• Communications for Statistical Applications and Methods
• /
• 제2권2호
• /
• pp.198-212
• /
• 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
• /
• 제20권1호
• /
• pp.85-96
• /
• 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.

• Journal of the Korean Data and Information Science Society
• /
• 제22권2호
• /
• pp.335-351
• /
• 2011

오경주와 김태윤 (2007) 등은 위기 관련 데이터의 희귀성 에서 발생하는 문제를 해결하기 위해 과거 금융시장이 안정적이었던 구간을 기준 구간으로 설정하고 기준 구간의 금융시장 움직임을 점 근 자기회귀 모형으로 적합한 후 현재의 금융시장 상황과 비교하여 불안정 지수를 도출할 것을 제안하였다. 그러나 비모수 기법인 신경망을 사용하여 도출된 불안정 지수가 기준 구간의 데이터에 지나치게 의존하는 관계로 불안정 지수가 종종 실제 경제상황을 제대로 반영하지 못하는 것으로 관찰되고 있다. 본 연구에서는 비모수 기법인 신경망과 모수 기법인 선형모형을 이용하여 기준구간에 대한 적합을 독립적으로 수행하여 두 종류의 불안정성 지수들을 도출한 후 이 둘을 결합한 통합 불안정성 지수를 사용할 것을 제안한다. 두 지수의 적절한 통합을 위해 신경망과 선형모형을 통해 도출된 두 지수의 최적 결합비율을 부여하는 방법을 제안하며 제안기법의 타당성을 국내 주식시장 대상으로 검증하였다.

• Journal of the Korean Statistical Society
• /
• 제34권4호
• /
• pp.345-366
• /
• 2005

This paper considers the cointegrating vector estimator in the error correction model with stationary covariates, which combines the stationary vector autoregressive model and the nonstationary error correction model. The cointegrating vector estimator is shown to follow the locally asymptotically mixed normal distribution. The variance of the estimator depends on the co­variate effect of stationary regressors, and the asymptotic efficiency improves as the magnitude of the covariate effect increases. An economic application of the money demand equation is provided.

• Journal of the Korean Statistical Society
• /
• 제26권1호
• /
• pp.31-46
• /
• 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
• /
• 제23권1호
• /
• pp.167-178
• /
• 1994

To estimate coefficient matrix in autoregressive model, usually ordinary least squares estimator or unconditional maximum likelihood estimator is used. It is unknown that for univariate AR(p) model, unconditional maximum likelihood estimator gives better power property that ordinary least squares estimator in testing for unit root with mean estimated. When autoregressive model contains multiple unit roots and unconditional likelihood function is used to estimate coefficient matrix, the seperation of nonstationary part and stationary part of the eigen-values in the estimated coefficient matrix in the limit is developed. This asymptotic property may give an idea to test for multiple unit roots.

• 한국통계학회:학술대회논문집
• /
• 한국통계학회 2002년도 추계 학술발표회 논문집
• /
• pp.265-272
• /
• 2002

An Integer-valued autoregressive integrated (INARI) model is introduced to eliminate stochastic trend and seasonality from time series of count data. This INARI extends the previous integer-valued ARMA model. We show that it is stationary and ergodic to establish asymptotic normality for conditional least squares estimator. Optimal estimating equations are used to reflect categorical and serial correlations arising from panel count data and variations arising from three random processes for obtaining observation into estimation. Under regularity conditions for martingale sequence, we show asymptotic normality for estimators from the estimating equations. Using cancer mortality data provided by the U.S. National Center for Health Statistics (NCHS), we apply our results to estimate the probability of cells classified by 4 causes of death and 6 age groups and to forecast death count of each cell. We also investigate impact of three random processes on estimation.

• Journal of the Korean Statistical Society
• /
• 제31권1호
• /
• pp.121-128
• /
• 2002

In this paper we provide a new proof of the asymptotic distributions of LAD estimators using the martingale limit theorem and show the efficiency of LAD estimators in a stationary AR(1) model setting.

• Communications for Statistical Applications and Methods
• /
• 제20권1호
• /
• pp.41-52
• /
• 2013

The stationary bootstrap of Politis and Romano (1994) is adopted to develop prediction intervals of returns and volatilities in a generalized autoregressive heteroskedastic (GARCH)(p, q) model. The stationary bootstrap method is applied to generate bootstrap observations of squared returns and residuals, through an ARMA representation of the GARCH model. The stationary bootstrap estimators of unknown parameters are defined and used to calculate the stationary bootstrap samples of volatilities. Estimates of future values of returns and volatilities in the GARCH process and the bootstrap prediction intervals are constructed based on the stationary bootstrap; in addition, asymptotic validities are also shown.

• 한국통계학회:학술대회논문집
• /
• 한국통계학회 2005년도 추계 학술발표회 논문집
• /
• pp.159-165
• /
• 2005

Recently, as a result of the growing interest in modelling stationary processes with discrete marginal distributions, several models for integer valued time series have been proposed in the literature. One of theses models is the integer-valued autoregressive(INAR) models. However, when modelling with integer-valued autoregressive processes, there is not yet distributional properties of forecasts, since INAR process contain an accrued level of complexity in using the Steutal and Van Harn(1979) thinning operator 'o'. In this study, a manageable expression for the asymptotic mean square error of predicting more than one-step ahead from an estimated poisson INAR(1) model is derived. And, we present a bootstrap methods developed for the calculation of forecast interval limits of INAR(p) model. Extensive finite sample Monte Carlo experiments are carried out to compare the performance of the several bootstrap procedures.