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Review of Managerial Science

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01.07.2015 | Original Paper

Prediction power of high-frequency based volatility measures: a model based approach

verfasst von: Alain Hamid

Erschienen in: Review of Managerial Science | Ausgabe 3/2015

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Abstract

This paper empirically compares the prediction power of popular high frequency measures of daily volatility, paying attention to different volatility models, loss functions and indices. We use data from 18 worldwide indices, covering a period from January 2000 till February 2013, and can show that the well known heterogeneous autoregressive (HAR) and mixed data sampling (MIDAS) models tend to prefer the same volatility measures, whereas a recently developed approach, relying on empirical similarity, shows some contrary results. The simultaneous consideration of volatility measures and models indicates that there is rather a best measure for one specific model, than for volatility prediction in general. This finding clarifies some contradicting results in existing literature on volatility forecasting and helps to derive straightforward recommendations for practitioners. Furthermore the usage of different loss functions for forecasting evaluation enables some interesting insights into the complex interplay between measure, model and loss function.

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See Henne et al. (2009) as an example for the application of volatility-based risk measures in the German stock market.

More precisely theoretical articles, for example Zhang et al. (2005), and Barndorff-Nielsen et al. (2008), usually examine which volatility estimator measures the unobservable volatility most exactly in the presence of distortions like noise and jumps in the price series. However the issues of measuring and predicting volatility exactly are highly related.

The idea in Patton and Sheppard (2009b) is to find the optimal combination of different measures in order to augment volatilityforecasts. However their empirical analysis includes results for various individual estimators, using the HAR model and focusing on the QLIKE distance.

See for example Ghysels et al. (2006), Patton and Sheppard (2009b) or Liu et al. (2012).

See Zhang et al. (2005) for an extensive description of the asymptotic properties of realized volatility and for possible efficiency gains through subsampling.

The two scale realized variance (TSRV) and multi-scale realized variance (MSRV) are further advancements of subsampled RV estimators, see Zhang et al. (2005) and Zhang (2006).

The optimal bandwidth \(H\) is determined using 20 min returns and end effects are not taken into account.

It should be mentioned that bipower variation in general depends on two parameters \(r\) and \(s\). The usage of \(r=s=1\) results in Eq. (8). In the case of no jumps bipower variation with this parameter choice converges to the same probability limit as realized variance.

See Pigorsch et al. (2012) for a recent overview on high-frequency based volatility measures.

More details on our data source are provided in Sect. 4.1.

See Gilboa and Schmeidler (1995, 1996a, b, 2003), Gilboa et al. (2002, 2006) and Billot et al. (2005, 2008) for an insight into the development and axiomatization of CBDT.

As reported in Ghysels et al. (2006) the weights are very close to zero after 25–30 days. Though a referee comment attracted our attention to the difference in lag lengths of the HAR and MIDAS models we keep the standard value of \(k^{\max }=50\) in the MIDAS model since the number of parameters is not influenced by the lag length and we want to analyse all models with their specifications commonly used in practice.

The usage of the Beta weight function, which is used in Ghysels et al. (2006), is computational intensive and we apply the Exponential Almon here, since results have been shown to be robust to a replacement between these two weight functions, as stated in Ghysels et al. (2005).

This example is borrowed from Gilboa et al. (2006).

There are numerous possibilities to specify the similarity function, some versions can be found in Golosnoy and Okhrin (2008), Guerdjikova (2008) or Lieberman (2010) amongst others. Moreover it is possible to involve asymmetric distance measures to account for Leverage effects as in Lieberman (2012).

Concerning the ES1 model we mean the normalized \(\theta _h\)-weights as in 20 and 21 when we talk about weights, whereas the estimated multiplicative parameters \(\left( \alpha ^{\left( d \right) }, \alpha ^{\left( w \right) } \text { and} \; \alpha ^{\left( m \right) } \right)\) denote the weights in the HAR model. These classes of weights are the natural counterparts in these two models.

We use a block bootstrap with block length 12 and 1,000 replications for each test.

We cannot involve absolute returns directly into our analysis, since this data is not available from our data source.

The heteroskedastic nature of volatility estimation leads to power deficiencies in tests using the MSE distance, see e.g. Patton (2011b).

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Titel: Prediction power of high-frequency based volatility measures: a model based approach
verfasst von: Alain Hamid
Publikationsdatum: 01.07.2015
Verlag: Springer Berlin Heidelberg
Erschienen in: Review of Managerial Science / Ausgabe 3/2015
Print ISSN: 1863-6683
Elektronische ISSN: 1863-6691
DOI: https://doi.org/10.1007/s11846-014-0130-z

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