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- Timestamp:
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Mar 23, 2009, 2:55:11 PM (16 years ago)
- Author:
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Víctor de Buen Remiro
- Comment:
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v4
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v5
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| 27 | 27 | 1. Then we can purpose residuals and initial values for current system as [[BR]][[LatexEquation(e \frac{\sigma}{\sigma'}e' $$)]] [[LatexEquation(u = \frac{\sigma}{\sigma'}u' $$)]] |
| 28 | 28 | 1. Le be [[BR]] [[LatexEquation( \epsilon=\frac{1}{\sigma}e $$)]] [[BR]] standarized multinormal residuals |
| 29 | | 1. By Bayes theorem conditional density [[LatexEquation(\beta|\epsilon $$)]] is proportional to conditional density [[LatexEquation(\epsilon|\beta $$)]] which logarithm can be calculated directly as [[BR]] [[LatexEquation(-\frac{T}{2}\log\left(2\pi\right)-\frac{1}{2}\sum_{t=1}^{T}\epsilon_{t}^{2}$$)]] |
| | 29 | 1. Since [[LatexEquation(\beta $$)]] are determined by [[LatexEquation(\epsilon $$)]] by mean of a full range linear equation, logarithm of denity of candidate vector can be calculated directly as [[BR]] [[LatexEquation(-\frac{T}{2}\log\left(2\pi\right)-\frac{1}{2}\sum_{t=1}^{T}\epsilon_{t}^{2}$$)]] |
| 30 | 30 | 1. ARIMA noise for current system becomes simply [[BR]][[LatexEquation(z_t = \frac{\theta\left(B\right)}{\phi\left(B\right)} e_t $$)]] |
| 31 | 31 | 1. Then, we can solve sparse linear system [[BR]][[LatexEquation(Y = X \beta + z $$)]] |
