• Journal of the Korean Statistical Society
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• v.32 no.2
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• pp.193-202
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• 2003

We consider a double threshold AR-ARCH type process and give sufficient conditions under which the higher-order moments exist. Geometric ergodicity and strict stationarity are also studied.

• Bulletin of the Korean Mathematical Society
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• v.43 no.4
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• pp.813-820
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• 2006

We consider a MAR model with ARCH type conditional heteroscedasticity. MAR-ARCH model can be derived as a smoothed version of the double threshold AR-ARCH model by adding a random error to the threshold parameters. Easy to check sufficient conditions for strict stationarity, ${\beta}-mixing$ property and existence of moments of the model are given via Markovian representation technique.

• Communications of the Korean Mathematical Society
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• v.17 no.2
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• pp.309-319
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• 2002

We consider the nonlinear autoregressive model with nonlinear ARCH errors, and find sufficient conditions for the existence of a strictly stationary process. New results are obtained, and known results are shown to emerge as special oases.