Auto-Tail Dependence Coefficients for Stationary Solutions of Linear Stochastic Recurrence Equations and for GARCH(1, 1)
نویسنده
چکیده
We examine the auto-dependence structure of strictly stationary solutions of linear stochastic recurrence equations and of strictly stationary GARCH(1, 1) processes from the point of view of ordinary and generalized tail dependence coefficients. Since such processes can easily be of infinite variance, a substitute for the usual auto-correlation function is needed. Mathematics Subject Classification (2000). 41A60, 60G70, 62E20, 62P05, 62P20, 91B30, 91B84.
منابع مشابه
Continuous dependence on coefficients for stochastic evolution equations with multiplicative Levy Noise and monotone nonlinearity
Semilinear stochastic evolution equations with multiplicative L'evy noise are considered. The drift term is assumed to be monotone nonlinear and with linear growth. Unlike other similar works, we do not impose coercivity conditions on coefficients. We establish the continuous dependence of the mild solution with respect to initial conditions and also on coefficients. As corollaries of ...
متن کاملAsymptotic Behavior of the Sample Autocovariance and Autocorrelation Function of the Ar(1) Process with Arch(1) Errors
We study the sample autocovariance and autocorrelation function of the stationary AR(1) process with ARCH(1) errors. In contrast to ARCH and GARCH processes, AR(1) processes with ARCH(1) errors can not be transformed into solutions of linear stochastic recurrence equations. However, we show that they still belong to the class of stationary sequences with regular varying nite-dimensional distrib...
متن کاملQUASI-MAXIMUM-LIKELIHOOD ESTIMATION IN CONDITIONALLY HETEROSCEDASTIC TIME SERIES: A STOCHASTIC RECURRENCE EQUATIONS APPROACH By Daniel Straumann and Thomas Mikosch
This paper studies the quasi-maximum-likelihood estimator (QMLE) in a general conditionally heteroscedastic time series model of multiplicative form Xt = σtZt, where the unobservable volatility σt is a parametric function of (Xt−1, . . . ,Xt−p, σt−1, . . . , σt−q) for some p, q ≥ 0, and (Zt) is standardized i.i.d. noise. We assume that these models are solutions to stochastic recurrence equatio...
متن کاملQuasi-maximum-likelihood Estimation in Conditionally Heteroscedastic Time Series: a Stochastic Recurrence Equations Approach1 by Daniel Straumann
This paper studies the quasi-maximum-likelihood estimator (QMLE) in a general conditionally heteroscedastic time series model of multiplicative form Xt = σtZt , where the unobservable volatility σt is a parametric function of (Xt−1, . . . ,Xt−p,σt−1, . . . , σt−q) for some p,q ≥ 0, and (Zt ) is standardized i.i.d. noise. We assume that these models are solutions to stochastic recurrence equatio...
متن کاملThe Stationary - NonStationary Process and The Variable Roots Difference Equations
Stochastic, processes can be stationary or nonstationary. They depend on the magnitude of shocks. In other words, in an auto regressive model of order one, the estimated coefficient is not constant. Another finding of this paper is the relation between estimated coefficients and residuals. We also develop a catastrophe and chaos theory for change of roots from stationary to a nonstationary one ...
متن کامل