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Extra info for Analysis of Integrated and Cointegrated Time Series with R
2 Vector Autoregressive Models 39 2 4 6 8 10 12 Fanchart for variable y2 0 100 200 300 400 500 Fig. 7. Fanchart of y2 of VAR(2)-process interpreted as the expected response of variable yi,t+s to a unit change in variable yjt . These eﬀects can be cumulated through time s = 1, 2, . , and hence one would obtain the cumulated impact of a unit change in variable j on the variable i at time s. Rather than these impulse response coeﬃcients, it is often conceivable to use orthogonal impulse responses as an alternative.
And Ω This test statistic is distributed as χ2 (qK 2 (K + 1)2 /4). test() contained in the package vars. The default is to compute the multivariate test only. only = FALSE, the univariate tests are computed, too. test() has three elements. The ﬁrst element is the matrix of residuals. uni, is a list object itself and holds the univariate test results for each of the series. mul. 2, these tests are applied to the object varsimest. The Jarque-Bera normality tests for univariate and multivariate series are implemented and applied to the residuals of a VAR(p) as well as separate tests for multivariate skewness and kurtosis (see Bera and Jarque , , Jarque and Bera , and L¨ utkepohl ).
B-model: A is set to IK (minimum number of restrictions to be imposed for identiﬁcation is the same as for A-model). • AB-model: restrictions can be placed on both matrices (minimum number of restrictions for identiﬁcation is K 2 + K(K − 1)/2). 2 Estimation Depending on the SVAR type, the estimation is similar to the estimation of a simultaneous multiple-equation model with covariance restrictions on the error terms. 31) ln |A2 | − ln |B 2 | − tr(A B −1 B −1 AΣ 2 2 2 ˆ u signiﬁes the estimated residual covariance matrix of the VAR(p)where Σ model.