Extremal behavior of the autoregressive process with ARCH(1) errors

DOI10.1016/S0304-4149(99)00073-3zbMath0991.62069OpenAlexW2087448895MaRDI QIDQ1613588

Milan Borkovec

Publication date: 29 August 2002

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0304-4149(99)00073-3

zbMATH Keywords

heavy tailsstrong mixingextremal indexautoregressive processescouplingcompound Poisson processesARCH modelextremal behaviorFrechet distributionheteroscedastic homogeneous Markov processesrecurrent Harris chainsseparating sequence

Mathematics Subject Classification ID

Time series, auto-correlation, regression, etc. in statistics (GARCH) (62M10) Extreme value theory; extremal stochastic processes (60G70) Statistics of extreme values; tail inference (62G32) Discrete-time Markov processes on general state spaces (60J05)

Related Items (16)

The tail of the stationary distribution of an autoregressive process with \(\text{ARCH}(1)\) errors ⋮ NON-STATIONARITY AND QUASI-MAXIMUM LIKELIHOOD ESTIMATION ON A DOUBLE AUTOREGRESSIVE MODEL ⋮ Extremal behaviour of models with multivariate random recurrence representation ⋮ Clustering of Markov chain exceedances ⋮ Regular variation of order 1 nonlinear AR-ARCH models ⋮ Evaluating the Lyapounov Exponent and Existence of Moments for Threshold AR-ARCH Models ⋮ The distribution of the maximum of a first order autoregressive process: The continuous case ⋮ High-level dependence in time series models ⋮ Tail estimates for stochastic fixed point equations via nonlinear renewal theory ⋮ Stability and the Lyapounov exponent of threshold AR-ARCH models ⋮ Testing for reduction to random walk in autoregressive conditional heteroskedasticity models ⋮ Local Estimation in AR Models with Nonparametric ARCH Errors ⋮ TAIL INDEX OF AN AR(1) MODEL WITH ARCH(1) ERRORS ⋮ Inference for the tail index of a GARCH(1,1) model and an AR(1) model with ARCH(1) errors ⋮ Double AR model without intercept: An alternative to modeling nonstationarity and heteroscedasticity ⋮ Sample path properties of an explosive double autoregressive model

Cites Work

• Extremes and related properties of random sequences and processes
• Extreme values for stationary and Markov sequences
• ARCH modeling in finance. A review of the theory and empirical evidence
• Random difference equations and renewal theory for products of random matrices
• Extremal behaviour of stationary Markov chains with applications
• Computing the extremal index of special Markov chains and queues
• Generalized autoregressive conditional heteroscedasticity
• Extremal behaviour of solutions to a stochastic difference equation with applications to ARCH processes
• On a stochastic difference equation and a representation of non–negative infinitely divisible random variables
• ARMA MODELS WITH ARCH ERRORS
• Maxima and exceedances of stationary Markov chains
• Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation
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