Volatility Forecast Comparison Using Imperfect Volatility Proxies

The use of a conditionally unbiased, but imperfect, volatility proxy can lead to undesirable outcomes in standard methods for comparing conditional variance forecasts. We derive necessary and sufficient conditions on functional form of the loss function for the ranking of competing volatility forecasts to be robust to the presence of noise in the volatility proxy, and derive some interesting special cases of this class of "robust" loss functions. We motivate the theory with analytical results on the distortions caused by some widely-used loss functions, when used with standard volatility proxies such as squared returns, the intra-daily range or realised volatility. The methods are illustrated with an application to the volatility of returns on IBM over the period 1993 to 2003.

[1]  Andrew J. Patton,et al.  Properties of Optimal Forecasts under Asymmetric Loss and Nonlinearity , 2007 .

[2]  Michael A. Salsburg,et al.  Modeling and Forecasting , 2007, Int. CMG Conference.

[3]  Q. Vuong,et al.  Efficientt Conditional Quantile Estimation: The Time Series Case , 2006 .

[4]  Kim Christensen,et al.  Realized Range-Based Estimation of Integrated Variance , 2006 .

[5]  Giuseppe Cavaliere.  Stochastic Volatility: Selected Readings , 2006 .

[6]  C. Granger,et al.  Handbook of Economic Forecasting , 2006 .

[7]  D. Dijk,et al.  Measuring volatility with the realized range , 2006 .

[8]  Miriam Maruöiaková.  Forecasting Financial Market Volatility , 2006 .

[9]  F. Diebold,et al.  Chapter 15 Volatility and Correlation Forecasting , 2006 .

[10]  Ken West,et al.  Chapter 3 Forecast Evaluation , 2006 .

[11]  F. Diebold,et al.  VOLATILITY AND CORRELATION FORECASTING , 2006 .

[12]  Kim Christensen,et al.  Asymptotic theory for range-based estimation of integrated variance of a continuous semi-martingale , 2005 .

[13]  Michael P. Clements.  Evaluating Econometric Forecasts of Economic and Financial Variables , 2005 .

[14]  C. H. Ted Hong.  Arbitrage Valuation of Variance Forecasts with Simulated Options , 2005 .

[15]  Torben G. Andersen,et al.  Correcting the errors: Volatility forecast evaluation using high-frequency data and realized volatilities , 2005 .

[16]  P. Hansen,et al.  A Forecast Comparison of Volatility Models: Does Anything Beat a Garch(1,1)? , 2004 .

[17]  B. Ripley,et al.  Robust Statistics , 2018, Wiley Series in Probability and Statistics.

[18]  P. Hansen,et al.  Consistent Ranking of Volatility Models , 2004 .

[19]  C. Granger,et al.  Forecasting Volatility in Financial Markets: A Review , 2003 .

[20]  Halbert White,et al.  Tests of Conditional Predictive Ability , 2003 .

[21]  N. Shephard,et al.  Econometric Analysis of Realized Covariation: High Frequency Based Covariance, Regression, and Correlation in Financial Economics , 2004 .

[22]  T. Bollerslev,et al.  Analytical Evaluation of Volatility Forecasts , 2002 .

[23]  Peter Christoffersen,et al.  Série Scientifique Scientific Series the Importance of the Loss Function in Option Valuation the Importance of the Loss Function in Option Valuation , 2022 .

[24]  N. Shephard,et al.  Econometric analysis of realized volatility and its use in estimating stochastic volatility models , 2002 .

[25]  P. Hansen,et al.  Technical Appendix A Forecast Comparison of Volatility Models: Does Anything Beat a GARCH(1,1)? , 2005 .

[26]  N. Meddahi,et al.  A theoretical comparison between integrated and realized volatility , 2002 .

[27]  Nour Meddahi.  A Theoretical Comparison Between Integrated andRealized Volatilities / A Theoretical Comparison Between Integrated and Realized Volatilities , 2001 .

[28]  Luca Benzoni,et al.  An Empirical Investigation of Continuous-Time Equity Return Models , 2001 .

[29]  F. Diebold,et al.  The distribution of realized stock return volatility , 2001 .

[30]  J. Detemple,et al.  Série Scientifique Scientific Series the Importance of the Loss Function in Option Pricing the Importance of the Loss Function in Option Pricing , 2022 .

