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GEOMETRIC ERGODICITY AND TRANSIENCE FOR NONLINEAR AUTOREGRESSIVE MONELS
Lee, Oe-Sook Korean Mathematical Society 1995 대한수학회논문집 Vol.10 No.2
We consider the $R^k$-valued $(k \geq 1)$ process ${X_n}$ generated by $X_n + 1 = f(X_n)+e_{n+1}$, where $f(x) = (h(x),x^{(1)},x^{(1)},\cdots,x{(k-1)})'$. We assume that h is a real-valued measuable function on $R^k$ and that $e_n = (e'_n,0,\cdot,0)'$ where ${e'_n}$ are independent and identically distributed random variables. We obtained a practical criteria guaranteeing a given process to be geometrically ergodic. Sufficient condition for transience is also given.
Geometric ergodicity and regular variation of stochastic unit root processes
Gawon Yoon 한국계량경제학회 2007 한국계량경제학회 학술대회 논문집 Vol.2007 No.2
This paper shows that stochastic unit root [STUR] processes, which are closely related to standard (fixed) unit root models and could be easily confused with them by standard unit root tests, are geometrically ergodic and regularly varying. On the contrary to the widely held belief, therefore, STUR processes are not long-memory, but short-memory. The phenomena of volatility-induced stationarity and long-memory are also discussed under STUR.
Geometric ergodicity for the augmented asymmetric power GARCH model
Park, S.,Kang, S.,Kim, S.,Lee, O. The Korean Data and Information Science Society 2011 한국데이터정보과학회지 Vol.22 No.6
An augmented asymmetric power GARCH(p, q) process is considered and conditions for stationarity, geometric ergodicity and ${\beta}$-mixing property with exponential decay rate are obtained.
Geometric ergodicity for the augmented asymmetric power GARCH model
박세나,강선영,김소희,이외숙 한국데이터정보과학회 2011 한국데이터정보과학회지 Vol.22 No.6
An augmented asymmetric power GARCH(p, q) process is considered and conditions for stationarity, geometric ergodicity and β-mixing property with exponential decay rate are obtained.
GEOMETRIC ERGODICITY AND EXISTENCE OF HIGHER-ORDER MOMENTS FOR DTARCH(p,q) PROCESS
Lee, Oe-Sook The Korean Statistical Society 2003 Journal of the Korean Statistical Society Vol.32 No.2
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.
Oe Sook Lee 한국데이터정보과학회 2011 한국데이터정보과학회지 Vol.22 No.2
We consider an asymmetric power transformed threshold GARCH(1.1) process and find sufficient conditions for the existence of a strictly stationary solution, geometric er-godicity and β-mixing property. Moments conditions are given. Box-Cox transformed threshold GARCH(1.1) process is also considered as a special case.
Lee, Oe-Sook The Korean Data and Information Science Society 2011 한국데이터정보과학회지 Vol.22 No.2
We consider an asymmetric power transformed threshold GARCH(1.1) process and find sufficient conditions for the existence of a strictly stationary solution, geometric ergodicity and ${\beta}$-mixing property. Moments conditions are given. Box-Cox transformed threshold GARCH(1.1) is also considered as a special case.
이외숙 한국데이터정보과학회 2011 한국데이터정보과학회지 Vol.22 No.2
We consider an asymmetric power transformed threshold GARCH(1.1) process and find sufficient conditions for the existence of a strictly stationary solution, geometric ergodicity and β-mixing property. Moments conditions are given. Box-Cox transformed threshold GARCH(1.1) process is also considered as a special case.
ON GEOMETRIC ERGODICITY OF AN AR-ARCH TYPE PROCESS WITH MARKOV SWITCHING
Lee, Oe-Sook,Shin, Dong-Wan Korean Mathematical Society 2004 대한수학회지 Vol.41 No.2
We consider a nonlinear AR-ARCH type process subject to Markov-switching and give sufficient conditions for geometric ergodicity of the process. Existence of moments is also obtained.
STATIONARY $\beta-MIXING$ FOR SUBDIAGONAL BILINEAR TIME SERIES
Lee Oe-Sook The Korean Statistical Society 2006 Journal of the Korean Statistical Society Vol.35 No.1
We consider the subdiagonal bilinear model and ARMA model with subdiagonal bilinear errors. Sufficient conditions for geometric ergodicity of associated Markov chains are derived by using results on generalized random coefficient autoregressive models and then strict stationarity and ,a-mixing property with exponential decay rates for given processes are obtained.