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I am doing an impulse response analysis involving 3 time series A, B, and C in R. Following Lutkepohl approach, I used the log and diff functions to make them stationary. After creating the VAR model, I did a Cholesky decomposition of the covariance matrix, and I getting this output:

A B C
A 0.04173162 0.00000000 0.000000000
B 0.01805572 0.22749823 0.000000000
C -0.0098590 0.00092583 0.1752258

If my understanding is correct, this suggests that a shock in time series A has contemporary effects on time series B and C, but the opposite is not true. Is it the correct interpretation? If not please correct me, any insight is very welcome. Please also feel free to point out any other findings I missed.

TIA

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  • $\begingroup$ Hi, I don't know anything about impulse response analysis, but I can tell that your interpretation is wrong: Cholesky decompositions are by definition lower triangular; the zeros in the top right three cells are not telling you anything about your data. $\endgroup$ Commented Jul 25, 2023 at 12:39

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Yes. Premultiplying your reduced-form VAR with the inverse of your Cholesky matrix gives you an SVAR with structural relations corresponding to the coefficients in the inverse Cholesky matrix. Changing the order of variables in your VAR might yield a different covariance structure and, hence, different contemporaneous relations.

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