The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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A Fast Bayesian Detection of Change Points Long-Memory Processes

장기억 과정에서 빠른 베이지안 변화점검출

  • Kim, Joo-Won (Office of Admissions, Seoul National University) ;
  • Cho, Sin-Sup (Department of Statistics, Seoul National University) ;
  • Yeo, In-Kwon (Department of Statistics, Sookmyoung Women's University)
  • Published : 2009.08.31
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Abstract

In this paper, we introduce a fast approach for Bayesian detection of change points in long-memory processes. Since a heavy computation is needed to evaluate the likelihood function of long-memory processes, a method for simplifying the computational process is required to efficiently implement a Bayesian inference. Instead of estimating the parameter, we consider selecting a element from the set of possible parameters obtained by categorizing the parameter space. This approach simplifies the detection algorithm and reduces the computational time to detect change points. Since the parameter space is (0, 0.5), there is no big difference between the result of parameter estimation and selection under a proper fractionation of the parameter space. The analysis of Nile river data showed the validation of the proposed method.

이 논문에서는 장기억 과정에서의 변화점을 빨리 검출하는 베이지안 추론방법에 대해 알아본다. 장기억 과정에서의 베이지안 추정은 장기억 모수값에 따라 전체 자료에 대한 부분차분을 계산해야 하기 때문에 수행시간이 많이 걸린다는 문제가 있다. 이 논문에서는 이러한 문제를 해결하고자 장기억 모수공간을 그룹화하여 순서형으로 범주화시킨 후 설명력이 가장 높은 범주의 대표값을 선택하게 하였다. 이 방법은 초기단계에서 범주의 대표값에 대해 한번씩만 부분차분을 계산하면 되기 때문에, 매번 계산해야 하는 추정하는 방법보다, 특히 시계열자료의 수가 많은 경우, 상대적으로 빠른 베인지안 추론이 가능하다. 또한 장기억 모수공간이 (0,0.5) 이기 때문에 모수공간을 적절하게 그룹화한다면 장기억 모수를 선택하는 것이 모수를 추정하는 것에 비해 큰 차이가 없다. 이 논문에서는 나일강 수위자료 실증분석을 통해 제안된 방법의 타당성을 확인해본다.

Keywords

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