• 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.

• 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.

• Journal of the Korean Statistical Society
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• v.35 no.1
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• pp.79-90
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• 2006

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.

• Journal of the Korean Society of Hazard Mitigation
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• v.7 no.5
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• pp.89-97
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• 2007

This study proposed new simple methodologies for testing the stationarity of rainfall quantiles, and applied to the rainfall data at Seoul. The methodologies in this study are based on the analysis of frequency change of rainfall quantiles, different from previous studies like Ahn et al. (2001) who analyzed the change of rainfall quantiles themselves. The different types of methodologies are proposed in this study; one is to evaluate the occurrence frequency of rainfall with its return period more than the data length, and the other is to evaluate the effect of new observation on the highest rainfall data recorded. The application of these methodologies shows that the rainfall quantiles at Seoul have no significant proof leading their non-stationarity.

• Journal of the Korean Institute of Telematics and Electronics S
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• v.34S no.2
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• pp.71-78
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• 1997

Markov random field models have extensively used in applications such as image segmentation and image restoration. In this paper, we consider the relation between the stationarity of parameters and the synthesized images for gauss-markov rnadom field which has the most popularly used among many MRF models. GMRF model, which is both wide-sense Markov and strict-sense markov, has AR representations and is also a kind of gibbs distribution. Therefore, we may approach in aspect of both AR models and gibbs models. We show the relation between the stationarity of parameters and the images which are synthesized by two approaching methods and derive the stationary regions of parameters in 1st order and isotropic 2nd order case.

• Journal of the Korean Statistical Society
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• v.36 no.2
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• pp.183-200
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• 2007

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.

• Journal of the Korean Statistical Society
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• v.28 no.4
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• pp.503-513
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• 1999

The Bayes factor for the identification of stationary ARM(p,q) models is exactly computed using the Monte Carlo method. As priors are used the uniform prior for (\ulcorner,\ulcorner) in its stationarity-invertibility region, the Jefferys prior and the reference prior that are noninformative improper for ($\mu$,$\sigma$\ulcorner).

• Journal of the Korean Data and Information Science Society
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• v.21 no.6
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• pp.1311-1317
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• 2010

A continuous time asymmetric power GARCH(1,1) model is suggested, based on a single background driving L$\'{e}$vy process. The stochastic differential equation for the given process is derived and the strict stationarity and kth order moment conditions are examined.

• Journal of the Korean Data and Information Science Society
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• v.22 no.6
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• pp.1233-1240
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• 2011

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.

• The Korean Journal of Applied Statistics
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• v.36 no.2
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• pp.129-139
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• 2023

Forecasting volatility is essential to avoiding the risk caused by the uncertainties of an financial asset. Complicated financial volatility features such as ambiguity between non-stationarity and stationarity, asymmetry, long-memory, sudden fairly large values like outliers bring great challenges to volatility forecasts. In order to address such complicated features implicity, we consider machine leaning models such as LSTM (1997) and GRU (2014), which are known to be suitable for existing time series forecasting. However, there are the problems of vanishing gradients, of enormous amount of computation, and of a huge memory. To solve these problems, a causal temporal convolutional network (TCN) model, an advanced form of 1D CNN, is also applied. It is confirmed that the overall forecasting power of TCN model is higher than that of the RNN models in forecasting VIX, VXD, and VXN, the daily volatility indices of S&P 500, DJIA, Nasdaq, respectively.