A multiple indicators model for volatility using intra-daily data

Abstract

Many ways exist to measure and model financial asset volatility. In principle, as the frequency of the data increases, the quality of forecasts should improve. Yet, there is no consensus about a "true" or "best" measure of volatility. In this paper we propose to jointly consider absolute daily returns, daily high-low range and daily realized volatility to develop a forecasting model based on their conditional dynamics. As all are non-negative series, we develop a multiplicative error model that is consistent and asymptotically normal under a wide range of specifications for the error density function. The estimation results show significant interactions between the indicators. We also show that one-month-ahead forecasts match well (both in and out of sample) the market-based volatility measure provided by an average of implied volatilities of index options as measured by VIX.

Nonparametric kernel density estimation near the boundary

“…, N t . Barndorff-Nielsen and Shephard (2002) show that, in the absence of noise and with the number of intraday returns approaching infinity, this basic estimator is consistent for Table 7 shows that the realized kernel estimates exhibit a similar persistence as trading volumes, which we account for by following Engle and Gallo (2006) and imposing a flexible MEM structure. Hence, we model the realized kernel value for day t, x (rk) t , analogously to (29), where the assumptions for the errors ε (rk) t remain the same, while a slightly different specification is chosen for the conditional mean µ (rk) t (see Appendix A).…”

“…As an alternative to the semiparametric approach, the plot also features the conditional density implied by maximum likelihood estimates of the MEM (29) assuming that the errors follow the widely-used gamma distribution (e.g. Engle and Gallo, 2006). The impact of the announcement on trading activity related to the Citigroup stock is clearly visible, as the conditional volume distribution for February 27 assigns considerably less weight to small transactions.…”

Predicting Time-Varying Parameters with Parameter-Driven and Observation-Driven Models

“…We consider dynamic count, intensity, duration, volatility and copula densities and focus on three approaches for modelling the time-varying parameters of interest: nonlinear non-Gaussian state space models as representatives of parameter-driven specifications; the flexible observation-driven generalised autoregressive score (GAS) class of Creal, Koopman, and Lucas (2012); and standard observation-driven models based on moments of the data, such as the generalised autoregressive conditional heteroscedasticity (GARCH) model of Engle (1982) and Bollerslev (1987), the autoregressive conditional duration (ACD) model of Engle and Russell (1998), and the multiplicative error models of Engle and Gallo (2006). For ease of reference, we group this latter set of models under the general heading of autoregressive conditional parameter (ACP) models.…”

Semiparametric Vector Mem

“…* This paper develops some ideas introduced in Cipollini, Engle and Gallo (2006) where estimation was based in the framework of estimating functions. Without implicating, we acknowledge comments by Nour Meddahi and Kevin Sheppard which led us to present the Estimating Functions approach in a more familiar GMM notation.…”