Estimated parameters for the Naphtha time series

To select an appropriate order for the supposed VARX model, models of various orders are fitted and compared based on standard information criteriad The information criteria suggest a model order ofp= 3 orp = 

The corresponding estimated parameter matrices can be found in Table 2.8 

Tkble 2.8 Coefficients of the initial VARX(Z) model for de-alkylation plant 

Subsequently, (2.67) is enhanced by the dummy variables for the outliers. To provide the 

While the estimates of the autocorrelation coefficients for the Cg time series (lower rows in 1 to ordy change slightly, the estimates the autocorrelation coefficients for the Benzene time series (upper rows in to 3) are clearly affected since three parameters are dropped from the model. The remaining coefficients are affected, too. In particular, the lagged cross-correlations to the Cg time series change from 1.67 to 2.51 and from -2.91 to -2.67 (right upper entries in 1 and This confirms the serious effect of even unobtrusive outliers in multivariate times series analysis. By incorporating the outliers effects, the model s AIC decreases from -4.22 to -4.72. Similarly, SIC decreases from -4.05 to -4.17. The analyses of residuals. show a similar pattern as for the initial model and reveal no serious hints for cross- or auto-correlation. i Now, the multivariate Jarque-Bera test does not reject the hypothesis of multivariate normally distributed variables (at a 5% level). The residuals empirical covariance matrix is finally estimated as 

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Table 2.7 Estimated parameters for the Naphtha time series...

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