[31]  Michael W. Brandt,et al.  Range-Based Estimation of Stochastic Volatility Models , 2001 .

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

[33]  Jonathan H. Wright,et al.  High-Frequency Data, Frequency Domain Inference, and Volatility Forecasting , 1999, Review of Economics and Statistics.

[34]  F. Diebold,et al.  The Distribution of Realized Exchange Rate Volatility , 2000 .

[35]  N. Shephard,et al.  Econometric analysis of realised volatility and its use in estimating stochastic volatility models , 2000 .

[36]  T. Bollerslev,et al.  Forecasting financial market volatility: Sample frequency vis-a-vis forecast horizon , 1999 .

[37]  T. Bollerslev,et al.  ANSWERING THE SKEPTICS: YES, STANDARD VOLATILITY MODELS DO PROVIDE ACCURATE FORECASTS* , 1998 .

[38]  F. Diebold,et al.  Optimal Prediction Under Asymmetric Loss , 1994, Econometric Theory.

[39]  David I. Harvey.  The evaluation of economic forecasts , 1997 .

[40]  Phelim P. Boyle,et al.  Advances in Futures and Options Research , 1996 .

[41]  F. Diebold,et al.  Forecast Evaluation and Combination , 1996 .

[42]  Christian Gourieroux,et al.  Statistics and econometric models , 1995 .

[43]  K. West,et al.  Asymptotic Inference about Predictive Ability , 1996 .

[44]  James D. Hamilton,et al.  Autoregressive conditional heteroskedasticity and changes in regime , 1994 .

[45]  Eric Ghysels,et al.  Periodic Autoregressive Conditional Heteroskedasticity , 1996 .

[46]  Tim Bollerslev,et al.  Chapter 49 Arch models , 1994 .

[47]  Daniel B. Nelson,et al.  ARCH MODELS a , 1994 .

[48]  Halbert White,et al.  Estimation, inference, and specification analysis , 1996 .

[49]  R. Engle.  On the limitations of comṕaring mean square forecast errors: Comment , 1993 .

[50]  Michael P. Clements,et al.  On the limitations of comparing mean square forecast errors , 1993 .

[51]  Christopher G. Lamoureux,et al.  Forecasting Stock-Return Variance: Toward an Understanding of Stochastic Implied Volatilities , 1993 .

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

[53]  P. Burridge,et al.  A Very Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix , 1991 .

[54]  Adrian Pagan,et al.  Alternative Models for Conditional Volatil-ity , 1990 .

[55]  Adrian Pagan,et al.  Alternative Models for Conditional Stock Volatility , 1989 .

[56]  Consistent M-estimators in a Semi-parametric model (1), no. 8720 , 1987 .

[57]  Gourieroux Christian,et al.  Consistent m-estimators in a semi-parametric model , 1987 .

[58]  W. Newey,et al.  A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelationconsistent Covariance Matrix , 1986 .

[59]  C. Gouriéroux,et al.  PSEUDO MAXIMUM LIKELIHOOD METHODS: THEORY , 1984 .

[60]  Walter N. Torous,et al.  The Maximum Likelihood Estimation of Security Price Volatility: Theory, Evidence, and Application to Option Pricing , 1984 .

[61]  R. Engle.  Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation , 1982 .

[62]  M. Parkinson.  The Extreme Value Method for Estimating the Variance of the Rate of Return , 1980 .

[63]  M. J. Klass,et al.  On the Estimation of Security Price Volatilities from Historical Data , 1980 .

[64]  J. Stiglitz,et al.  Economic Forecasts and Expectations. , 1971 .

[65]  Clive W. J. Granger,et al.  Prediction with a generalized cost of error function , 1969 .

[66]  H. Theil,et al.  Economic Forecasts and Policy. , 1959 .

[67]  W. Feller.  The Asymptotic Distribution of the Range of Sums of Independent Random Variables , 1951 .

[68]  A. Cowles.  Can Stock Market Forecasters Forecast , 1933 .

[69]  K. West,et al.  FORECAST EVALUATION , 2022 .

[70]  P. Phillips.  BOOTSTRAPPING I(1) DATA BY PETER C. B. PHILLIPS COWLES FOUNDATION PAPER NO. 1310 COWLES FOUNDATION FOR RESEARCH IN ECONOMICS , 2010 .