Journal of the Korean Data and Information Science Society

The Korean Data and Information Science Society (한국데이터정보과학회)
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Prediction for spatial time series models with several weight matrices

여러 가지 가중행렬을 가진 공간 시계열 모형들의 예측

  • Lee, Sung Duck (Department of Information and Statistics, Chungbuk National University) ;
  • Ju, Su In (Department of Information and Statistics, Chungbuk National University) ;
  • Lee, So Hyun (Department of genome Epidemiology, Korea National Institute of Health)
  • 이성덕 (충북대학교 정보통계학과) ;
  • 주수인 (충북대학교 정보통계학과) ;
  • 이소현 (국립보건연구원 유전체역학과)
  • Received : 2016.12.19
  • Accepted : 2017.01.04
  • Published : 2017.01.31
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Abstract

In this paper, we introduced linear spatial time series (space-time autoregressive and moving average model) and nonlinear spatial time series (space-time bilinear model). Also we estimated the parameters by Kalman Filter method and made comparative studies of power of forecast in the final model. We proposed several weight matrices such as equal proportion allocation, reciprocal proportion between distances, and proportion of population sizes. For applications, we collected Mumps data at Korea Center for Disease Control and Prevention from January 2001 until August 2008. We compared three approaches of weight matrices using the Mumps data. Finally, we also decided the most effective model based on sum of square forecast error.

시간의 변화뿐만 아니라 공간 위치의 변화를 함께 고려한 자료를 공간 시계열 자료라고 한다. 공간 시계열 자기회귀 이동평균 모형과 공간 시계열 중선형 모형에 대해 소개하고 각각의 Kalman Filter 방법에 의한 모수 추정의 과정을 거쳐 최종 선택된 모형의 예측력을 비교하였다. 또한 공간 시계열 자료의 모형에 포함되는 가중행렬에 대하여 기존의 방법인 동일한 가중치와 더불어 거리에 비례한 가중치와 인구수에 비례한 가중치를 제안하였다. 실증분석을 위해 한국질병관리본부에서 수집한 유행성 이하 선염 자료를 활용하여 가중치를 달리한 공간 시계열 모형을 적합시키고 예측하였다. 예측 오차 제곱합을 활용하여 어느 모형이 가장 효과적인 모형인지 판정하였다.

Keywords

References

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