Stationarity and Ergodicity of Univariate Generalized Autoregressive Score Processes

2012

62 citations recorded by the source corpus.

This discussion paper led to a publication in the Electronic Journal of Statistics , 2014, 8, 1088-1112. We characterize the dynamic properties of Generalized Autoregressive Score (GAS) processes by identifying regions of the parameter space that imply stationarity and ergodicity. We show how these regions are affected by the choice of parameterization and scaling, which are key features of GAS models compared to other observation driven models. The Dudley entropy integral is used to ensure the non-degeneracy of such regions. Furthermore, we show how to obtain bounds for these regions in models for time-varying means, variances, or higher-order moments.

Subfields: Economics and Econometrics, Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/95b4c81572f08ca4af0e8696cc9afa9aadb1d167

Citations in the corpus

• Time‐Varying Transition Probabilities for Markov Regime Switching Models (2017, unknown): “The SE nature of the filtered sequence is also an important ingredient in obtaining proofs of consistency and asymptotic normality of the maximum likelihood estimator that rely on an application of laws of large numbers and central limit theorems; see Blasques et al. (2014) for more details. (2)We s”
• Feasible invertibility conditions and maximum likelihood estimation for observation-driven models (2018, unknown): “In the case of correct specification, stationarity and ergodicity can be checked studying the properties of the data generating process, see [7] for sufficient conditions for a wide class of observation driven processes.”
• Information Theoretic Optimality of Observation Driven Time Series Models (2014, unknown): “The consistency and asymptotic normality of the ML estimator to a pseudo-true parameter under model misspecification is ensured by the results of Blasques et al. (2014). We have verified that”
• Time-Varying Systemic Risk: Evidence From a Dynamic Copula Model of CDS Spreads (2018, unknown): “where sit @ log c(ut; t; z; z; ")=@ log it and t [ 1t; :::; Nt] : The dynamic copula model implied by equations (5) and (8) contains N + 2 parameters for the GAS dynamics, 3 parameters for the shape of the common and idiosyncratic variables, for a total of N + 5 parameters.”
• Maximum Likelihood Estimation for Generalized Autoregressive Score Models (2014, unknown): “We easily recognize (2) as the familiar GARCH model of Engle (1982) and Bollerslev (1986); see for example Straumann (2005), Straumann and Mikosch (2006) and Francq and Zaköıan (2010) for overviews of asymptotic results for the GARCH model. We refer to Creal et al. (2013) and Harvey (2013) for more ”