The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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L-Estimation for the Parameter of the AR(l) Model

AR(1) 모형의 모수에 대한 L-추정법

  • 한상문 (서울시립대학교 통계학과) ;
  • 정병철 (성신여자대학교 통계학과)
  • Published : 2005.03.01
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Abstract

In this study, a robust estimation method for the first-order autocorrelation coefficient in the time series model following AR(l) process with additive outlier(AO) is investigated. We propose the L-type trimmed least squares estimation method using the preliminary estimator (PE) suggested by Rupport and Carroll (1980) in multiple regression model. In addition, using Mallows' weight function in order to down-weight the outlier of X-axis, the bounded-influence PE (BIPE) estimator is obtained and the mean squared error (MSE) performance of various estimators for autocorrelation coefficient are compared using Monte Carlo experiments. From the results of Monte-Carlo study, the efficiency of BIPE(LAD) estimator using the generalized-LAD to preliminary estimator performs well relative to other estimators.

본 연구에서는 AR(1) 과정을 따르는 시계열 모형에서 가산적 이상치(Additive Out-lier)가 존재하는 경우, 1차 자기상관계수에 대한 로버스트 추정방법으로 Rupport 와 Carroll (1980)에 의해 회귀모형에서 제안된 L-추정법 형태의 절사최소제곱추정 (PE 추정)방법을 제안하였다. 더불어 X축의 이상치에 대한 비중강하(down-weight)의 방법으로 Mallows의 가중함수를 고려한 유계영향 절사최소제곱 (bounded influence PE, BIPE)추정량을 제안하였으며 모의 실험을 통하여 각 추정량의 효율성을 비교하였다. 모의실험 결과, 다양한 자료의 오염률상에서 일반화 LAD추정치를 예비 추정치로 고려한 BIPE(LAD)-추정량의 효율이 좋은 것으로 나타났다.

Keywords

References

  1. De Jongh, P.J. and De Wet T. (1985). Trimmed mean and bounded influence estimators for the parameters of the AR(1) process, Communications in Statistics -Theory and Methods, 14, 1361-1375 https://doi.org/10.1080/03610928508828981
  2. Denby, L. and Martin, RD. (1979). Robust estimation of the first-order autoregressive parameter, Journal of the American Statistical Association, 74, 140-146 https://doi.org/10.2307/2286743
  3. Fox, A.J. (1972). Outliers in time series. Journal of the Royal Statistical Society, Series B, 34, 350-363
  4. Guo, J-H. (2000). Robust estimation for the coefficient if a first order autoregressive process, Communications in Statistics -Theory and Methods, 29, 55-66 https://doi.org/10.1080/03610920008832468
  5. Haddad, J.N. (2000). On robust estimation in the first order autoregressive processes, Communications in Statistics -Theory and Methods, 29, 45-54 https://doi.org/10.1080/03610920008832467
  6. Koenker, R and Bassett, G. (1978). Regression quantiles, Econometrica, 46, 33-50 https://doi.org/10.2307/1913643
  7. Mallows, C.L. (1973). Influence functions, Unpublished paper presented at a conference on robust regression held at Cambridge, Mass., and sponsored by the National Bureau of Economic Research
  8. Rupport, D. and Carroll, R (1980). Trimmed least squares estimation in the linear model, Journal of the American Statistical Association, 75, 828-838 https://doi.org/10.2307/2287169