Commodity prices at the quantiles

Abstract

Commodity price stationarity grants good predictability and effective policy intervention. The analysis at the quantiles shows that prices are stationary at the lower but not at the higher quantiles. The non-stationarity of commodity prices is often related to the behavior of the US exchange rate series. Quantile regression estimates show changing coefficients across quantiles. This signals the presence of heteroscedasticity in the series. Stationarity holds throughout once the series are corrected for heteroscedasticity, exchange rate included. This finding weakens the claim that exchange rates cause persistence in commodity prices. The price-exchange rate correlation mirrors their common heteroscedasticity. The correlation declines in the cleaned/homoscedastic series.

KEYWORDS:

• Unit root tests
• quantile regression
• heteroscedasticity

Compliance with ethical standards

This research has not been funded. The author has no conflict of interest. This article does not contain any study with human participants or animals performed by the author.

Notes

Notes

¹ The annual data in Presno, Landajo, and Fernández (2014) cover the period 1870–990, while the monthly data in Enders and Holt (2012) are for years 1960–2010.

² For the general quantile regression, computed at the quantile 0$\le \theta \le 1$, the ρ-function becomes $\rho (e_t)=e_t$ ($\theta -1(e_t\le 0)$).

³ The use of the White heteroskedasticity consistent covariance matrix (HCCM) estimator would reduce the number of rejections in the Dickey–Fuller test, since HCCM yields generally larger estimates of the coefficient standard error.

⁴ The inclusion of a time trend or the exclusion of the constant term would further reduce the number of stationary series in the Dickey–Fuller test.

⁵ A slightly different method to clean the data would divide the dependent variable by $g_t=\sqrt{{\widehat{e}}_t^2/\mathit{var}({\widehat{e}}_t)}$. The latter is a standard approach to clean heteroskedastic data, which considers only the changing part of the variance. The $y_t/g_t$ transformation yields results that are comparable to the $y_t/\left|{\widehat{e}}_t\right|$ case.

⁶ Ideally, the correction for heteroskedasticity could be applied to homoscedastic series as well. Following Beare (2016), applying the heteroskedasticity correction to homoscedastic series does not cause any loss in power.

⁷ The source of the exchange rate (series ID: TWEXMANL) is the Federal Reserve Bank of St. Louis Economic Research Database (FRED: http://research.stlouisfed.org/fred2/).