Residual-Based Garch Bootstrap and Second Order Asymptotic Refinement

Jeong, M. S.

doi:10.1017/s0266466616000104

Cited by 15 publications

(12 citation statements)

References 30 publications

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“…Pascual et al () exploit the recursive bootstrap for out‐of‐sample prediction. Jeong () considers asymptotic refinements of the recursive bootstrap for the GARCH(1,1) model by relying on Edgeworth expansions of t ‐statistics. Hall and Yao () propose a (‘ m out of n ’) recursive bootstrap in the heavy‐tailed case, where the distribution of the innovation is in the domain of attraction of a stable law.…”

Section: Introductionmentioning

confidence: 99%

The Fixed Volatility Bootstrap for a Class of Arch(q) Models

Cavaliere

Pedersen

Rahbek

2018

Journal Time Series Analysis

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The 'fixed regressor' -or 'fixed design' -bootstrap is usually considered in the context of classic regression, or conditional mean (autoregressive) models, see for example, Goncalves and Kilian, 2004). We consider here inference for a general class of (non)linear ARCH models of order q, based on a 'Fixed Volatility' bootstrap. In the Fixed Volatility bootstrap, the lagged variables in the conditional variance equation are kept fixed at their values in the original series, while the bootstrap innovations are, as is standard, resampled with replacement from the estimated residuals based on quasi maximum likelihood estimation. We derive a full asymptotic theory to establish validity for the Fixed Volatility bootstrap applied to Wald statistics for general restrictions on the parameters. A key feature of the Fixed Volatility bootstrap is that the bootstrap sample, conditional on the original data, is an independent sequence. Inspection of the proof of bootstrap validity reveals that such conditional independence simplifies the asymptotic analysis considerably. In contrast to other bootstrap methods, one does not have to take into account the conditional dependence structure of the bootstrap process itself. We also investigate the finite sample performance of the Fixed Volatility bootstrap by means of a small scale Monte Carlo experiment. We find evidence that for small sample sizes, the Fixed Volatility bootstrap test is superior to the asymptotic test, and to the recursive bootstrap-based test. For large samples, both bootstrap schemes and the asymptotic test share properties, as expected from the asymptotic theory. Its appealing theoretical properties, together with its good finite sample performance, suggest that the proposed Fixed Volatility bootstrap may be an important tool for the analysis of the bootstrap in more general volatility models. FIXED VOLATILITY BOOTSTRAP 921With respect to the fixed design bootstrap in regression models, which keep the conditional mean of the bootstrap data fixed among bootstrap repetitions, when dealing with volatility models the fixed design bootstrap maintains the conditional volatility fixed among bootstrap repetitions. This requires generating heteroskedasticity in the bootstrap data by recolouring the (conditionally i.i.d.) bootstrap innovations with some estimates of the volatility process which depend on the original data only. Hence, and in contrast to other bootstrap methods such as the recursive bootstrap, this method -which we label the 'Fixed Volatility' bootstrap in what follows -generates bootstrap samples which, conditional on the original data, features the same conditional volatility process.The recursive bootstrap for ARCH type model has been explored in the existing literature. For instance, Hidalgo and Zaffaroni (2007) propose a recursive bootstrap scheme for model specification tests in ARCH(∞) models. Corradi and Iglesias (2008) compare recursive bootstrap with block bootstrap methods in terms of asymptotic refinements. Pascual et al. (2006) exploit the rec...

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Section: Introductionmentioning

confidence: 99%

The Fixed Volatility Bootstrap for a Class of Arch(q) Models

Cavaliere

Pedersen

Rahbek

2018

Journal Time Series Analysis

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“…The recursive bootstrap scheme applied is standard in the context of GARCH models, see e.g. Hidalgo and Za¤aroni (2007) or Jeong (2017). The bootstrap algorithm is as follows:…”

Section: Bootstrap Algorithm For Testing Reduced Rankmentioning

confidence: 99%

Dynamic Conditional Eigenvalue GARCH

2019

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In this paper we consider a multivariate generalized autoregressive conditional heteroskedastic (GARCH) class of models where the eigenvalues of the conditional covariance matrix are time-varying. The proposed dynamics of the eigenvalues is based on applying the general theory of dynamic conditional score models as proposed by Creal, Koopman and Lucas (2013) and Harvey (2013). We denote the obtained GARCH model with dynamic conditional eigenvalues (and constant conditional eigenvectors) as the-GARCH model. We provide new results on asymptotic theory for the Gaussian QMLE, and for testing of reduced rank of the (G)ARCH loading matrices of the time-varying eigenvalues. The theory is applied to US data, where we …nd that the eigenvalue structure can be reduced similar to testing for the number in factors in volatility models.

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“…However, the sacrifice is worthwhile, as the second-order correctness is unachievable anyway because of the non-smooth objective function in step 2. Actually, in the literature, bootstrap methods with second-order correctness are still limited to the GARCH.1, 1/ model and are unavailable for the general GARCH model (Corradi and Iglesias, 2008;Jeong, 2017).…”

Section: A Mixed Bootstrapping Proceduresmentioning

confidence: 99%

Hybrid Quantile Regression Estimation for Time Series Models with Conditional Heteroscedasticity

Zheng

Zhu

et al. 2018

Journal of the Royal Statistical Society Series B: Statistical Methodology

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Summary Estimating conditional quantiles of financial time series is essential for risk management and many other financial applications. For time series models with conditional heteroscedasticity, although it is the generalized auto‐regressive conditional heteroscedastic (GARCH) model that has the greatest popularity, quantile regression for this model usually gives rise to non‐smooth non‐convex optimization which may hinder its practical feasibility. The paper proposes an easy‐to‐implement hybrid quantile regression estimation procedure for the GARCH model, where we overcome the intractability due to the square‐root form of the conditional quantile function by a simple transformation. The method takes advantage of the efficiency of the GARCH model in modelling the volatility globally as well as the flexibility of quantile regression in fitting quantiles at a specific level. The asymptotic distribution of the estimator is derived and is approximated by a novel mixed bootstrapping procedure. A portmanteau test is further constructed to check the adequacy of fitted conditional quantiles. The finite sample performance of the method is examined by simulation studies, and its advantages over existing methods are illustrated by an empirical application to value‐at‐risk forecasting.

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Residual-Based Garch Bootstrap and Second Order Asymptotic Refinement

Cited by 15 publications

References 30 publications

The Fixed Volatility Bootstrap for a Class of Arch(q) Models

The Fixed Volatility Bootstrap for a Class of Arch(q) Models

Dynamic Conditional Eigenvalue GARCH

Hybrid Quantile Regression Estimation for Time Series Models with Conditional Heteroscedasticity

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