Asymptotic behaviour of the sample autocovariance and autocorrelation function of the \(AR(1)\) process with \(\text{ARCH}(1)\) errors

DOI10.2307/3318623zbMath0996.62077OpenAlexW2006863423MaRDI QIDQ1611570

Milan Borkovec

Publication date: 5 November 2002

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/3318623

zbMATH Keywords

point processesheavy tailsstrong mixingextremal indexgeometric ergodicityautoregressive processARCH modelmultivariate regular variationsample autocovariance function

Mathematics Subject Classification ID

Time series, auto-correlation, regression, etc. in statistics (GARCH) (62M10) Central limit and other weak theorems (60F05)

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The tail of the stationary distribution of an autoregressive process with \(\text{ARCH}(1)\) errors ⋮ Regular variation of order 1 nonlinear AR-ARCH models ⋮ Structure of a double autoregressive process driven by a hidden Markov chain ⋮ High-level dependence in time series models ⋮ Conditional variance estimation in heteroscedastic regression models ⋮ Local GMM estimation of time series models with conditional moment restrictions ⋮ EMPIRICAL-LIKELIHOOD-BASED CONFIDENCE INTERVALS FOR CONDITIONAL VARIANCE IN HETEROSKEDASTIC REGRESSION MODELS ⋮ Local Estimation in AR Models with Nonparametric ARCH Errors ⋮ TAIL INDEX OF AN AR(1) MODEL WITH ARCH(1) ERRORS ⋮ Local M-estimation for Conditional Variance in Heteroscedastic Regression Models ⋮ Inference for the tail index of a GARCH(1,1) model and an AR(1) model with ARCH(1) errors ⋮ Sample path properties of an explosive double autoregressive model

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