A Boosting Approach to Forecasting the Volatility of Gold-Price Fluctuations Under Flexible Loss

We use a boosting approach to study the time-varying out-of-sample informational content of various financial and macroeconomic variables for forecasting the volatility of gold-price fluctuations. We use an out-of-sample R2 statistic to evaluate forecasts as a function of the shape of a forecaster’s loss function. We show that, when compared to an autoregressive benchmark forecast, those forecasters tend to benefit from using predictions implied by the boosting approach who encounter a larger loss when underestimating rather than overestimating the future volatility of gold-price fluctuations. We use a simulation experiment to study the significance of this benefit.

[1]  Robert E. Wright,et al.  Short-run and long-run determinants of the price of gold , 2006 .

[2]  Christian Pierdzioch,et al.  Forecasting gold-price fluctuations: a real-time boosting approach , 2015 .

[3]  Francis X. Diebold,et al.  Modeling and Forecasting Realized Volatility , 2001 .

[4]  Peter Buhlmann,et al.  BOOSTING ALGORITHMS: REGULARIZATION, PREDICTION AND MODEL FITTING , 2007, 0804.2752.

[5]  P. Bühlmann Boosting for high-dimensional linear models , 2006 .

[6]  Jonathan A. Batten,et al.  On the Economic Determinants of the Gold-Inflation Relation , 2014 .

[7]  S. Bentes,et al.  Forecasting volatility in gold returns under the GARCH, IGARCH and FIGARCH frameworks: New evidence , 2015 .

[8]  N. Shephard,et al.  Estimating quadratic variation using realized variance , 2002 .

[9]  Christian Pierdzioch,et al.  The international business cycle and gold-price fluctuations , 2014 .

[10]  Klaus Wohlrabe,et al.  Assessing the Macroeconomic Forecasting Performance of Boosting - Evidence for the United States, the Euro Area, and Germany , 2013, SSRN Electronic Journal.

[11]  Andros Kourtellos,et al.  Volatility Forecast Combinations using Asymmetric Loss Functions , 2012 .

[12]  Serena Ng,et al.  Boosting diffusion indices , 2009 .

[13]  Herschel I. Grossman,et al.  Rational Bubbles in the Price of Gold , 1984 .

[14]  A. Cukierman,et al.  The Inflation Bias Revisited: Theory and Some International Evidence , 2003 .

[15]  Rob Bauer,et al.  Dynamic Commodity Timing Strategies , 2004 .

[16]  P. Bühlmann,et al.  Boosting with the L2-loss: regression and classification , 2001 .

[17]  J. Beckmann,et al.  Gold as an Inflation Hedge in a Time-Varying Coefficient Framework , 2012 .

[18]  Christian Pierdzioch,et al.  Economic and financial crises and the predictability of U.S. stock returns , 2008 .

[19]  Charlotte Christiansen,et al.  A Comprehensive Look at Financial Volatility Prediction by Economic Variables , 2011 .

[20]  The Macroeconomic Determinants of Volatility in Precious Metals Markets , 2008 .

[21]  Nikolay Robinzonov,et al.  Boosting the Anatomy of Volatility , 2012 .

[22]  R. Wright,et al.  Gold as an inflation hedge , 2004 .

[23]  Travis J. Berge FORECASTING DISCONNECTED EXCHANGE RATES , 2014 .

[24]  D. Baur,et al.  Institute for International Integration Studies Is Gold a Safe Haven? International Evidence Is Gold a Safe Haven? International Evidence Is Gold a Safe Haven? International Evidence , 2022 .

[25]  V. Akgiray Conditional Heteroscedasticity in Time Series of Stock Returns: Evidence and Forecasts , 1989 .

[26]  Christian Pierdzioch,et al.  On the efficiency of the gold market: Results of a real-time forecasting approach , 2014 .

[27]  Juan C. Reboredo,et al.  Is gold a safe haven or a hedge for the US dollar? Implications for risk management , 2013 .

[28]  K. West,et al.  A Utility Based Comparison of Some Models of Exchange Rate Volatility , 1992 .

[29]  P. Bühlmann,et al.  Volatility estimation with functional gradient descent for very high-dimensional financial time series , 2003 .

[30]  Christian Pierdzioch,et al.  A boosting approach to forecasting gold and silver returns: economic and statistical forecast evaluation , 2016 .

