Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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Estimation of Layered Periodic Autoregressive Moving Average Models

계층형 주기적 자기회귀 이동평균 모형의 추정

  • Lee, Sung-Duck (Department of Information & Statistics, Chungbuk National University) ;
  • Kim, Jung-Gun (Department of Information & Statistics, Chungbuk National University) ;
  • Kim, Sun-Woo (Department of Information & Statistics, Chungbuk National University)
  • 이성덕 (충북대학교 정보통계학과) ;
  • 김정군 (충북대학교 정보통계학과) ;
  • 김선우 (충북대학교 정보통계학과)
  • Received : 2012.04.17
  • Accepted : 2012.05.08
  • Published : 2012.05.31
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Abstract

We study time series models for seasonal time series data with a covariance structure that depends on time and the periodic autocorrelation at various lags $k$. In this paper, we introduce an ARMA model with periodically varying coefficients(PARMA) and analyze Arosa ozone data with a periodic correlation in the practical case study. Finally, we use a PARMA model and a seasonal ARIMA model for data analysis and show the performance of a PARMA model with a comparison to the SARIMA model.

시계열의 상관구조가 시점에 의존하며 주기적인 상관성을 보이는 계절성 시계열 자료에 대한 시계열 모형들이 비교 분석된다. 주기적 자기회귀이동평균 모형을 소개하고, 실증분석으로 주기적 상관성을 지닌 스위스 Arosa 지방의 성층권 오존 월별 시계열에 계층형 모형인 주기적 자기회귀이동평균 모형과 계절 누적자기회귀이동 평균 모형의 적합을 통하여 주기적 자기회귀이동평균 모형의 우월성을 비교한다.

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References

  1. Cipra, T. (1985). Periodic moving average process, Aplikace Matematiky, 30, 218-229.
  2. Lund, R. B. and Basawa, I. V. (1999). Modeling for periodically correlated time series, Asymptotics, Nonparametrics, and Time Series, 37-62.
  3. McLeod, A. I. (1993). Parsimony, model adequacy and periodic correlation in time series forecasting, International Statistical Review, 61, 387-393. https://doi.org/10.2307/1403750
  4. Osborn, D. R. (1991). The implications of periodically varying coefficients for seasonal time series process, Journal of Econometrics, 48, 373-384. https://doi.org/10.1016/0304-4076(91)90069-P
  5. Pagano, M. (1978). On periodic and multiple autoregressions, The Annals of Statistics, 6, 1310-1317. https://doi.org/10.1214/aos/1176344376
  6. Tiao, G. C. and Grupe, M. R. (1980). Hidden periodic autoregressive moving average models in time series data, Biometrika, 67, 365-373.
  7. Vecchia, A. V. (1985). Maximum likelihood estimation for Periodic Autoregressive Moving-Average process, Technometrics, 27, 375-384. https://doi.org/10.1080/00401706.1985.10488076

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