of the 24 individual commodity series forming the GYCPI are found in Fahmy (2011).

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  1. University of Waterloo, Ontario, Canada

    Hany Fahmy

  2. HF Consulting, Ontario, Canada

    Hany Fahmy

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Fahmy, H. Modelling nonlinearities in commodity prices using smooth transition regression models with exogenous transition variables. Stat Methods Appl 23, 577–600 (2014). https://doi.org/10.1007/s10260-014-0275-6

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