## 2003), “Correcting the Errors: Volatility Forecast Evaluation Using High-Frequency Data and Realized Volatilities,” working paper

### Cached

### Download Links

Citations: | 50 - 10 self |

### BibTeX

@MISC{Andersen_2003),“correcting,

author = {Torben G. Andersen and Tim Bollerslev and Nour Meddahi},

title = {2003), “Correcting the Errors: Volatility Forecast Evaluation Using High-Frequency Data and Realized Volatilities,” working paper},

year = {}

}

### OpenURL

### Abstract

We develop general model-free adjustment procedures for the calculation of unbiased volatility loss functions based on practically feasible realized volatility benchmarks. The procedures, which exploit the recent non-parametric asymptotic distributional results in Barndorff-Nielsen and Shephard (2002a) along with new results explicitly allowing for leverage effects, are both easy-to-implement and highly accurate in empirically realistic situations. On properly accounting for the measurement errors in the volatility forecast evaluations reported in Andersen, Bollerslev, Diebold and Labys (2003), the adjustments result in markedly higher estimates for the true degree of return volatility predictability.

### Citations

736 |
Conditional Heteroskedasticity in Asset Returns: A New Approach
- Nelson
- 1991
(Show Context)
Citation Context ...s section formally rule out leverage effects. This is especially problematic for equity index returns, which are often found to be negatively correlated with future volatility (e.g., Black, 1976; and =-=Nelson, 1991-=-). Meanwhile, as noted above Barndorff-Nielsen and Shephard (2004b) have recently shown that the same approximate Central Limit Theorem in equation (6) remains valid in this situation, so that in part... |

688 | The pricing of options on assets with stochastic volatilities - Hull, White - 1987 |

426 |
Studies of stock price volatility changes
- Black
- 1976
(Show Context)
Citation Context ...ed in the previous section formally rule out leverage effects. This is especially problematic for equity index returns, which are often found to be negatively correlated with future volatility (e.g., =-=Black, 1976-=-; and Nelson, 1991). Meanwhile, as noted above Barndorff-Nielsen and Shephard (2004b) have recently shown that the same approximate Central Limit Theorem in equation (6) remains valid in this situatio... |

364 | Modeling and forecasting realized volatility - Andersen, Bollerslev, et al. |

361 | Answering the skeptics: yes, standard volatility models do provide accurate forecasts
- Andersen, Bollerslev
- 1998
(Show Context)
Citation Context ...olatility under quite general conditions, where importantly, the latter concept corresponds to the realization of the (cumulative) instantaneous variance process over the relevant horizon (see, e.g., =-=Andersen and Bollerslev, 1998-=-; Andersen, Bollerslev, Diebold and Labys, 2001; Barndorff-Nielsen and Shephard, 2001, 2002a,b, 2004a; Comte and Renault, 1998; along with the recent survey by Andersen, Bollerslev and Diebold, 2003).... |

300 | Non-Gaussian Ornstein–Uhlenbeckbased models and some of their uses in financial economics (with discussion - Barndorff-Nielsen, Shephard - 2001 |

205 | An Introduction to High-Frequency Finance - Dacorogna, Müller, et al. - 2001 |

199 |
Stochastic Integration and Differential Equations – A New Approach
- Protter
- 1990
(Show Context)
Citation Context ...ictable and of finite variation, and σt is a càd-làg process such that ∫ t 0 σ2 udu < ∞ a.s. for any t > 0. Consequently, σtdWt is a local martingale and log(St) a semi-martingale (see, for instance, =-=Protter, 1995-=-). 2.1 Integrated and Realized Volatility Although the sde in equation (1) is very convenient from a theoretical arbitrage-free pricing perspective, practical return calculations and volatility measur... |

167 | Arch models as diffusion approximations - Nelson - 1990 |

165 | 2002), “An Empirical Investigation of ContinuousTime Equity Return Models - Andersen, Benzoni, et al. |

158 | 2002, “Econometric Analysis of Realised Volatility and its Use in Estimating Stochastic Volatility Models - Barndorff-Nielsen, Shephard |

150 | A Closed Form Solution for Options with Stochastic Volatility, with -97Applications to Bond and Currency Options - Heston - 1993 |

133 | The distribution of exchange rate volatility - Andersen, Bollerslev, et al. - 2001 |

125 | Back to the future: Generating moment implication for continuous-time Markov processes - Hansen, Scheinkman - 1995 |

112 | Stochastic integration and differential equations. Second edition - Protter - 2004 |

104 | Econometric evaluation of linear macro-economic models - Chong, Hendry - 1986 |

102 | The Evaluation of Economic Forecasts - Mincer, Zarnowitz - 1969 |

96 |
A Theoretical Comparison Between Integrated and Realized Volatility
- Meddahi
- 2002
(Show Context)
Citation Context ... the numerical calculations in Andreou and Ghysels, 2002, and Bai, Russell, and Tiao, 2000). The exact form of the measurement error will, of course, depend on the assumed model structure (see, e.g., =-=Meddahi, 2002-=-, and Barndorff-Nielsen and Shephard, 2002a), but it will generally result in a downward bias in the estimated degree of predictability obtained through any forecast evaluation criterion that simply u... |

