Cross-border exchanges and volatility forecasting

Abstract

We test for the performance of a series of volatility forecasting models (GARCH 1,1; EGARCH 1,1; CGARCH) in the context of several indices from the two oldest cross-border exchanges (Euronext; OMX). Our findings overall indicate that the EGARCH (1,1) model outperforms the other two, both before and after the outbreak of the global financial crisis. Controlling for the presence of feedback traders, the accuracy of the EGARCH (1,1) model is not affected, something further confirmed for both the pre and post crisis periods. Overall, ARCH effects can be found in the Euronext and OMX indices, with our results further indicating the presence of significant positive feedback trading in several of our tests.

Keywords:

• Volatility forecasting
• Exchange groups
• Feedback trading
• Global financial crisis

JEL Classification:

• G01
• G02
• G15
• G17

Notes

¹ Examples of GARCH model-specifications that allow for non-symmetrical dependencies are the Exponential GARCH by Nelson (1991) and the Threshold GARCH (also known as GJR GARCH) by Glosten, Jagannathan and Runkle (1993). Volatility persistence is another feature captured by this class of models; examples of long memory models include the Integrated GARCH by Engle and Bollerslev (1986), the Fractionally Integrated GARCH by Baillie et al. (1996), the Fractionally Integrated Exponential GARCH by Bollerslev and Mikkelsen (1996) and the Component GARCH by Engle and Lee (1999).

² The data for the time window of our study amounts to 3,330 daily observations for each of our sample indices.

³ Stationarity is achieved provided (α + β)(1 - ρ) + ρ < 1, which in turn requires ρ < 1 and (α + β) < 1. The transitory component then converges to zero with powers of α + β, whilst the long-run component converges on q_t with powers of ρ.

⁴ We obtained the earliest possible data for all our indices. Data prior to 1/1/2003 were not available for several of our indices; for consistency the start date of our sample is 1/1/2003.

⁵ For the pre-crisis period the in-sample (out-of-sample) period contains 1218 (261) daily observations.

⁶ For the post-crisis period the in-sample (out-of-sample) period contains 2174 (869) daily observations.

⁷ Examples of studies where the MZ regression is used as a volatility comparison measure are Andersen and Bollerslev (1998) and Ericsson (2017), amongst others.

⁸ Squared returns as a true volatility proxy are known to be a noisy measure of true volatility and often very low R² values are reported; see Andersen and Bollerslev (1998).

⁹ To test for the robustness of our results, smaller sub-samples restrictive to the European Crisis were also considered (2009–2013, 2010–2014) in which again the asymmetric EGARCH model performed the best.

¹⁰ We also forecast volatility on the premises of the TGARCH model (Glosten et al. 1993) as a second representative asymmetric model. Again here, EGARCH outperformed TGARCH in terms of forecast accuracy; results are not reported here for brevity reasons and are available from the authors upon request.

¹¹ The only exceptions here are the OMX Baltic 10 index results pre and post crisis, where is insignificant.

¹² See, for example, the evidence on this in the review paper on feedback trading by Koutmos (2014).