A note on a simple Markov bilinear stochastic process

DOI10.1016/S0167-7152(01)00192-4zbMath0999.60067MaRDI QIDQ1613001

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

Publication date: 5 September 2002

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

zbMATH Keywords

Markov processlimiting distributiongeometric ergodicitybilinear processARCH-type errorsdrift criteria

Mathematics Subject Classification ID

Discrete-time Markov processes on general state spaces (60J05)

Related Items (8)

Random autoregressive models: A structured overview ⋮ Regular variation of order 1 nonlinear AR-ARCH models ⋮ Two-stage weighted least squares estimation of nonstationary random coefficient autoregressions ⋮ Robustness of iterated function systems of Lipschitz maps ⋮ Blockwise bootstrap testing for stationarity ⋮ Modeling extreme negative returns using marked renewal Hawkes processes ⋮ On stationarity and ergodicity of the bilinear model with applications to GARCH models ⋮ On an independent and identically distributed mixture bilinear time-series model

Cites Work

• Markov chains and stochastic stability
• Sufficient conditions for ergodicity and recurrence of Markov chains on a general state space
• Verifying irreducibility and continuity of a nonlinear time series
• Stability and the Lyapounov exponent of threshold AR-ARCH models
• A NOTE ON A MARKOV BILINEAR STOCHASTIC PROCESS IN DISCRETE TIME
• A NOTE ON THE EXISTENCE OF STRICTLY STATIONARY SOLUTIONS TO BILINEAR EQUATIONS
• Stability of Markovian processes I: criteria for discrete-time Chains

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