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ON STRICT STATIONARITY OF NONLINEAR ARMA PROCESSES WITH NONLINEAR GARCH INNOVATIONS
Lee, O. The Korean Statistical Society 2007 Journal of the Korean Statistical Society Vol.36 No.2
We consider a nonlinear autoregressive moving average model with nonlinear GARCH errors, and find sufficient conditions for the existence of a strictly stationary solution of three related time series equations. We also consider a geometric ergodicity and functional central limit theorem for a nonlinear autoregressive model with nonlinear ARCH errors. The given model includes broad classes of nonlinear models. New results are obtained, and known results are shown to emerge as special cases.
이외숙,김경화 한국데이터정보과학회 2007 한국데이터정보과학회지 Vol.18 No.1
Nonlinear ARMA model is considered and easy-to-check sufficient condition for strict stationarity of without some irreducibility or continuity assumption is given. Threshold ARMA(p, q) and momentum threshold ARMA(p, q) models are examined as special cases.
On Strict Stationarity of Nonlinear ARMA Processeswith Nonlinear GARCH Innovations
이외숙 한국통계학회 2007 Journal of the Korean Statistical Society Vol.36 No.3
We consider a nonlinear autoregressive moving average model with non-linear GARCH errors, and nd sucient conditions for the existence of astrictly stationary solution of three related time series equations. We alsoconsider a geometric ergodicity and functional central limit theorem for anonlinear autoregressive model with nonlinear ARCH errors. The givenmodel includes broad classes of nonlinear models. New results are obtained,and known results are shown to emerge as special cases.
Lee, Oe-Sook,Kim, Kyung-Hwa Korean Data and Information Science Society 2007 한국데이터정보과학회지 Vol.18 No.1
Nonlinear ARMA model $X_n\;=\;h(X_{n-1},{\cdots},X_{n-p},e_{n-1},{\cdots},e_{n-p})+e_n$ is considered and easy-to-check sufficient condition for strict stationarity of {$X_n$} without some irreducibility or continuity assumption is given. Threshold ARMA(p, q) and momentum threshold ARMA(p, q) models are examined as special cases.