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Changes between Version 12 and Version 13 of Ticket #664


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Timestamp:
Mar 25, 2009, 7:10:39 PM (16 years ago)
Author:
Víctor de Buen Remiro
Comment:

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  • Ticket #664 – Description

    v12 v13  
    2727 1. Let be the standarized multinormal residuals [[BR]] [[LatexEquation( \epsilon' =\frac{1}{\sigma'}e' $$)]] [[BR]]
    2828 1. Since [[LatexEquation(\beta' $$)]] are determined by [[LatexEquation(\epsilon' $$)]] by means of a full range linear equation, their densities have constant ratio, and logarithm of density of candidate vector can be calculated directly as [[BR]] [[LatexEquation(cte -\frac{T}{2}\log\left(2\pi\right)-\frac{1}{2}\sum_{t=1}^{T}\epsilon'_{t}^{2}$$)]]
    29  1. Then we can propose residuals and initial values for current system as [[BR]][[LatexEquation(e^{*} = \frac{\sigma}{\sigma'}e' $$)]] [[BR]] [[LatexEquation(u = \frac{\sigma}{\sigma'}u' $$)]]
     29 1. Then we can propose residuals and initial values for current system as [[BR]][[LatexEquation(e^{*} = \frac{\sigma}{\sigma'}e' $$)]] [[BR]] [[LatexEquation(u^{*} = \frac{\sigma}{\sigma'}u' $$)]]
    3030 1. ARIMA noise for current system becomes simply [[BR]][[LatexEquation(z^{*}_t = \frac{\theta\left(B\right)}{\phi\left(B\right)} e^{*}_t $$)]]
    3131 1. In order to get the refined candidate, we will take minimum residuals solution of sparse linear system  [[BR]][[LatexEquation(X \beta = Y-z^{*} $$)]]