• Journal of the Korean Data and Information Science Society
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• 제18권1호
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• pp.211-218
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• 2007

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.

• Communications for Statistical Applications and Methods
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• 제20권4호
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• pp.339-345
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• 2013

In this paper, we give a tractable sufficient condition for functional central limit theorem to hold in Markov switching ARMA (p, q) model.

• Journal of applied mathematics & informatics
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• 제5권2호
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• pp.373-382
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• 1998

Most of the works in Time Series Analysis are based on the Auto Regressive Integrated Moving Average (ARIMA) models presented by Box and Jeckins(1976). If the data exhibits no ap-parent deviation from stationarity and if it has rapidly decreasing autocorrelation function then a suitable ARIMA(p,q) model is fit to the given data. Selection of the orders of p and q is one of the crucial steps in Time Series Analysis. Most of the methods to determine p and q are based on the autocorrelation function and partial autocor-relation function as suggested by Box and Jenkins (1976). many new techniques have emerged in the literature and it is found that most of them are over very little use in determining the orders of p and q when both of them are non-zero. The Durbin-Levinson algorithm and Innovation algorithm (Brockwell and Davis 1987) are used as recur-sive methods for computing best linear predictors in an ARMA(p,q)model. These algorithms are modified to yield an effective method for ARMA model identification so that the values of order p and q can be determined from them. The new method is developed and its validity and usefulness is illustrated by many theoretical examples. This method can also be applied to an real world data.

• Journal of the Korean Statistical Society
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• 제21권1호
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• pp.47-58
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• 1992

The autocorrelation function structures of bilinear time series model BL(p, q, r, s), $r \geq s$ are obtained and shown to be analogous to those of ARMA(p, l), l=max(q, s). Simulation studies are performed to investigate the adequacy of Akaike information criteria for identification between ARMA(p, l) and BL(p, q, r, s) models and for determination of orders of BL(p, q, r, s) models. It is suggested that the model of having minimum Akaike information criteria is selected for a suitable model.

• Journal of applied mathematics & informatics
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• 제4권1호
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• pp.135-135
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• 1997

Times series modeling plays an important role in the field of engineering, Statistics, Biomedicine etc. Model identification is one of crucial steps in the modeling of an AutoRegreesive Moving Average(ARMA(p, q)) process for real world problems. Many techniques have been developed in the literature (Salas et al., McLeod et al. etc.) for the identification of an ARMA(p, q) Model. In this paper, a new technique called The Generalised Parameters Technique is formulated for seasonal and non-seasonal ARMA model identification. This technique is very simple and can e applied to any given time series. Initial estimates of the AR parameters of the ARMA model are also obtained by this method. This model identification technique is validated through many theoretical and simulated examples.

• 대한수학회논문집
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• 제21권3호
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• pp.533-541
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• 2006

We consider a autoregressive moving average process of order p and q with Markov switching coefficients and find sufficient conditions for irreducibility of the process. Identifying small sets is also examined.

• 응용통계연구
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• 제28권3호
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• pp.511-527
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• 2015

ARMA(p, q) 모형 분석에서 분산 안정화 또는 정규화를 위해 멱변환(power transformation)이 사용된다. 변환된 자료를 이용하여 분석이 이루어지며 원 자료의 예측을 위해 재변환이 사용된다. 이때 흔히 변환된 자료 분석에서 얻어진 예측값의 역함수 값이 원자료 예측값으로 사용되지만 이는 편향이 있는 것으로 알려져 있다. 이를 해결하기 위해 로그 변환의 경우 Granger과 Newbold (1976)는 로그-정규분포의 기댓값을 이용할 것을 제안하였다. 본 연구에서는 모의실험을 통하여 제곱근 변환과 로그 변환 후 재변환을 사용할 때 예측값으로 기댓값의 역함수를 이용하는 방법과 역함수의 기댓값을 사용하였을 때의 추정의 결과를 모의실험을 통하여 비교하였다.

• Journal of the Korean Statistical Society
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• 제27권2호
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• pp.165-187
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• 1998

Shin and Sarkar (1993, 1994) studied the problem of testing for a unit root in an AR(p) signal observed with MA(q) noise when the MA parameters are known. In this paper we consider the case when the MA parameters are unknown and to be estimated. Test statistics are defined using unit root parameter estimates based on three different estimation methods of Hannan and Rissanen (1982), Kohn (1979) and Shin and Sarkar (1995). An AR(p) process contaminated by MA(q) noise is a .estricted ARMA model, for which Shin and Sarkar (1995) derived an easy-to-compute Newton- Raphson estimator The two-stage estimation p.ocedu.e of Hannan and Rissanen (1982) is used to compute initial parameter estimates in implementing the iterative estimation methods of both Shin and Sarkar (1995) and Kohn (1979). In a simulation study we compare the relative performance of these unit root tests with respect to both size and power for p=q=1.

• Journal of the Korean Statistical Society
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• 제30권1호
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• pp.115-125
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• 2001

We consider the threshold autoregressive moving average(TARMA) process and find a sufficient condition for strict stationarity of the proces. Given region for stationarity of TARMA(p,q) model is the same as that of TAR(p) model given by Chan and Tong(1985), which shows that the moving average part of TARMA(p,q) process does not affect the stationarity of the process. We find also a sufficient condition for the existence of kth moments(k$\geq$1) of the process with respect to the stationary distribution.

• 응용통계연구
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• 제24권2호
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• pp.293-305
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• 2011

변동성은 최근 경제가 급변하면서 옵션의 가격 결정과 자산의 위험관리에서 그 중요성이 더 커지고 있다. 이러한 변동성은 분산을 지칭하며, 위험(risk)을 측정하는 수단이 되므로 정확한 추정과 예측이 매우 필요하다. 본 논문에서는 변동성에 대한 모형으로 오차항이 ARMA(p, q)-GARCH(r, s) 모형을 따르는 회귀모형을 설정하고, 이 모형의 모수에 대해 베이지안 추정법을 제시하였다. 또한 평균과 분산(변동성)에 대한 예측값을 구하고 이에 대한 베이지안 구간추정을 하였다. 이를 500개의 모의실험 자료를 통해 최우추정법과 비교하였다. 뿐만 아니라, 베이지안 방법을 이용하여 Frequentist의 관점에서는 구하기 어려운 GARCH 모형에서의 일종의 단위근이 존재할 확률을 구하였다.