IRF From Estimated VECM with DCC-MGARCH

[cmcknigh]

Hello,

I have estimated a VECM with a DCC-MGARCH specification and I am wondering how to recover IRF's for the underlying mean equation (i.e. the VECM). I am new to RATS so any help would be greatly appreciated. My general code to estimate this system is:

Code: Select all

equation(coeffs=cv) ecteq *
# WHEAT CORN ETHANOL GAS
system(model=basevecm)
variables WHEAT CORN ETHANOL GAS
lags 1 2
det constant
ect ecteq
end(system)
estimate(residuals=resids)

garch(model=basevecm,mv=dcc,asymmetric,stdresids=stdu,hmatrices=hh,rvectors=rr,method=bhhh,iters=1000)

[TomDoan]

You can simply do IMPULSE(MODEL=BASEVECM,other options). The one thing about impulse responses in GARCH models is that there isn't a single covariance matrix for the model like there is in the typical VAR. You would need to figure out what shock sizes you want.

[cmcknigh]

Thank you for your response @TomDoan. A couple of quick follow up questions. (1) How would I go about calculating confidence bands if I wanted to graph these IRF's? (2) Is the default shock simply a one standard deviation shock? and (3) I know in other statistical software like Stata and EViews, the VECM output breaks down the ECT parameter into something like 〖ECT〗_(t-1)=1.000*〖wheat〗_(t-1)-1.66876*〖corn〗_(t-1)+1.852559*〖ethanol〗_(t-1)-0.465659*〖gasoline〗_(t-1)-4.432442. However in the RATS output, I only see one estimated coefficient on the EC1{1} parameter. Is there a way to break it down? Thanks again for your help.

[TomDoan]

Thank you for your response @TomDoan. A couple of quick follow up questions. (1) How would I go about calculating confidence bands if I wanted to graph these IRF's?

Unfortunately, that's very complicated because the lag coefficients are being estimated as part of a non-linear estimation, so there's no simple density from which to do the simulations like there is for a VAR or a VECM without GARCH errors. It's doable, but requires a technique like Markov Chain Monte Carlo which usually requires some experimentation to get the chain to work properly.

(2) Is the default shock simply a one standard deviation shock?

I don't think you want that. It looks like unit shocks (or .01 shocks if you didn't multiply up by 100) would make more sense under the circumstances. (FACTOR=%IDENTITY(%NVAR) or FACTOR=.01*%IDENTITY(%NVAR) depending upon the desired scale).

(3) I know in other statistical software like Stata and EViews, the VECM output breaks down the ECT parameter into something like 〖ECT〗_(t-1)=1.000*〖wheat〗_(t-1)-1.66876*〖corn〗_(t-1)+1.852559*〖ethanol〗_(t-1)-0.465659*〖gasoline〗_(t-1)-4.432442. However in the RATS output, I only see one estimated coefficient on the EC1{1} parameter. Is there a way to break it down?

You can do

display ecteq

to see the linear combination used in the error correction term. I'm not sure how writing that out accomplishes much.

[cmcknigh]

Thanks again for this help. My data is logged price series, so what could I do if I wanted to graph a shock of 10% and not a unit increase?

[TomDoan]

The recommendation would be use 100*log(..) which makes it possible to do everything naturally as a percentage (rather than using decimals). With that, the 10% shocks to each variable would be FACTOR=10*%IDENTITY(%NVAR).