Generalized Autoregressive Score Models with Applications

Department of Finance, VU University Amsterdam, and Duisenberg School of Finance, Amsterdam, Netherlands
Journal of Applied Econometrics (Impact Factor: 1.76). 08/2013; 28(5). DOI: 10.1002/jae.1279

ABSTRACT We propose a class of observation-driven time series models referred to as generalized autoregressive score (GAS) models. The mechanism to update the parameters over time is the scaled score of the likelihood function. This new approach provides a unified and consistent framework for introducing time-varying parameters in a wide class of nonlinear models. The GAS model encompasses other well-known models such as the generalized autoregressive conditional heteroskedasticity, autoregressive conditional duration, autoregressive conditional intensity, and Poisson count models with time-varying mean. In addition, our approach can lead to new formulations of observation-driven models. We illustrate our framework by introducing new model specifications for time-varying copula functions and for multivariate point processes with time-varying parameters. We study the models in detail and provide simulation and empirical evidence. Copyright © 2012 John Wiley & Sons, Ltd.

Download full-text


Available from: Andre Lucas, Aug 13, 2015
  • Source
    • "The alternative class of observation-driven models, by contrast, allows parameters to vary over time as functions of lagged dependent variable values and exogenous variables. By way of an example, the recently introduced Generalized Autoregressive Score (GAS) models (Creal et al., 2013), also known as Dynamic Conditional Score (DCS) models, also provide a general framework for modelling time variation in parametric models as functions of lagged dependent variables and exogenous variables (see also Creal et al., 2011). Thus, the GAS model is an observation-driven time series model assuming that we can compute the score of the parametric conditional observation density with respect to the time varying parameter. "
    [Show abstract] [Hide abstract]
    ABSTRACT: In many settings of empirical interest, time variation in the distribution parameters is important for capturing the dynamic behaviour of time series processes. Although the fitting of heavy tail distributions has become easier due to computational advances, the joint and explicit modelling of time-varying conditional skewness and kurtosis is a challenging task. We propose a class of parameter-driven time series models referred to as the generalized structural time series (GEST) model. The GEST model extends Gaussian structural time series models by a) allowing the distribution of the dependent variable to come from any parametric distribution, including highly skewed and kurtotic distributions (and mixed distributions) and b) expanding the systematic part of parameter-driven time series models to allow the joint and explicit modelling of all the distribution parameters as structural terms and (smoothed) functions of independent variables. The paper makes an applied contribution in the development of a fast local estimation algorithm for the evaluation of a penalised likelihood function to update the distribution parameters over time without the need for evaluation of a high-dimensional integral based on simulation methods.
  • Source
    • "For other possible choices of a we refer to Creal et al. (2013). "
    [Show abstract] [Hide abstract]
    ABSTRACT: This paper compares the Value--at--Risk (VaR) forecasts delivered by alternative model specifications using the Model Confidence Set (MCS) procedure recently developed by Hansen et al. (2011). The direct VaR estimate provided by the Conditional Autoregressive Value--at--Risk (CAViaR) models of Eengle and Manganelli (2004) are compared to those obtained by the popular Autoregressive Conditional Heteroskedasticity (ARCH) models of Engle (1982) and to the recently introduced Generalised Autoregressive Score (GAS) models of Creal et al. (2013) and Harvey (2013). The Hansen's procedure consists on a sequence of tests which permits to construct a set of "superior" models, where the null hypothesis of Equal Predictive Ability (EPA) is not rejected at a certain confidence level. Our empirical results, suggest that, after the Global Financial Crisis (GFC) of 2007-2008, highly non-linear volatility models deliver better VaR forecasts for the European countries as opposed to other regions. The R package MCS is introduced for performing the model comparisons whose main features are discussed throughout the paper.
  • Source
    • "Despite their popularity, they do not exhaust the set of models introduced for dynamic conditional volatility modelling which includes also the stochastic volatility models initially proposed by Taylor (1994) and extensively studied by Harvey and Shephard (1996) and Gallant, Hsieh, and Tauchen (1997) within the context of non–linear state space models. The family of dynamic conditional volatility models has been recently enlarged by the Dynamic Conditional Score models of Harvey (2013) and Creal, Koopman, and Lucas (2013) also known as Generalised Autoregressive Score models. The availability of such an enormous number of models raises the question of providing a statistical method or procedure that delivers the " best " models with respect to a given criterium. "
    [Show abstract] [Hide abstract]
    ABSTRACT: This paper presents the R package MCS which implements the Model Confidence Set (MCS) procedure recently developed by Hansen, Lunde, and Nason (2011). The Hansen's procedure consists on a sequence of tests which permits to construct a set of "superior" models, where the null hypothesis of Equal Predictive Ability (EPA) is not rejected at a certain confidence level. The EPA statistic tests is calculated for an arbitrary loss function, meaning that we could test models on various aspects, for example punctual forecasts. The relevance of the package is shown using an example which aims at illustrating in details the use of the functions provided by the package. The example compares the ability of different models belonging to the ARCH family to predict large financial losses. We also discuss the implementation of the ARCH–type models and their maximum likelihood estimation using the popular R package rugarch developed by Ghalanos (2014).
Show more