The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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Estimation for the Exponential ARMA Model

지수혼합 시계열 모형의 추정

  • Won Kyung Kim (Department of Mathematics, Korea National University of Education, Chungbook 363-791, Korea) ;
  • In Kyu Kim (Department of Computer Science, Deajon Vocational Junior College, Deajon 300-100, Korea)
  • Published : 1994.09.01
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Abstract

The Yule-Walker estimator and the approximate conditional least squares estimator of the parameter of the EARMA(1, 1) model are obtained. These two estimators are compared by simulation study. It is shown that the approximate conditional least squares estimator is better in the sense of the mean square error than the Yul-Walker estimator.

지수혼합 시계열 모형인 EARMA(1,1) 모형이 율-워커 추정법과 조건최소제곱 추정법으로 추정되었다. 율-워커 추정량은 이동평균모수가 포함된 ERAMA(1,1) 모형인 경우 유일하지 못하므로 가역 조건을 만족하는 추정량이 유일한 추정량으로 얻어졌고, 조건최소제곱 추정량은 근사추정량이 얻어졌다. 모의 실험을 통하여 근사조건제곱 추정량은 율-워커 추정량보다 평균제곱오차면에서 훨씬 좋은 추정량으로 나타났다.

Keywords

References

  1. Journal of Time series analysis v.12 Estimation of parameters of an EAR(p) process Billard,L.;Mohamed,F.Y.
  2. An Introduction to Bilinear Time Series Models Granger,C.W.J.;Anderson,A.P.
  3. Advanced Applied Probability v.9 A mixed autoregressive-moving average exponential sequence and point process(EARMA(1.1)) Jacobs,P.A.;Lewis,P.A.W.
  4. Annals of Statistics v.6 On conditional least squares estimation for stochastic process Klimko,L.A.;Nelson,P.I.
  5. Journal of Applied Probability v.14 An exponential moving average sequence and point process, EMA(1) Lawrance,A.J.;Lewis,P.A.W.
  6. Journal of Applied Probability v.12 The mixed exponential solution to the first order autoregressive model Lawrance,A.J.
  7. Journal of Royal Statistical Society, Ser. B v.42 The exponential autoregressive moving average EARMA(p,q) process Lawrance,A.J.;Lewis,P.A.W.
  8. Proceedings, 1979 Winter Simulation Conf. Simulation of some autoregressive Markovian sequences of positive random variables Lawrance,A.J.;Lewis,P.A.W.;H.J.Hihgland(eds.);M.G.Spigel(eds.);R.J.Shanon(eds.)