# FEVD using bandpass\_filter = \[6 32\] in stoch\_simul, interpretation?

**URL:** <https://forum.dynare.org/t/fevd-using-bandpass-filter-6-32-in-stoch-simul-interpretation/18019>\
**Category:** Stochastic simulations\
**Created:** [2 May 2021 00:46 UTC](https://forum.dynare.org/t/fevd-using-bandpass-filter-6-32-in-stoch-simul-interpretation/18019 "2021-05-02T00:46:51Z")\
**Posts on this page:** 2\
**Page:** 1

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**Author:** ![jay1](https://forum.dynare.org/letter_avatar_proxy/v4/letter/j/9d8465/32.png) [@jay1](https://forum.dynare.org/u/jay1)\
**Post date:** [2 May 2021 00:46 UTC](https://forum.dynare.org/t/fevd-using-bandpass-filter-6-32-in-stoch-simul-interpretation/18019/1 "2021-05-02T00:46:51Z")

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Hi,

If I am using the bandpass\_filter = [6 32] when computing a forecast error variance decomposition after simulating my model, am I getting the FEVD corresponding to 6 period ahead to 32 period ahead terms? Is this the correct interpretation of what the outputs are?

For example, simple state space model given by:

s\_t = A s\_{t-1} + B \epsilon\_t

Recursively substituting yields,

s\_t = \sum\_{j=0}^{\infty} A^{j} B \epsilon\_{t-j} \tag{0}, or  
s\_{t+k} = \sum\_{j=0}^{\infty} A^{j} B \epsilon\_{t+k-j} \tag{1}

While the expectation of the state space is all shocks occurring at and prior to the expectation iterated through. Which says

E\_t s\_{t+k} = \sum\_{j=k}^{\infty} A^{j} B \epsilon\_{t+k-j} \tag{2}

Then, for example, using (1) and (2) the thiry-two period ahead FEVD is given by:

(E\_t s\_{t+32} - s\_{t+32})(E\_t s\_{t+32} - s\_{t+32})' = (B \epsilon\_{t+32} + AB \epsilon\_{t+31} + \dots)(B \epsilon\_{t+32} + AB \epsilon\_{t+31} + \dots)'

So if I use bandpass\_filter = [6 32] after a stochastic simulation, is this returning to me:

= BVB' + ABVB'A' + A^{2}B V B' A^{2'} \dots + A^{27} B V B' A^{27'} ?

That is, I would be dropping the 28-32 terms, or the first 5 forecast periods?

Thanks

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**Author:** ![jpfeifer](https://forum.dynare.org/user_avatar/forum.dynare.org/jpfeifer/32/5044_2.png) [@jpfeifer](https://forum.dynare.org/u/jpfeifer)\
**Post date:** [2 May 2021 11:57 UTC](https://forum.dynare.org/t/fevd-using-bandpass-filter-6-32-in-stoch-simul-interpretation/18019/2 "2021-05-02T11:57:54Z")

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No, that’s not it. Rather, you use a transformation to the frequency domain and apply the ideal band-pass filter there. See [https://www.sfu.ca/~kkasa/uhlig1.pdf](https://www.sfu.ca/~kkasa/uhlig1.pdf)