72 | Estimating stochastic volatility diffusion using conditional moments of integrated volatility - Bollerslev, Zhou - 2002 |

55 | How accurate is the asymptotic approximation to the distribution of realized variance - Barndorff-Nielsen, Shephard - 2005 |

54 | 2002), “Estimating Quadratic Variation Using Realised Variance - Barndorff-Nielsen, Shephard |

48 | An Eigenfunction Approach for Volatility Modeling,” Working Paper - Meddahi - 2001 |

44 |
Long Memory in Continuous Time Stochastic Volatility Models
- Comte, Renault
- 1998
(Show Context)
Citation Context ...nstantaneous variance process over the relevant horizon (see, e.g., Andersen and Bollerslev, 1998; Andersen, Bollerslev, Diebold and Labys, 2001; Barndorff-Nielsen and Shephard, 2001, 2002a,b, 2004a; =-=Comte and Renault, 1998-=-; along with the recent survey by Andersen, Bollerslev and Diebold, 2003). Unfortunately, market microstructure frictions distort the measurement of returns at the highest frequencies so that, e.g., t... |

43 | 2003a), “Realised Power Variation and Stochastic Volatility - Barndorff-Nielsen, Shephard |

32 | Tauchen (2003), “Alternative Models for Stock Price Dynamics - Chernov, Gallant, et al. |

31 | 2004, Econometric Analysis of Realized Covariation - Barndor¤-Nielsen, Shephard |

30 | Pictet (2001): An Introduction to High-Frequency Finance - Dacorogna, Gençay, et al. |

20 | Probability and Measure (Third Ed - BILLINGSLEY - 1995 |

19 | 2002), “Rolling-Sample Volatility Estimators: Some New Theoretical - Andreou, Ghysels |

18 | 2003), “Power Variation and Stochastic Volatility: A Review and Some New Results,” Journal of Applied Probability, forthcoming - Barndorff-Nielsen, Graversen, et al. |

17 | The Evaluation of Economic Forecasts,’’ in Economic Forecasts and Expectations - Mincer, Zarnowitz - 1969 |

14 | Empirical reverse engineering of the pricing kernel - Chernov - 2003 |

13 | La variation d’ordre p des semi-martingales. Zeitschrift fur Wahrscheinlichkeitstheorie und Verwandte Gebiete 36 - Lepingle - 1976 |

9 | Tiao (2000). Beyond mertons utopia: Effects of nonnormality and dependence on the precision of variance estimates using high-frequency financial data - Bai, Russell, et al. |

7 | Thórèmes limites pour des processus discrétisés - Becker - 1998 |

5 | A Feasible Central Limit Theory for Realised Volatility under Leverage.Manuscript - Barndorff-Nielson, Shephard - 2004 |

5 | 2003): “Option Pricing Models - GARCIA, GHYSELS, et al. |

5 | Probability with a view towards statistics, vol. I - Hoffman-Jørgensen - 1994 |

5 | 2003b), “The Evolving Effects - Andersen, Bollerslev, et al. |

3 |
Probability and Measure, Third Edition, New-York
- Billingsley
- 1994
(Show Context)
Citation Context ...hers. 7 Assuming that the underlying continuous time process satisfies a weak uniform integrability condition so that the consistency of RQt(h) for IQt also guarantees convergence in mean (see, e.g., =-=Billingsley, 1995-=-, page 338, and Hoffmann-Jørgensen, 1994, Section 5.13, page 376), it follows directly from the definition in equation (5) that, V ar[RVt(h)] = V ar[IVt] + V ar[Ut(h)] + 2Cov(Ut(h), IVt). Meanwhile, e... |

3 | 2000), “Principal Components and the Long Run,” unpublished manuscript - Chen, Hansen, et al. |

1 | 2003), “The Evolving Effects of Macroeconomic News on Global Stock, Bond and Foreign Exchange Markets,” unpublished manuscript - Andersen, Bollerslev, et al. |

1 | Empirical reverse Engineering of the Pricing Kernel - unknown authors - 2003 |

1 | 2000), “Principal Components and the Long Run,” unpublished manuscript - X, Scheinkman |

1 | MEDDAHI (2003): “Correcting the Errors: Volatility Forecast Evaluation Using High-Frequency Data and Realized Volatilities,” Unpublished - ANDERSEN, BOLLERSLEV, et al. |

1 | Econometric Evaluation of Linear Macro-Economic Models,” Review of Economic Studies - ANDERSEN, BOLLERSLEV, et al. - 1986 |

1 | Probability with a View Toward Statistics - HOFFMAN-JØRGENSEN - 1994 |