Inference in ARCH and GARCH models with heavy-tailed errors

By Peter Hall, Qiwei Yao. 2003

402 citations recorded by the source corpus.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/afe06e7eec73bc3d3b04a3fd5a43fb11b907d091

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Citations in the corpus

Autoregressive Conditional Heteroscedasticity (ARCH) Models: A Review (2004, background): “Hall and Yao (2003) showed that for heavy tailed innovations, the asymptotic distribution of quasi-maximum likelihood parameter estimators is non-normal and suggested percentile-t subsample bootstrap approximations to estimator distributions.”
Persistence and Kurtosis in GARCH and Stochastic Volatility Models (2004, background): “On the other hand, whether the distribution of «t is gaussian or has fat tails has implications mainly for inference on the models fitted to represent the dynamic evolution of volatility [see, e.g., Hall and Yao (2003)].”
High moment partial sum processes of residuals in GARCH models and their applications (2005, neutral): “MR0403125 [14] Hall, P. and Yao, Q. (2003).”
Quasi-maximum likelihood estimation in GARCH processes when some coefficients are equal to zero (2007, methodology): “Recent references dealing with the QML estimation of general GARCH(p, q) are the dissertation by Boussama [9], the monograph by Straumann [25] and the papers by Berkes and Horváth [4,3], Berkes, Horváth and Kokoszka [5], Hall and Yao [14] for GARCH models with heavy tailed errors, and Francq and Zak”
Break detection in the covariance structure of multivariate time series models (2009, background): “Theoretical results such as limit theorems for the sample autocorrelation function and the quasi-likelihood estimation of the unknown model parameters has for heavy-tailed univariate ARCH and GARCH processes been discussed in [21, 27, 41], among others.”
Self-weighted and local quasi-maximum likelihood estimators for ARMA-GARCH/IGARCH models (2007, background): “The same results were proved by Hall and Yao (2003) and Francq and Zakoı̈an (2004).”
Global self-weighted and local quasi-maximum exponential likelihood estimators for ARMA–GARCH/IGARCH models (2011, methodology): “ of the QMLE were obtained by Lee and Hansen (1994) and Lumsdaine (1996) for the GARCH(1,1) model, and by Berkes, Horva´th and Kokoszka (2003) and Francq and Zako¨ıan (2004) for the GARCH(r,s) model. Hall and Yao (2003) established the asymptotic theory of the QMLE for the GARCH model when Eε2 t &lt”
Least absolute deviation estimation for fractionally integrated autoregressive moving average time series models with conditional heteroscedasticity (2008, methodology): “This may reflect the fact that the heavier are the tails, the slower is the convergence rate of the maximum likelihood estimation, see Hall and Yao (2003).”
QML INFERENCE FOR VOLATILITY MODELS WITH COVARIATES (2015, background): “Hall and Yao (2003) showed that the asymptotic distribution of the QMLE is in general nonstandard when the score does not admit a second order moment.”
Bayesian Inference Methods for Univariate and Multivariate GARCH Models: A Survey (2014, neutral): “Finally, Hall & Yao (2003) add that the ML approach presents some limitations when the errors are heavy tailed, also the convergence rate is slow and the estimators may not be asymptotically Gaussian.”
ESTIMATION FOR A NONSTATIONARY SEMI-STRONG GARCH(1,1) MODEL WITH HEAVY-TAILED ERRORS (2009, methodology): “Then, as in Hall and Yao (2003), we have a−1n ( n(θ̃∗ − θ0) ,n1/2τ̃ ) d−→ ((W (1)κ ) ,W (2)κ ) , (11) where W (1)κ and W (2) κ are the same as in (9).”
Recent Advances in ARCH Modelling (2007, methodology): “…in the case of GARCH(p, q) and general p, q. Asymptotic properties of the corresponding estimators for general GARCH(p, q) models were established by Hall and Yao (2003), who used in (54) the following approximation of the conditional variance σ 2 t = Var(r t |r 1 , ..., r t−1 ): ˜ σ t (θ) 2 = α 0…”
Multivariate GARCH Models: A Survey (2003, methodology): “However, Hall and Yao (2003) show that the asymptotic distribution of the QMLE in the univariate GARCH(p, q) model is not normal, but is a multivariate stable distribution (with fatter tails than the normal), if the innovations are in the domain of attraction of a stable law with exponent smaller…”
Income distribution and inequality measurement: The problem of extreme values (2007, neutral): “However, the choice of the size of the bootstrap samples m can be a problem, particularly for skewed distributions (Hall and Yao 2003).”
Quantile Regression Estimator for GARCH Models (2013, methodology): “…Taylor (1999), Chernozhukov & Umantsev (2001), and Engle & Manganelli (2004), who used quantile regression to study the value at risk (VaR) of asset returns; Peng & Yao (2003), who applied a modified LAD estimation to generalized autoregressive conditional heteroscedasticity (GARCH) models.”