This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.View Full Document
Unformatted text preview: A FORECAST COMPARISON OF VOLATILITY MODELS: DOES ANYTHING BEAT A GARCH(1,1)? PETER R. HANSEN a * AND ASGER LUNDE b a Brown University, Department of Economics, Box B, Providence, RI 02912, USA b Aarhus School of Business, Department of Information Science, Denmark SUMMARY We compare 330 ARCH-type models in terms of their ability to describe the conditional vari- ance. The models are compared out-of-sample using DM-$ exchange rate data and IBM return data, where the latter is based on a new data set of realized variance. We find no evidence that a GARCH(1,1) is outperformed by more sophisticated models in our analysis of exchange rates, whereas the GARCH(1,1) is clearly inferior to models that can accommodate a leverage effect in our analysis of IBM returns. The models are compared with the test for superior predictive ability (SPA) and the reality check for data snooping (RC). Our empirical results show that the RC lacks power to an extent that makes it unable to distinguish ‘good’ and ‘bad’ models in our analysis. 1. INTRODUCTION The conditional variance of financial time-series is important for pricing derivatives, calculating measures of risk, and hedging. This has sparked an enormous interest in modelling the condi- tional variance and a large number of volatility models have been developed since the seminal paper of Engle (1982), see Poon & Granger (2003) for an extensive review and references. The aim of this paper is to examine whether sophisticated volatility models provide a better description of financial time-series than more parsimonious models. We address this question by comparing 330 GARCH-type models in terms of their ability to forecast the one-day-ahead conditional variance. The models are evaluated out-of-sample using six different loss functions, where the realized variance is substituted for the latent conditional variance. We use the test for * Corresponding author, email: [email protected] 1 A FORECAST COMPARISON OF VOLATILITY MODELS superior predictive ability (SPA) of Hansen (2001) and the reality check for data snooping (RC) by White (2000) to benchmark the 330 volatility models to the GARCH(1,1) of Bollerslev (1986). These tests have the advantage that they properly account for the full set of models, without the use of probability inequalities, such as the Bonferroni bound, that typically lead to conservative tests. We compare the models using daily DM-$ exchange rate data and daily IBM returns. There are three main findings of our empirical analysis: First, in the analysis of the exchange rate data we find no evidence that the GARCH(1,1) is inferior to other models, whereas the GARCH(1,1) is clearly outperformed in the analysis of IBM returns. Second, our model-space includes mod- els with many distinct characteristics that are interesting to compare, 1 and some interesting details emerge from the out-of-sample analysis. The models that perform well in the IBM return data are primarily those that can accommodate a leverage effect, and the best overall...
View Full Document