The SPA test always finds the ARCH(1) model to be inferior, which shows that the SPA test has power in these applications and is therefore more likely to detect superior models when such exist. In fact, the RC even suggests that an ARCH(1) may be the best model in many cases, which does not conform with the existing empirical evidence. This makes an important difference in our application, because the RC cannot detect that the GARCH(1,1) is significantly outperformed by other models in the analysis of IBM returns. Third, our empirical analysis shows that the RC has less power than the SPA test. The different mean specifications, zero-mean, constant mean and GARCH-in-mean, result in almost identical performances. While the t-distributed specification of standardized returns generally leads to a better average performance than the Gaussian in the analysis of exchange rates, the opposite is the case in our analysis of IBM returns. Other aspects of the volatility models are more ambiguous. The models that perform well in the IBM return data are primarily those that can accommodate a leverage effect, and the best overall performance is achieved by the A-PARCH(2,2) model of Ding et al.
Second, our model space includes models with many distinct characteristics that are interesting to compare, 1 and some interesting details emerge from the out-of-sample 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. There are three main findings of our empirical analysis. We compare the models using daily DM–$ exchange rate data and daily IBM returns.
#LOOPMAN ROYALE BEAT FULL#
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 use the test for 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). The models are evaluated out-of-sample using six different loss functions, where the realized variance is substituted for the latent conditional variance.
We address this question by comparing 330 GARCH-type models in terms of their ability to forecast the one-day-ahead conditional variance.
#LOOPMAN ROYALE BEAT SERIES#
The aim of this paper is to examine whether sophisticated volatility models provide a better description of financial time series than more parsimonious models. This has sparked an enormous interest in modelling the conditional variance and a large number of volatility models have been developed since the seminal paper of Engle ( 1982) see Poon and Granger ( 2003) for an extensive review and references. The conditional variance of financial time series is important for pricing derivatives, calculating measures of risk, and hedging.
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