Stochastic Limit Theory

Davidson, James

doi:10.1093/0198774036.001.0001

Cited by 801 publications

(373 citation statements)

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“…Further, Z t is L p -bounded for all p 40 hence fs t g is L p -NED on fZ t g with size 1 2 for any p 4 0 by repeated application of Theorem 17.16 of Davidson (1994).…”

Section: Examplesmentioning

confidence: 99%

“…For future reference, we say some {z t } is L p -NED on fI t g or on fe t g with size l40 if for constants {d t } and coefficients fj l g, l l j l -0 as l-1 (Gallant and White, 1988;Davidson, 1994;Nze and Doukhan, 2004):…”

Section: Extremal-near Epoch Dependencementioning

confidence: 99%

“…In general NED does not imply mixing, or may hold when mixing is unknown. Examples include a stationary AR(1) with iid Bernoulli errors (Andrews, 1984;Davidson, 1994), and hyperbolic memory GARCH (Davidson, 2004). Further, very heavy tailed GARCH not known to be mixing or NED may be E-NED (Hill, forthcoming).…”

Section: þ: ð18þmentioning

confidence: 99%

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Extremal memory of stochastic volatility with an application to tail shape inference

Hill

2011

Journal of Statistical Planning and Inference

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a b s t r a c tWe characterize joint tails and tail dependence for a class of stochastic volatility processes. We derive the exact joint tail shape of multivariate stochastic volatility with innovations that have a regularly varying distribution tail. This is used to give four new characterizations of tail dependence. In three cases tail dependence is a non-trivial function of linear volatility memory parametrically represented by tail scales, while tail power indices do not provide any relevant dependence information. Although tail dependence is associated with linear volatility memory, tail dependence itself is nonlinear. In the fourth case a linear function of tail events and exceedances is linearly independent. Tail dependence falls in a class that implies the celebrated Hill (1975) tail index estimator is asymptotically normal, while linear independence of nonlinear tail arrays ensures the asymptotic variance is the same as the iid case. We illustrate the latter finding by simulation.

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“…Further, Z t is L p -bounded for all p 40 hence fs t g is L p -NED on fZ t g with size 1 2 for any p 4 0 by repeated application of Theorem 17.16 of Davidson (1994).…”

Section: Examplesmentioning

confidence: 99%

Section: Extremal-near Epoch Dependencementioning

confidence: 99%

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Extremal memory of stochastic volatility with an application to tail shape inference

Hill

2011

Journal of Statistical Planning and Inference

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“…The "coe¢ cients" # l gauge hyperbolic memory decay according to "size" , and geometric memory # l = o( l ) means size is arbitrarily large. The property characterizes linear and nonlinear distributed lags with hyperbolic or geometric memory, thin or thick tailed shocks, bilinear data, covariance stationary GARCH (Davidson 1994(Davidson , 2004 and SV (Hill 2011).…”

Section: Tail Memory: Events and Exceedancesmentioning

confidence: 99%

Tail and Nontail Memory With Applications to Extreme Value and Robust Statistics

Hill¹

2011

Econom. Theory

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New notions of tail and non-tail dependence are used to characterize separately extremal and non-extremal information, including tail log-exceedances and events, and tail-trimmed levels. We prove Near Epoch Dependence (McLeish 1975, Gallant andWhite 1988) and L 0 -Approximability (Pötscher and Prucha 1991) are equivalent for tail events and tail-trimmed levels, ensuring a Gaussian central limit theory for important extreme value and robust statistics under general conditions. We apply the theory to characterize the extremal and nonextremal memory properties of possibly very heavy tailed GARCH processes and distributed lags. This in turn is used to verify Gaussian limits for tail index, tail dependence and tail trimmed sums of these data, allowing for Gaussian asymptotics for a new Tail-Trimmed Least Squares estimator for heavy tailed processes.

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“…is finite for some δ > 0 (see Davidson, 1994, Theorem 12.10); and (iii) finally, the pointwise convergence of…”

Section: Lemma 4 Let Assumptions D F1 and I1 Hold And Assume That Tmentioning

confidence: 99%

General Trimmed Estimation: Robust Approach to Nonlinear and Limited Dependent Variable Models

Čı́žek

2008

Econom. Theory

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High breakdown-point regression estimators protect against large errors and data contamination. Motivated by some -the least trimmed squares and maximum trimmed likelihood estimators -we propose a general trimmed estimator, which unifies and extends many existing robust procedures. We derive here the consistency and rate of convergence of the proposed general trimmed estimator under mild β-mixing conditions and demonstrate its applicability in nonlinear regression, time series, limited dependent variable models, and panel data.

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Stochastic Limit Theory

Cited by 801 publications

References 0 publications

Extremal memory of stochastic volatility with an application to tail shape inference

Extremal memory of stochastic volatility with an application to tail shape inference

Tail and Nontail Memory With Applications to Extreme Value and Robust Statistics

General Trimmed Estimation: Robust Approach to Nonlinear and Limited Dependent Variable Models

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