On the Ergodicity of First‐Order Threshold Autoregressive Moving‐Average Processes

DOI10.1111/jtsa.12440zbMath1419.62222OpenAlexW2902078188MaRDI QIDQ5382479

Kung-Sik Chan, Greta Goracci

Publication date: 17 June 2019

Published in: Journal of Time Series Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1111/jtsa.12440

zbMATH Keywords

recurrenceMarkov chainstationarityirreducibilitynonlinear time seriesdrift criteria

Mathematics Subject Classification ID

Time series, auto-correlation, regression, etc. in statistics (GARCH) (62M10) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Time series analysis of dynamical systems (37M10)

Related Items (6)

The marginal distribution function of threshold-type processes with central symmetric innovations ⋮ An empirical study on the parsimony and descriptive power of TARMA models ⋮ Testing for Threshold Effects in the TARMA Framework ⋮ The Marginal Density of a TMA(1) Process ⋮ Revisiting the Canadian Lynx Time Series Analysis Through TARMA Models ⋮ Generalized threshold latent variable model

Cites Work

• Unnamed Item
• On the central limit theorem for an ergodic Markov chain
• Ergodicity and invertibility of threshold moving-average models
• A note on the invertibility of nonlinear ARMA models
• Markovian representation of stochastic processes and its application to the analysis of autoregressive moving average processes
• On the null recurrence and transience of a first-order SETAR model
• ON MARKOV-SWITCHING ARMA PROCESSES—STATIONARITY, EXISTENCE OF MOMENTS, AND GEOMETRIC ERGODICITY
• The existence of moments for stationary Markov chains
• On the use of the deterministic Lyapunov function for the ergodicity of stochastic difference equations
• A multiple-threshold AR(1) model
• ON THE EXISTENCE OF STATIONARY THRESHOLD AUTOREGRESSIVE MOVING-AVERAGE PROCESSES
• On strict stationarity and ergodicity of a non-linear ARMA model
• Criteria for classifying general Markov chains
• Ergodic Theorems for Discrete Time Stochastic Systems Using a Stochastic Lyapunov Function
• On the probabilistic properties of a double threshold ARMA conditional heteroskedastic model
• Towards a Unified Approach for Proving Geometric Ergodicity and Mixing Properties of Nonlinear Autoregressive Processes

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