Value-at-Risk Prediction in R with the GAS Package

Abstract

GAS models have been recently proposed in time-series econometrics as valuable tools for signal extraction and prediction. This paper details how financial risk managers can use GAS models for Value-at-Risk (VaR) prediction using the novel GAS package for R. Details and code snippets for prediction, comparison and backtesting with GAS models are presented. An empirical application considering Dow Jones Index constituents investigates the VaR forecasting performance of GAS models.Recently, the new class of Score Driven (SD) models has been introduced by Creal et al. (2013) andHarvey (2013) offering an alternative to the Generalized AutoRegressive Heteroscedasticity (GARCH) framework pioneered by Bollerslev (1986) to model the conditional variance of financial returns. SD models are also referred to as Generalized Autoregressive Score (GAS) and Dynamic Conditional Score (DCS) models. In this paper, we follow the GAS nomenclature.Formally, in GAS models the vector of time-varying parameters, θ t , is updated through a dynamic equation based on the score of the conditional 2 probability density function of r t , f (·; θ t , ψ), i.e.:where s t is the scaled score of f (·; θ t , ψ) with respect to θ t , evaluated in r t ; see Creal et al. (2013). The coefficients κ, A and B control for the evolution of θ t and need to be estimated along with ψ from the data, usually by Maximum Likelihood. GAS models have been employed for a variety of applications in financial econometrics, mostly because they offer a link between the two most common frameworks to model volatility, namely: GARCH models and stochastic volatility (SV) models (Taylor, 1986). Indeed, while resorting on straightforward estimation procedures as for GARCH, they update models parameters accounting for the whole shape of the conditional distribution of the data, as in the SV context; see . Hence, they offer a good trade-of between ease of estimation and flexibility.Within the R statistical environment, the GAS package of Catania et al. (2016) allows practitioners 1 Sometimes VaR is defined with respect to the the loss variable l t = −r t , i.e., the negative of the return. Clearly, all the arguments of this paper can be easily adapted to this case. 2 The conditioning is intended with respect to the past observations r t−s (s > 0), however, for notational purposes, this is not always reported. arXiv:1611.06010v1 [q-fin.RM]

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