• Journal of the Korean Mathematical Society
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• v.33 no.2
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• pp.227-234
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• 1996

Consider nonlinear autoregressive processes of order 1 defined by the random iteration $$ (1) X_{n + 1} = f(X_n) + \epsilon_{n + 1} (n \geq 0) $$ where f is real-valued Borel measurable functin on $R^1, {\epsilon_n : n \geq 1}$ is an i.i.d.sequence whose common distribution F has a non-zero absolutely continuous component with a positive density, $E$\mid$\epsilon_n$\mid$ < \infty$, and the initial $X_0$ is independent of ${\epsilon_n : n > \geq 1}$.

• 제어로봇시스템학회:학술대회논문집
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• 1992.10b
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• pp.272-275
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• 1992

A novel fault diagnosis method based on likelihood decomposition is proposed for linear stochastic systems described by autoregressive (AR) model. Assuming that at some time instant .tau. the fault of one of the following two types is occurs: innovation fault (actuator fault); and observation fault (sensor fault), the log-likelihood function is decomposed into two components based on the observations before and after .tau., respectively, Then, the type of the fault is determined by comparing the log-likelihoods corresponding two types of faults. Numerical examples demonstrate the usefulness of the proposed diagnosis method.

• Proceedings of the Korean Statistical Society Conference
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• 2003.05a
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• pp.281-286
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• 2003

The stationarity is one of the most important properties of a time series. We propose robust sign tests for seasonal autoregressive process to determine whether or not a time series is stationary. The tests have an exact binomial null distribution and are robust to the outliers and the heteroscedastic errors. Monte-Carlo simulation shows that the sign test is locally more powerful than the OLSE-based tests for heavy-tailed and/or heteroscedastic error distributions.

• Proceedings of the Korean Statistical Society Conference
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• 2003.05a
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• pp.183-189
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• 2003

A momentum threshold autoregressive (MTAR) model, a nonlinear autoregressive model, is analyzed in a Bayesian framework. Parameter estimation in the presence of missing data is done by using Markov chain Monte Carlo methods. We also propose simple Bayesian test procedures for asymmetry and unit roots. The proposed method is applied to a set of Korea unemployment rate data and reveals evidence for asymmetry and a unit root.

• Journal of the Korean Data and Information Science Society
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• v.3 no.1
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• pp.65-78
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• 1992

In this paper, we obtain the natural estimators of the coefficient parameters and propose strongly consistent estimators of the parameter in the autoregressive model of order three with non-negative innovations. It is shown that the natural estimators are also strongly consistent for the parameters. We also compare the proposed estimators with the natural estimators and the least square estimators via Monte Carlo simulation studies.

• Journal of the Korean Data and Information Science Society
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• v.24 no.3
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• pp.637-642
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• 2013

In this paper, we consider the maximum entropy test in in nite order autoregressiv models. Its asymptotic distribution is derived under the null hypothesis. A bootstrap version of the test is discussed and its performance is evaluated through Monte Carlo simulations.

• Journal of the Korean Mathematical Society
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• v.41 no.6
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• pp.1071-1086
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• 2004

This paper is concerned with the strong consistency of the estimators of the autocovariance function and the spectral density function for the autoregressive process in the case where only an amplitude modulated process with missing data is observed. These results will give a simple and practical sufficient condition for the strong consistency of those estimators. Finally, some examples are given to illustrate the application of main result.

• Communications for Statistical Applications and Methods
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• v.2 no.2
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• pp.198-212
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• 1995

This study provides a nonparametric procedure for the statistical inference of the parameters in stationary autoregressive processes. A confidence region and a hypothesis testing procedure based on a class of signed linear rank statistics are proposed and the asymptotic distributions of the test statistic both underthe null hypothesis and under a sequence of local alternatives are investigated. Some desirable asymptotic properties including the asymptotic relative efficiency are discussed for various score functions.

• Communications for Statistical Applications and Methods
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• v.3 no.1
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• pp.257-265
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• 1996

We consider nonstationary autoregressive autoregressive process with infinite variance of error. In the case of infinite cariance, the limiting distribution of the estimated coefficient is different from that under the finite cariance assumption. In this paper we show that the bootstrap method can be used to approximate the distribution of ordinary least squares estimator of the coefficient in the first order random walk process with infinite variance through some empirical studies and we suggest a test procedure based on bootstrap method for the unit root test.

• Journal of the Korean Statistical Society
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• v.25 no.3
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• pp.359-368
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• 1996

The maximum likelihood estimation is discussed for the NLAR model with Laplacian marginals. Since the explicit form of the estimates cannot be obtained due to the complicated nature of the likelihood function we utilize the automatic computer optimization subroutine using a direct search complex algorithm. The conditional least square estimates are used as initial estimates in maximum likelihood procedures. The results of a simulation study for the maximum likelihood estimates of the NLAR(1) and the NLAR(2) models are presented.