Stability and the Lyapounov exponent of threshold AR-ARCH models

DOI10.1214/105051604000000431zbMath1072.62069arXivmath/0503547OpenAlexW3106421898MaRDI QIDQ1769418

Daren B. H. Cline, Huay-min H. Pu

Publication date: 21 March 2005

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0503547

zbMATH Keywords

ergodicityMarkov chainARCHnonlinear time seriesLyapounov exponent

Mathematics Subject Classification ID

Time series, auto-correlation, regression, etc. in statistics (GARCH) (62M10) Stationary stochastic processes (60G10) Economic time series analysis (91B84) Discrete-time Markov processes on general state spaces (60J05)

Related Items (30)

A note on a simple Markov bilinear stochastic process ⋮ Self-exciting threshold binomial autoregressive processes ⋮ On Guaranteed Sequential Change Point Detection for TAR(1)/ARCH(1) Process ⋮ PIGGYBACKING THRESHOLD PROCESSES WITH A FINITE STATE MARKOV CHAIN ⋮ NON-STATIONARITY AND QUASI-MAXIMUM LIKELIHOOD ESTIMATION ON A DOUBLE AUTOREGRESSIVE MODEL ⋮ Asymmetric linear double autoregression ⋮ Regular variation of order 1 nonlinear AR-ARCH models ⋮ Asymptotic inference in multiple-threshold double autoregressive models ⋮ Evaluating the Lyapounov Exponent and Existence of Moments for Threshold AR-ARCH Models ⋮ Estimation of the empirical risk‐return relation: A generalized‐risk‐in‐mean model ⋮ On moving-average models with feedback ⋮ The Marginal Density of a TMA(1) Process ⋮ Maximum likelihood estimation for \(\alpha\)-stable double autoregressive models ⋮ Stationarity and ergodic properties for some observation-driven models in random environments ⋮ On the three‐step non‐Gaussian quasi‐maximum likelihood estimation of heavy‐tailed double autoregressive models ⋮ Stability of nonlinear AR-GARCH models ⋮ Semiparametric estimation of volatility: some models and complexity choice in the adaptive functional-coefficient class ⋮ A note on the geometric ergodicity of a nonlinear AR-ARCH model ⋮ Strict stationarity testing and GLAD estimation of double autoregressive models ⋮ The stationarity and invertibility of a class of nonlinear ARMA models ⋮ Stability of nonlinear stochastic recursions with application to nonlinear AR-GARCH models ⋮ TAIL AND NONTAIL MEMORY WITH APPLICATIONS TO EXTREME VALUE AND ROBUST STATISTICS ⋮ Stationarity and geometric ergodicity of a class of nonlinear ARCH models ⋮ Properties of some statistics for AR-ARCH model with application to technical analysis ⋮ On the least squares estimation of multiple-regime threshold autoregressive models ⋮ Non-standard inference for augmented double autoregressive models with null volatility coefficients ⋮ Estimation and Asymptotic Inference in the AR-ARCH Model ⋮ ASYMPTOTIC THEORY ON THE LEAST SQUARES ESTIMATION OF THRESHOLD MOVING-AVERAGE MODELS ⋮ Double AR model without intercept: An alternative to modeling nonstationarity and heteroscedasticity ⋮ Sample path properties of an explosive double autoregressive model

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Markov chains and stochastic stability
• Implicit renewal theory and tails of solutions of random equations
• Stationarity of GARCH processes and of some nonnegative time series
• Qualitative threshold ARCH models
• Strict stationarity of generalized autoregressive processes
• Random difference equations and renewal theory for products of random matrices
• Subadditive ergodic theory
• Verifying irreducibility and continuity of a nonlinear time series
• On a threshold autoregression with conditional heteroscedastic variances
• Extremal behavior of the autoregressive process with ARCH(1) errors
• Regular variation of GARCH processes.
• Tightness of products of random matrices and stability of linear stochastic systems
• Stability of perpetuities
• The tail of the stationary distribution of an autoregressive process with \(\text{ARCH}(1)\) errors
• On the use of the deterministic Lyapunov function for the ergodicity of stochastic difference equations
• The stochastic equation Y_n+1=A_nY_n + B_n with stationary coefficients
• ON ESTIMATING THRESHOLDS IN AUTOREGRESSIVE MODELS
• Modelling the persistence of conditional variances
• Iterated Random Functions
• Products of Random Matrices
• Non‐linear GARCH models for highly persistent volatility
• Threshold heteroskedastic models
• \(L_1\) geometric ergodicity of a multivariate nonlinear AR model with an ARCH term.
• Threshold \(\text{Arch}(1)\) processes: Asymptotic inference

This page was built for publication: Stability and the Lyapounov exponent of threshold AR-ARCH models