Academic journal article Journal of Economics and Finance

Improving (E)GARCH Forecasts with Robust Realized Range Measures: Evidence from International Markets

Academic journal article Journal of Economics and Finance

Improving (E)GARCH Forecasts with Robust Realized Range Measures: Evidence from International Markets

Article excerpt

(ProQuest: ... denotes formulae omitted.)

1 Introduction

GARCH type models are designed to capture and describe the volatility clusters exhibited by almost every asset return series. The number of publications motivated by the seminal works of Engle (1982) and Bollerslev (1986) is huge and after more than three decades of intense research on this topic, this number is still growing.

Despite the undeniable success of GARCH type models, many authors such as Jorion (1995), Franses and Van Dijk (1995), and Figlewski (1997) have reported the poor performance of their out-of-sample predictions. As discussed in Andersen et al. (2003), the information brought in by squared (absolute) past returns may not be enough to deal with situations where the volatility process quickly moves to a different level. On the other hand, as pointed out in Andersen and Bollerslev (1998), the above mentioned poor performance might be related to the choice of the proxy for the unobservable conditional variance. It is now well known that the squared return overestimates the true volatility process. As such, there is indeed room for improvements.

A simple method for improving GARCH forecasts is to incorporate a meaningful explanatory variable X in the GARCH volatility equation, giving rise to the socalled GARCH-X model (Engle 2002). The X variable could be the trading volume (Lamoureux and Lastrapes 1990), interest rates levels (Glosten et al. 1993), overnight returns (Gallo and Pacini 1998), macroeconomic variables (Flannery and Protopapadakis 2002) and recently several types of realized variance measures, see Engle and Gallo (2006) and Shephard and Sheppard (2010).

Empirical studies have shown that volatility estimates provided by the GARCH volatility equation augmented with lagged realized variance measures quickly respond to changes in the variance level, being much more effective than past squared returns. For example, see Zhang and Hu (2013) in the emerging Chinese stock market.

Although simple to implement and very appealing, the GARCH-X model suffers the drawback of being "incomplete" in the sense that it treats X as fixed, being thus unable to provide two or more steps ahead out-of-sample volatility forecasts (Hansen et al. 2012). Aiming to fix this problem, some models have recently been proposed in the literature, modeling the short memory in the series of realized measures. The multiplicative error model (MEM) of Engle and Gallo (2006), based on a proposal of Engle (2002), includes a latent volatility process for the realized measure X. The MEM framework is nested in the HEAVY model mathematical structure. The Realized GARCH (REALGARCH) of Hansen et al. (2012) links the conditional variance and the realized measure X in a VARMAI, q) structure. This model may be rewritten in an interesting reduced form, useful for forecasting, since the expression for predicting the volatility many steps ahead does not involve actual predictions of X, only requiring the X-coefficient estimate.

However, the REALGARCH model is computationally expensive and requires more skilled programmers and end users. There are many issues (left to the practitioner) to be taken into account such as the orders p and q to be considered, the underlying conditional distribution, conditions for algorithm convergence, and so on. More important, the original REALGARCH specification is not able to capture the long memory pattern usually exhibited by realized measures. The Huang et al. (2016) paper just recently came to our attention where a parsimonious variant of the model was derived by introducing the HAR specification of Corsi (2009) into the volatility dynamics.

Accordingly, in this paper we overcame this computational complexity by simply fitting separately the GARCH-X model to estimate the conditional variance a}, and the powerful ARFIMA(^, d, q) model to the realized measure X to capture its short and long range serial dependence. …

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