A boosting approach to forecasting gold and silver returns: economic and statistical forecast evaluation

Abstract

We use a boosting algorithm to forecast the returns of gold and silver prices. We then study the implications of using different information criteria to terminate the boosting algorithm in terms of the statistical and economic performance of a forecasting model. Our findings demonstrate that information criteria that select parsimonious forecasting models perform better in statistical terms than information criteria that select relatively complex forecasting models, but this good performance does not necessarily survive an economic performance evaluation.

KEYWORDS:

• Precious metals
• forecasting
• boosting
• economic forecast evaluation

JEL classification:

• C53
• E44
• G02

Acknowledgements

We thank an anonymous reviewer for helpful comments. The usual disclaimer applies.

Notes

¹ See Vrugt et al. (2007), Pukthuanthong and Roll (2011), Reboredo (2013) and Pierdzioch, Risse, and Rohloff (2014a, 2014b), among others.

² Our description of the L2-boosting algorithm follows Pierdzioch, Risse, and Rohloff (2015) and, thus, is relatively brief. We estimate the boosting approach on demeaned data.

³ We follow the boosting literature and set .

⁴ Similar to the algorithm proposed by Mayr, Hofner, and Schmid (2012), we determine the final updating iteration, , that minimizes the by running the real-time boosting algorithm times. If satisfies , we stop. Otherwise, we set and run 10 further updating iterations, and so on. We stop when .

⁵ The matrix is updated using the recursion given in Bühlmann (2006) and Bühlmann and Hothorn (2007).

⁶ Most of the data are downloaded from the homepage of the Federal Reserve of St. Louis (see http://research.stlouisfed.org/fred2/), except the data on the S&P 500 dividend yields and the price of silver. The data on the dividends yields are from Robert J. Shiller’s web page, see http://www.econ.yale.edu/ shiller/ The data on the price of silver are from the web page http://www.lbma.org.uk/

⁷ We use an autocorrelation-corrected measure of realized volatility of daily returns (see Marquering and Verbeek 2004).

⁸ All computations were coded up using the Python programming language (version 3.4.1).

⁹ The historical mean of excess returns can be interpreted as a filter that prevents costly high-frequency trading. Pierdzioch, Risse, and Rohloff (2015) study the same trading rule (slightly different from how they describe the trading rule) so that results are directly comparable. Andrada-Félix and Fernándenz-Rodríguez (2008, 446) use a filter to ‘…avoid costly overactive technical trading rules derived from the boosting and the other learning methods…’.

¹⁰ Using the results for a training period of 48 months as an example, the active set identified by the comprises only approximately one third of the regressors selected by the .

¹¹ Deleting industrial production from the predictor variables improves the performance of the trading rule in the case of gold, but the gold market continues to be informationally efficient with respect to the remaining predictors (see Pierdzioch, Risse, and Rohloff 2015).