form_boldA function

Form the $(dp\times dp)$ "bold A" matrices related to the VAR processes

form_boldA creates the "bold A" (companien form) coefficient matrices related to VAR processes.

form_boldA(p, M, d, all_A)

Arguments

• p: the autoregressive order of the model
• M: the number of regimes
• d: the number of time series in the system, i.e., the dimension
• all_A: 4D array containing all coefficient matrices $A_{m,i}$, obtained from pick_allA.

Returns

Returns 3D array containing the $(dp \times dp)$ "bold A" matrices related to each component VAR-process. The matrix A_{m} can be obtained by choosing [, , m].

Details

The "bold A" (companion form) matrix is given, for instance, in Lütkepohl (2005, p. 15).

Warning

No argument checks!

References

• Lütkepohl H. 2005. New Introduction to Multiple Time Series Analysis, Springer.