• Journal of the Korean Statistical Society
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• 제24권1호
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• pp.243-248
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• 1995

In this article we show that a class of random coefficient autoregressive processes including the NEAR (New exponential autoregressive) process has the strong mixing property in the sense of Rosenblatt with mixing order decaying to zero. The result can be used to construct model free prediction interval for the future observation in the NEAR processes.

• Communications for Statistical Applications and Methods
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• 제2권2호
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• pp.94-100
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• 1995

Vector autoregressive process disturbed by measurement error is a vector autoregressive process with nonlineat parametric restrictions on the parameter. A Newton-Raphson procedure for estimating the parameter which take advantage of the information contained in the restrictions is proposed.

• Journal of the Korean Statistical Society
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• 제22권2호
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• pp.271-282
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• 1993

Unit root test for temporally aggregated first order autoregressive process is considered. The temporal aggregate of fist order autoregression is an autoregressive moving average of order (1,1) with moving average parameter being function of the autoregressive parameter. One-step Gauss-Newton estimators are proposed and are shown to have the same limiting distribution as the ordinary least squares estimator for unit root when complete observations are available. A Monte-Carlo simulation shows that the temporal aggregation have no effect on the size. The power of the suggested test are nearly the same as the powers of the test based on complete observations.

• Journal of the Korean Data and Information Science Society
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• 제20권5호
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• pp.949-954
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• 2009

The autoregressive process is applied in this paper to kernel regression in order to infer nonlinear models for predicting responses. We propose a kernel method for the autoregressive data which estimates the mean function by kernel machines. We also present the model selection method which employs the cross validation techniques for choosing the hyper-parameters which affect the performance of kernel regression. Artificial and real examples are provided to indicate the usefulness of the proposed method for the estimation of mean function in the presence of autocorrelation between data.

• Journal of the Korean Data and Information Science Society
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• 제25권6호
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• pp.1539-1547
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• 2014

In this paper we apply the autoregressive process to the nonlinear quantile regression in order to infer nonlinear quantile regression models for the autocorrelated data. We propose a kernel method for the autoregressive data which estimates the nonlinear quantile regression function by kernel machines. Artificial and real examples are provided to indicate the usefulness of the proposed method for the estimation of quantile regression function in the presence of autocorrelation between data.

• Journal of the Korean Statistical Society
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• 제22권2호
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• pp.259-269
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• 1993

A moving average model, LMA(q) and an autoregressive-moving average model, NLARMA(p, q), with Laplacian marginal distribution are constructed and their properties are discussed; Their autocorrelation structures are completely analogus to those of Gaussian process and they are partially time reversible in the third order moments. Finally, we study the mixing property of NLARMA process.

• 응용통계연구
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• 제27권6호
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• pp.1049-1068
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• 2014

자기회귀 모형(autoregressive model)은 일변량(univaraite) 시계열자료의 분석에서 널리 사용되는 방법 중 하나이다. 그러나 이 방법은 자료에 일정한 추세가 있다고 가정하기 때문에 자료에 분절(structural break)이 존재할 때 적절하지 않을 수 있다. 이러한 문제점을 해결하기 위한 방법으로 국면전환(regime-switching) 모형인 임계자기회귀 모형(threshold autoregressive model)이 제안되었는데 최근 지연 모수(delay parameter)을 포함한 이 국면전환(two regime-switching) 모형으로 확장되어 많은 연구가 활발히 진행되고 있다. 본 논문에서는 이 국면전환 임계자기회귀 모형을 베이지안(Bayesian) 관점에서 살펴본다. 베이지안 분석을 위해 모수적 임계자기 회귀 모형 뿐만 아니라 디리슐레 과정(Dirichlet Process) 사전분포를 이용하는 비모수적 임계자기 회귀 모형을 고려하도록 한다. 두 가지 베이지안 임계자기 회귀 모형을 바탕으로 사후분포를 유도하고 마코프 체인 몬테 카를로(Markov chain Monte Carlo) 방법을 통해 사후추론을 실시한다. 모형 간의 성능을 비교하기 위해 모의실험을 통한 자료 분석을 고려하고, 더 나아가 한국과 미국의 국내 총생산(Gross Domestic Product)에 대한 실증적 자료 분석을 실시한다.

• Communications for Statistical Applications and Methods
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• 제3권2호
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• pp.77-83
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• 1996

This paper is concerned with an estimation problem for the AR(1) process $Y_t, t=0, {\pm}1, {\cdots}$with time carying autoregressive coefficient, where coefficient itself is also stochastic process. Attention is directed to the problem of finding a consistent estimator of ${\Phi}$, the mean level of autoregressive coefficient. The asymptotic distribution of the resulting consistent estimator of ${\Phi}$, is them discussed. We do not assume any time series model for the time varying autoregressive coefficient.

• Journal of the Korean Statistical Society
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• 제26권1호
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• pp.31-46
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• 1997

Let $X_{t}$ = .beta. $X_{{t-1}}$ + .epsilon.$_{t}$ be an autoregressive process where $\mid$.beta.$\mid$ < 1 and {.epsilon.$_{t}$} is independent and identically distriubted with regularly varying tail probabilities. This process is called the asymptotically stationary first-order autoregressive process (AR(1)) with infinite variance. In this paper, we obtain a host of weak convergences of some point processes based on bootstrapping of { $X_{t}$}. These kinds of results can be generalized under the infinite variance assumption to ensure the asymptotic validity of the bootstrap method for various functionals of { $X_{t}$} such as partial sums, sample covariance and sample correlation functions, etc.ions, etc.

• Journal of the Korean Statistical Society
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• 제22권2호
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• pp.307-324
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• 1993

The limiting distribution of the excess over the boundary is determined for the autoregressive process.