• Communications for Statistical Applications and Methods
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• v.22 no.5
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• pp.463-473
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• 2015

We consider a nonparametric AR(1) model with nonparametric ARCH(1) errors. In order to estimate the unknown function of the ARCH part, we apply the stationary bootstrap procedure, which is characterized by geometrically distributed random length of bootstrap blocks and has the advantage of capturing the dependence structure of the original data. The proposed method is composed of four steps: the first step estimates the AR part by a typical kernel smoothing to calculate AR residuals, the second step estimates the ARCH part via the Nadaraya-Watson kernel from the AR residuals to compute ARCH residuals, the third step applies the stationary bootstrap procedure to the ARCH residuals, and the fourth step defines the stationary bootstrapped Nadaraya-Watson estimator for the ARCH function with the stationary bootstrapped residuals. We prove the asymptotic validity of the stationary bootstrap estimator for the unknown ARCH function by showing the same limiting distribution as the Nadaraya-Watson estimator in the second step.

• The Korean Journal of Applied Statistics
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• v.16 no.1
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• pp.141-150
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• 2003

This paper presents the multiple testing method of an autoregressive parameter in stationary AR(1) model using the usual Bayes factor. As prior distributions of parameters in each model, uniform prior and noninformative improper priors are assumed. Posterior probabilities through the usual Bayes factors are used for the model selection. Finally, to check whether these theoretical results are correct, simulated data and real data are analyzed.

• The Korean Journal of Applied Statistics
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• v.1 no.1
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• pp.57-67
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• 1987

In time series analysis, we usually require the assumption that time series are stationary. But we may often encounter time series whose parameter values subject to change. Inthis paper w propose a method which can detect the variance change point in anAR(1) model which is subjct to changesat non-predictable time points. Proposed method is compared with other methods using the simulated and real data.

• Communications for Statistical Applications and Methods
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• v.20 no.1
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• pp.85-96
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• 2013

A new bootstrap method combined with the stationary bootstrap of Politis and Romano (1994) and the classical residual-based bootstrap is applied to stationary autoregressive (AR) time series models. A stationary bootstrap procedure is implemented for the ordinary least squares estimator (OLSE), along with classical bootstrap residuals for estimated errors, and its large sample validity is proved. A finite sample study numerically compares the proposed bootstrap estimator with the estimator based on the classical residual-based bootstrapping. The study shows that the proposed bootstrapping is more effective in estimating the AR coefficients than the residual-based bootstrapping.

• Communications for Statistical Applications and Methods
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• v.13 no.3
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• pp.745-754
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• 2006

It has been shown that LAD estimates are more efficient than LS estimates when the error distribution is double exponential in AR(1) model. In order to explore the performance of LAD estimates one can use bootstrap approaches. In this paper we consider the efficiencies of bootstrap methods when we apply LAD estimates with highly variable data. Monte Carlo simulation results are given for comparing generalized bootstrap, stationary bootstrap and threshold bootstrap methods.

• Journal of the Korean Statistical Society
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• v.27 no.3
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• pp.349-358
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• 1998

Consider the AR(1) model $X_{t}$=$\beta$ $X_{t-1}$+$\varepsilon$$_{t}$ where $\beta$ < 1 is an unknown parameter to be estimated and {$\varepsilon$$_{t}$} denotes the independent and identically distributed error terms with unknown common distribution function F. In this paper, a strong representation for the least absolute deviation (LAD) estimate of $\beta$ in AR(1) models is obtained under some mild conditions on F. on F.F.

• Journal of the Korean Statistical Society
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• v.26 no.3
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• pp.383-395
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• 1997

This paper proves that the standard bootstrap approximation for the least absolute deviation (LAD) estimate of .beta. in AR(1) processes with infinite variance error terms is asymptotically valid in probability when the bootstrap resample size is much smaller than the original sample size. The theoretical validity results are supported by simulation studies.

• Journal of the Korean Data and Information Science Society
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• v.16 no.1
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• pp.71-78
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• 2005

Recently an important issue in Bayesian methodology is determination of noninformative prior distributions, often required when there is no idea of prior information. In this thesis attention is focused on the development of noninformative priors for stationary AR(1) model. The noninformative priors primarily discussed are the Jeffreys prior, and the reference priors. The remarkable points in the result are that the Jeffreys prior coincides with the reference prior for the case that $\rho$ is the parameter of interest.

• Journal of the Korean Data and Information Science Society
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• v.18 no.1
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• pp.73-80
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• 2007

Cointegration(together with VARMA(vector ARMA)) has been proven to be useful for analyzing multivariate non-stationary data in the field of financial time series. It provides a linear combination (which turns out to be stationary series) of non-stationary component series. This linear combination equation is referred to as long term equilibrium between the component series. We consider two sets of Korean bivariate financial time series and then illustrate cointegration analysis. Specifically estimated VAR(vector AR) and VECM(vector error correction model) are obtained and CV(cointegrating vector) is found for each data sets.

• Journal of the Korean Statistical Society
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• v.26 no.3
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• pp.407-416
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• 1997

Suppose that { $X_{i}$ } is a stationary AR(1) process and { $Y_{j}$ } is an ARX process with { $X_{i}$ } as exogeneous variables. Let $Y_{j}$ $^{*}$ be the stochastic process which is the sum of $Y_{j}$ and a nonstochastic trend. In this paper we consider the problem of estimating the conditional probability that $Y_{{n+1}}$$^{*}$ is bigger than $X_{{n+1}}$, given $X_{1}$, $Y_{1}$$^{*}$,..., $X_{n}$ , $Y_{n}$ $^{*}$. As an estimator for the tolerance probability, an Mann-Whitney statistic based on least squares residuars is suggested. It is shown that the deviations between the estimator and true probability are stochatically bounded with $n^{{-1}$2}/ order. The result may be applied to the stress-strength reliability theory when the stress and strength variables violate the classical iid assumption.umption.n.