Commodity currencies and commodity prices: modelling static and time-varying dependence

ABSTRACT

This article employs the copula approach to study the relationship between exchange rates and commodity prices for large commodity exporters. Using data for the nominal exchange rates of four commodity currencies (Australian, Canadian and New Zealand dollars, and Norwegian krone) against the US dollar and the relevant country-specific commodity price indices, constructed on a daily basis, we find (1) a positive dependence between the values of commodity currencies and commodity indices, i.e. a commodity index increases when a respective currency appreciates and provides several explanations for this finding; (2) no major asymmetries in the tail dependence for most pairs of exchange rates and commodity indices and (3) a pronounced increase in the time-varying tail dependence following the global financial crisis.

KEYWORDS:

• Independently floating exchange rates
• commodity prices
• dependence modelling
• copulas

JEL CLASSIFICATION:

• C13
• C22
• C52
• F31

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ Reboredo (2012) also considers time-varying dependence but does this only for the Student-t and normal copulas that do not generate any asymmetric tail dependence.

² http://www.indexmundi.com.

³ Note that for the purpose of graphical representation of all FX rates in one figure, we scale the exchange rate USD/NOK by factor 0.2.

⁴ Since copula functions remain invariant under strictly increasing transformations of $X$ (e.g. standardization of the marginal distributions), see (Nelsen (1998)), the copula of a $t_d(\nu ,\mu ,\mathrm{\Sigma })$ distribution is identical to that of a $t_d(\nu ,0,\mathrm{\Psi })$.

⁵ For instance, see Hurst and Platen (1997), Platen and Rendek (2008), Hu and Kercheval (2007), Ignatieva and Platen (2010) and Ignatieva, Platen, and Rendek (2011).

⁶ We do not consider the case when $-1<\lambda <0$, since it corresponds to $\nu <2$ for which the normalization constant diverges, see Platen and Rendek (2008).

⁷ The KS distance, defined as $KS={sup}_{x\in \mathcal{R}}\left|F_s(x)-\hat{F}(x)\right|$, is more sensitive closer to the centre of the distribution and fails to capture the tails.

⁸ GARCH(1,1) is a parsimonious model providing a good fit to the data (even if time series are volatile and exhibit jumps), see e.g. Morana (2001), Lin and Tamvakis (2001), Garcia et al. (2005), Misiorek, Trueck, and Weron (2006), Worthington, Kay-Spratley, and Higgs (2005) and Ketterer (2012). In particular, Andersen and Bollerslev (1998) and Wang and Wu (2012) argue that the GARCH model can often deliver more precise estimates compared to more complex models.

⁹ We use the initial sample of $n=252$ observations corresponding to 1 year to obtain the first estimate of volatility on 1 January 2002. Please note that using approximately 1 year of data as a moving window is a standard choice in the literature that uses time-varying copulas for dependence modelling (see e.g. Aussenegg and Cech 2009; Ignatieva, Platen, and Rendek 2011; Kim 2014; Fengler and Okhrin 2016; Ignatieva and Trück 2016).

¹⁰ Note, that the first year of data (2001) corresponding to 252 observations is used in a moving window procedure to estimate time-dependent volatilities from the GARCH model.

¹¹ This result is also consistent with the estimated number of degrees of freedom for the Student-t copula of the pair (New Zealand, USD/NZD) – it corresponds to 168. A large number of Student-t degrees of freedom indicate that the distribution approaches Gaussian. For the other copula models the number of degrees of freedom of the Student-t copula corresponds to 11, 28, and 15 for (Canada, USD/CAD), (Norway, USD/NOK) and (Australia, USD/AUD), respectively.