ISSN:
1432-0770
Source:
Springer Online Journal Archives 1860-2000
Topics:
Biology
,
Computer Science
,
Physics
Notes:
Abstract To evaluate the order and the values of Markov properties of the time series of events, we have proposed a statistical measure “dependency”:D m = (H 0 −H m )/H 0 , whereH 0 andH m are Shannon's entropy and them-th order conditional entropy, respectively. It is indicated that $$\tilde D_m = \sum\limits_{v = 1}^m {(\hat D_v - \bar D_v^{sh} } )$$ is a better point estimator ofD m, giving a total value of them-th order Markov process. Here $$\hat D_m $$ and $$\bar D_m^{sh} $$ are the estimate ofD m and the arithmetic mean of $$\hat D_m^{sh} $$ when them-th order shuffling is made many times for a given observed series, respectively. The value $$\hat D_m - \bar D_m^{sh} = d_m $$ represents Markov value of the orderm. Under the assumption that the series has continuous variables and the normal distribution, simplified dependency is defined by , where |S m | is the determinant of serial correlation coefficients. It is shown that is practically useful for the estimation of the order and the values of Markov processes with small sample size. It is also indicated that analysis is basically equivalent to the least mean-square analysis of autoregressive models.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01885639
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