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| 概要 |
Some groundworks in the analysis of vector time series and the method of stochastic extrapolation are developed here, utilizing the correlation matrix function and H. Wold's idea of one dimensional ca...se. The following theorem is fundamental: Theorem, Let $ X(t) $ be a stationary vector stochastic sequence with the vanishing mean value, then it is uniquely decomposed in the form $ X(t) = X^{(1)}(t) + X^{(2)}(t) $, where $ X^{(1)}(t) $ and $ X^{(2)}(t) $ are mutually uncorrelated stationary stochastic sequence with mean value 0 and 1) $ X^{(1)}(t) $ has a continuous spectral matrix function and is expressed in the form $ X^{(1)}(t) = Y(t) + B^{(1)}Y(t-1) + B^{(2)}Y(t-2) + cdotcdotcdotcdot $, where $ Y(t) $ is a non-autocorrelated stationary stochastic sequence and is uncorrelated with $ X(t-i) $, (i=1,2, ), 2) $ X^{(2)}(t) $ is a singular stochastic sequence, i.e. it satisfies the finite difference equation with constant matrices A^{(i)} as its coefficients $ X^{(2)}(t) + A^{(1)}X^{(2)}(t-1) + A^{(2)}X^{(2)}(t-2) + cdotcdotcdotcdot + A^{(h)}X^{(2)}(t-h) = 0 $, $ h leqq infty $ ; sucn stationary singular sequence is equivalent to the vector $ B_2 $-sequence (components of which are mutually independent Slutsky's $ B_2 $-sequence) except for random variables independent of time and has a discontinuous spectral matrix function.続きを見る
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Mendeley出力