[31]  L. Blose,et al.  Gold prices, cost of carry, and expected inflation , 2010 .

[32]  Frederic S. Mishkin,et al.  Predicting U.S. Recessions: Financial Variables as Leading Indicators , 1995, Review of Economics and Statistics.

[33]  B. Lucey,et al.  A power GARCH examination of the gold market , 2007 .

[34]  Marno Verbeek,et al.  The Economic Value of Predicting Stock Index Returns and Volatility , 2001, Journal of Financial and Quantitative Analysis.

[35]  D. Ruppert The Elements of Statistical Learning: Data Mining, Inference, and Prediction , 2004 .

[36]  Christian Pierdzioch,et al.  A real-time quantile-regression approach to forecasting gold returns under asymmetric loss , 2015 .

[37]  Richard Roll,et al.  Gold and the Dollar (and the Euro, Pound, and Yen) , 2011 .

[38]  Christian Pierdzioch,et al.  Forecasting Stock Market Volatility with Macroeconomic Variables in Real Time , 2008, SSRN Electronic Journal.

[39]  Allan Timmermann,et al.  Estimation and Testing of Forecast Rationality under Flexible Loss , 2005 .

[40]  Andrew J. Patton Volatility Forecast Comparison Using Imperfect Volatility Proxies , 2006 .

[41]  Patrick M. Stephan,et al.  The Gold Price in Times of Crisis , 2013 .

[42]  Clifford M. Hurvich,et al.  Smoothing parameter selection in nonparametric regression using an improved Akaike information criterion , 1998 .

[43]  R. Shiller Human Behavior and the Efficiency of the Financial System , 1998 .

[44]  R. Thaler,et al.  A Survey of Behavioral Finance , 2002 .

[45]  P. Hansen,et al.  Consistent Ranking of Volatility Models , 2006 .

[46]  Trevor Hastie Comment: Boosting Algorithms: Regularization, Prediction and Model Fitting , 2007 .

[47]  Shawkat Hammoudeh,et al.  Metal volatility in presence of oil and interest rate shocks , 2008 .

[48]  Michael C. S. Wong,et al.  What moves the gold market , 2001 .

[49]  J. Fortune,et al.  The inflation rate of the price of gold, expected prices and interest rates , 1987 .

[50]  M. Kenward,et al.  An Introduction to the Bootstrap , 2007 .

[51]  M. Nicolau,et al.  Dynamic relationships between spot and futures prices. The case of energy and gold commodities , 2015 .

[52]  S. B. Thompson,et al.  Predicting Excess Stock Returns Out of Sample: Can Anything Beat the Historical Average? , 2008 .

[53]  Joseph P. Romano,et al.  The stationary bootstrap , 1994 .

[54]  J. Friedman Special Invited Paper-Additive logistic regression: A statistical view of boosting , 2000 .

[55]  Allan Timmermann,et al.  Biases in Macroeconomic Forecasts: Irrationality or Asymmetric Loss? , 2008 .

[56]  M. Schmid,et al.  The Importance of Knowing When to Stop , 2012, Methods of Information in Medicine.

[57]  R. Engle,et al.  Index-option pricing with stochastic volatility and the value of accurate variance forecasts , 1993 .

[58]  L. Sjaastad,et al.  The price of gold and the exchange rates: Once again , 2008 .

[59]  J. Friedman Greedy function approximation: A gradient boosting machine. , 2001 .

[60]  A. Timmermann,et al.  Predictability of Stock Returns: Robustness and Economic Significance , 1995 .

[61]  M. Wohar,et al.  Commodity volatility breaks , 2012 .

[62]  B. Lucey,et al.  Institute for International Integration Studies Is Gold a Hedge or a Safe Haven? an Analysis of Stocks, Bonds and Gold Is Gold a Hedge or a Safe Haven? an Analysis of Stocks, Bonds and Gold , 2022 .

[63]  Werner Kristjanpoller,et al.  Gold price volatility: A forecasting approach using the Artificial Neural Network-GARCH model , 2015, Expert Syst. Appl..

[64]  Christian Pierdzioch,et al.  The business cycle and the equity risk premium in real time , 2010 .

[65]  G. Kapetanios,et al.  Forecasting Large Datasets with Bayesian Reduced Rank Multivariate Models , 2009 .

[66]  M. Saqib Is Gold a Hedge or a Safe Haven? An Analysis of Stocks, Bonds, and Gold , 2010 .