Forecasting realised volatility using ARFIMA and HAR models

Abstract

Recent literature provides mixed empirical evidence with respect to the forecasting performance of ARFIMA and HAR models. This paper compares the forecasting performance of both models using high frequency data of 100 stocks representing 10 business sectors for the period 2000-2010. We allow for different sectors, changing market conditions, variation in the sampling frequency and forecasting horizons. For the overall sample and using the 300 sec sampling frequency, the forecasting performance of both models is indistinguishable. However, differences arise under different market regimes, forecasting horizons and sampling frequencies. ARFIMA models are superior for the crisis and pre-crisis sub-samples. HAR forecasts are less sensitive to regime change and to longer forecasting horizons. Variations in forecasting performance could also be explained using differences in the levels of persistence underlying each model.

Keywords:

• High-frequency data
• Market conditions
• Market sectors
• Realised variance
• HAR
• ARFIMA

Acknowledgements

We would like to thank the participants of INFINITI Conference on International Finance (2013), Aix-en-Provence, France and the 7th International Conference on Computational and Financial Econometrics (2013). We would like to thank John Maheu and Rodrigo Hizmeri for their valuable comments. The authors are grateful to the Gulf One Lab for computational and Economic Research (GOLCER) for support.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Marwan Izzeldin http://orcid.org/0000-0003-1662-1584

Vasileios Pappas https://orcid.org/0000-0003-1885-4832

Mike Tsionas http://orcid.org/0000-0001-7254-6166

Notes

† Tick Data is a data base provides data on a commercial basis for futures, Index and equity markets. Tick Data is sourced from NYSE’s TAQ (Trade and Quote) database. Tick adjusts the TAQ database for ticker mapping, code filtering, price splits and dividend payments.

‡ https://www.tickdata.com/.

† Extensions of the HAR have appeared in the literature, see Andersen et al. (2011) and Corsi et al. (2010) for example. Also, papers using ARFIMA models have also modelled the short-memory process by setting $p>0$, see for example Martens et al. (2009). Nevertheless, we feel that for our research question the baseline models are more appropriate as they model the long-memory process of the realised volatility.

† We have used additional loss functions (MSE, QLIKE) in line with the arguments presented in Patton (2011), however these do not change the qualitative nature of our findings.

‡ Long-memory models have generally been found to be sensitive to structural breaks. Related to this, Granger and Joyeux, (1980) distinguish between genuine and spurious long memory processes where in the former case the property is inherent in the series, while in the latter it is caused by structural breaks. Several aspects of structural breaks and the long memory property of a series have been investigated by Granger and Terasvirta (1999) and Gourieroux and Jasiak (2001) among others.

† The Kruskal-Wallis Singed Rank Test is suitable in this context forecasts of 100 stocks based on two models (ARFIMA and HAR) are compared against a common benchmark.