응용통계연구 (The Korean Journal of Applied Statistics)

  • 제9권1호
  • /
  • Pages.111-124
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  • 1996
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  • 1225-066X(pISSN)
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  • 2383-5818(eISSN)
한국통계학회 (The Korean Statistical Society)
권호 표지

주변분포가 음이항 분포를 따르는 INAR(1)모형에서 추정량의 점근분포

Asymptotic distribution of estimator in INAR(1) process with negative binomial marginal

  • 김희영 ((136-701) 서울특별시 성북구 안암동 5-1, 고려대학교 정경대학 통계학과 이학석사) ;
  • 박유성 ((136-701) 서울특별시 성북구 안암동 5-1, 고려대학교 정경대학 통계학과)
  • 발행 : 1996.03.01
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⟨ 이전 논문 다음 논문 ⟩

초록

본 논문은 비음의 정수값을 가지는 시계열 모형중 시계열의 상관관계가 연속형 AR(1) 모형과 비슷한 행태를 가지는 INAR(1)(Integer Valued Autogressive of order 1) 모형을 고려하고 있다. 주변분포가 음이항분포를 따르는 INAR(1) 모형에 포함된 모수의 다양한 추정량을 도출하고, 이 추정량들의 점근분포를 유도하였다. 또한, 추정량들의 비교를 위하여 모의실험을 실시한 결과 본 논문에서 제시한 통계량이 Klimko and Nelson(1978)이 제시한 통계량보다 우수하다는 것을 볼 수 있다. 응용으로써 M/M/ 대기행렬과정에서의 모수를 추정하였다.

In this paper, we consider the first-order integer valued autoregressive(INAR(1)) model where correlation structure is similar to that of the continuous valued AR(1) process. Several methods for estimating the parameters of the INAR(1) process with negative binomial marginal are discussed. We derive asymptotic distributions of these estimators. The results of a simulation study for these estimators methods show that the estimator which we present in this paper is better than the estimator which Klimko and Nelson(1978) presented. As an application we considered the estimator of M/M/1 queue length.

키워드

참고문헌

  1. Journal of Times Series Analysis v.8 no.3 First-order integer-valued autorgressive (INAR(1)) process Al-Osh, M. A.;Alzaid A. A.
  2. Journal of Multivariate Analysis v.50 On some integer-valued autoregressive moving average models Aly, A. A.;Bouzar, N.
  3. Journal of Applied Probability v.27 An integer valued pth-order autoregressive struucture(INAR(P)) process Alzaid, A. A.;Al-Osh, M.
  4. Advanced in Applied Probability v.12 First order autocoregressive gamma-sequences and point processes Gaver, D. P.;Lewis, P. A. W.
  5. Advanced in Probability v.9 A mixed autoregressive moving average exponential sequences and point process(EARMA(1,1)) Jacobs, P. A.;Lewis, P. A. W.
  6. Annals of Statistics v.6 On conditinal least squares estimation for stochastic processes Klimko. L. A.;Nelson. P. I
  7. Scandinavian Journal of Statistics v.9 The innovation distribution of a gamma distributed autogressive process Lawrence, A. J.
  8. Journal of the Royal Statistical Society v.B42 The exponential autoregressive moving average EARMA(p,q) process Lawrence, A. J.;Lewis, P. A. W.
  9. Advances in Applied Probability v.18 Autoregressive moving-average processes with negative-binomial and geonetric marginal distribution Mckenzie, E.
  10. Advances in Applied Probability v.20 Some ARMA models for dependent sequences of Poission counts Mckenzie, E.
  11. Operations Research v.3 no.3 Stochastic properties of wating times Morse, P. M.
  12. On autocovariance function in INAR(1) process with negative binomial marginals unpublished Park, Y. S.;Kim K.
  13. Annals of Probability v.7 no.5 Discrete analogues of self-decomposabilty and stability Steutel. F. W.;Van Harn. K.
  14. Management Science v.23 A times series approach to queueing systems with applications for modelling jobs-shop in process inventories Steudel, H. J.;Wu, S. M.