Volatility forecasting of strategically linked commodity ETFs: gold-silver

Abstract

We apply heterogeneous autoregressive (HAR) models—including nine univariate, two multivariate and three combination models—to high-frequency data to predict the one-day forward volatilities of two strategically linked commodities, gold and silver. We provide evidence that it is difficult to beat the benchmark HAR model using univariate models and that, a much better strategy is to average the forecasts from many models. In addition, the forecasts are not improved by using volatilities from strategically linked commodities; thus, no volatility spillovers are detected. Interestingly, when the two strategically linked commodities are modelled together using the generalized HAR model, the forecasts are comparable to those of combination forecast models.

Keywords:

• Gold
• Silver
• HAR
• Forecasting
• Volatility spillovers

JEL Classification:

• C53
• Q02

Notes

¹ See e.g. Christie-David et al. (2000), Hammoudeh and Yuan (2008), Batten et al. (2010), Hammoudeh et al. (2011), Arouri et al. (2012), Hammoudeh et al. (2013), Chkili et al. (2014).

² One example is a factory for manufacturing connection strips, which contain gold.

³ Elder et al. (2012) study the impact of macroeconomic news on the realized volatility of gold, silver and copper. Caporin et al. (2015) find evidence of periodic volatility patterns matching the trading hours of the most active markets around-the-clock.

⁴ In the case of gold, 86% of the volume is traded in spot markets, and 10% of the volume is traded in futures markets. See Murray (2011) and GFMS (2014).

⁵ More sophisticated combination forecasts are possible. For example, Cheng and Hansen (2015) used factor models. However, we decided to use the benchmark approach in the combination forecast literature, the simple equally weighted average.

⁶ In equations (22) and (23), |·| denotes the cardinality of a set.

⁷ The test of Hansen et al. (2011) was performed using the procedures developed in the package of Bernardi and Catania (2014) for the R software package.

⁸ Alternatively, the HAR model might be the best specification; however, as we show later, that is certainly not true because combination forecasts and GHAR models outperform the benchmark.