Least absolute deviations estimation for ARCH and GARCH models

By Liang Peng, Qiwei Yao. 2003

198 citations recorded by the source corpus.

Subfields: Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/66d232271acfc73caff05a2e65feca45933c09b7

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Citations in the corpus

GARCH Models (2010, unknown): “Under the moment assumption E 21 ∞ and some regularity assumptions, Peng and Yao (2003) show that there exists a local solution of (9.30) which is weakly consistent and asymptotically normal, with rate of convergence n1/2.”
Global self-weighted and local quasi-maximum exponential likelihood estimators for ARMA–GARCH/IGARCH models (2011, methodology): “We adopt the method in Lemma 4 of Pollard (1985). Let F = {ft (u) : ‖u‖ ≤ η} be a collection of functions indexed by u.”
Quasi-Maximum Likelihood Estimation of GARCH Models With Heavy-Tailed Likelihoods (2014, unknown): “Related works also include Peng and Yao (2003) and Huang, Wang, and Yao (2008) for LAD type of estimators.”
Optimal predictions of powers of conditionally heteroscedastic processes (2013, methodology): “In this section, we consider a special case of M-estimation: the LADE that was defined and studied by Peng and Yao (2003) in the context of GARCH models.”
Self-weighted and local quasi-maximum likelihood estimators for ARMA-GARCH/IGARCH models (2007, result): “We also refer to recent works by Peng and Yao (2003) and Berkes and Horvath (2004) in this area.”
Recent Advances in ARCH Modelling (2007, methodology): “1) was used by Robinson (1991) for testing for long memory in ARCH(∞). Note that (5.1) is only approximate because σ∗ t (2)(θ, b) is not equal to Eθ,b(r(2) t |rt−1, . . . , r1). The MLE of (θ0, b0) is defined by (θ̃, b̃) = arg max `N (θ, b), where the maximization is taken over a suitable subset of ”
Robust Regression Shrinkage and Consistent Variable Selection Through the LAD-Lasso (2007, background): “…effort has been devoted to establish the √ n -consistency and asymptotic normality of various LAD estimators (Bassett and Koenker 1978; Pollard 1991; Bloomﬁeld and Steiger 1983; Knight 1998; Peng and Yao 2003; Ling 2005), which left the important problem of robust model selection open for study.”
Modelling multivariate volatilities via conditionally uncorrelated components (2008, background): “Formally confidence sets for θj could also be constructed on the basis of asymptotic distributions of, for example, the least absolute deviation estimator θ̂j, which may be derived in a similar manner to that of Peng and Yao (2003).”
Interval estimation of value-at-risk based on GARCH models with heavy-tailed innovations (2007, methodology): “As shown in Peng and Yao (2003), we can re-parameterize the model (1) in such a way that the median of 2t is equal to 1 while keeping E( t) = 0 unchanged.”
Conditional variance estimation in heteroscedastic regression models (2009, background): “Peng and Yao (2003) investigated this effect in least absolute estimation of the parameters in ARCH and GARCH models.”
Robust estimates for GARCH models (2008, methodology): “Peng and Yao (2003) propose estimates for the GARCH model which are also variations of the LAD criterion.”
Self‐weighted least absolute deviation estimation for infinite variance autoregressive models (2005, methodology): “In the regression set-up, one advantage of LAD estimation is that it does not require any moment condition on the errors to obtain asymptotic normality (see Koenker and Bassett (1978)).”
Least absolute deviation estimation for fractionally integrated autoregressive moving average time series models with conditional heteroscedasticity (2008, methodology): “Peng and Yao (2003) considered a least absolute deviation estimation for the pure GARCH models under a finite second-order moment of ut only.”
ESTIMATION FOR A NONSTATIONARY SEMI-STRONG GARCH(1,1) MODEL WITH HEAVY-TAILED ERRORS (2009, methodology): “Peng and Yao (2003) show that, in contrast, the least absolute deviations estimator (LADE) is asymptotically Gaussian with convergence rate √ n provided Eε2t <+∞.”
UNIFORM BAHADUR REPRESENTATION FOR LOCAL POLYNOMIAL ESTIMATES OF M-REGRESSION AND ITS APPLICATION TO THE ADDITIVE MODEL (2007, unknown): “Peng and Yao (2003) have applied LAD estimation to parametric ARCH and GARCH models and have shown the superior robustness property of this procedure over Gaussian QMLE with regard to heavy tailed innovations.”
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.”