[R-SIG-Finance] Problem understanding the code of dse::simulate

[Degang WU]

Paul,

Thanks for your clear and insightful answers!

Degang

> On 24 Jan, 2016, at 9:33 pm, Paul Gilbert <pgilbert902 at gmail.com> wrote:
> 
> On 01/22/2016 11:17 AM, Degang WU wrote:
>> Hi, I want to simulate a VAR process using the following code
>> library(dse) AR   <- array(c(1, .5, .3, 0, .2, .1, 0, .2, .05, 1, .5,
>> .3) ,c(3,2,2)) VAR  <- ARMA(A=AR, B=diag(1,2)) print(VAR) simData <-
>> simulate(VAR) Inside dse::simulate:
>> 
>> if (p == 1) invA0 <- matrix(1/A[1, , ], 1, 1) else invA0 <-
>> solve(A[1, , ]) for (l in 1:a) A[l, , ] <- invA0 %*% A[l, , ] for (l
>> in 1:b) B[l, , ] <- invA0 %*% B[l, , ]
>> 
>> Where A[,,,] are the coefficient matrix for the process. I have no
>> idea why the inverse of A[1, ,] is involved in the simulation.
> 
> Degang
> 
> In response to your previous question I said the dse specification is
> 
> y_t + A_1 y_{t-1} + A_2 y_{t-2} + .. A_p y_{t-p} = e_t (2)
> 
> but that is the form corresponding to your specification. In general, VAR models can be written
> 
> A_0 y_t + A_1 y_{t-1} + A_2 y_{t-2} + .. A_p y_{t-p} = e_t (3)
> 
> In your specification A_0 is the identity matrix. For simulation it is convenient to re-write (3) as
> 
> y_t = (A_0)^-1 (-A_1 y_{t-1} - A_2 y_{t-2} - ... - A_p y_{t-p} + e_t)
> 
> R indexes arrays starting with 1, so A_0 is stored in A[1,,]. If A_0 is the identity, as in your specification, the inverse will also be identity and the multiplication is not necessary.
> 
> Paul
>> 
>> Thanks!
>> 
>> Regards, Degang [[alternative HTML version deleted]]
>> 
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