Multivariate HP filter

[lauren29]

Hello
I would like to implement a multivariate HP filter (HPMV) to US GDP. I have already done the univariate method (trend+cycle), but now I would like to add a new piece of information to the model.
Namely I want to include information about the financial cycle (eg: credit growth) to obtain a "better" measure of the output gap.

In the following article (http://www.rba.gov.au/publications/rdp/ ... dp9809.pdf) the authors define the loss function to minimize.



I was wondering how to estimate that kind of model in Eviews.
I'd be very grateful for any help

Thanks

[trubador]

HP filter can be formulated as a special case of local linear trend model: http://forums.eviews.com/viewtopic.php? ... 46&p=16856
Therefore, I would also suggest the use of multivariate extension: http://forums.eviews.com/viewtopic.php? ... 13&p=27359

[lauren29]

Thank you very much for your reply.
I thought there was an alternative to the use of state space model for such specification (I aim at comparing HPMV and multivariate SSPACE models performances for estimating the output gap), so I guess it doesn't make sense tryng to do so.
Regards
Lauren

[trubador]

You can still do the comparison, if you like. Do not get confused with the estimation framework of the paper you cited. You can build a multivariate state space model. The only difference between the two would be the fixed variances. So, you can estimate them both and see if relaxing variances yields any significant improvement.

[lauren29]

Thank you Trubador

OK I will try do to that. I just want to make sure of one thing : when you say that the HPMV implies fixed variances, you refer to the lambda (for quarterly data = 1600), the ratio of the variance of noise to the variance of the signal, right?

Regards

[trubador]

Yes, that is correct.

[lauren29]

Hello,

I have formulated the following state space model :

Code: Select all

@signal lgdp=trend+cycle @state trend=c(1) + trend(-1) + [var=exp(c(2))] @state cycle=c(3) * cycle(-1) + c(4) *lcycle(-1) + [var=exp(c(5))] @state lcycle=cycle(-1) @signal dhouse_p=c(6)*dhouse_p(-1) + c(7)*cycle + [var=exp(c(8))] param c(1)0.66 c(2) -8.767 c(3) 1.17 c(4) -0.31 c(5) -8.767 c(6) 0.86 c(7) -0.11 c(8) -8.767 @mprior a0 @vprior v0

The results look alright

Now I want to modify that code (as Trubador suggested), so with the help of that topic : http://forums.eviews.com/viewtopic.php? ... 46&p=16856 I formulated the following HPMV model where I have imposed the following constraint:
(variance of noise / variance of the signal)=1600 (lambda)

Code: Select all

@signal lgdp=trend+cycle + [var=exp(c(5))] @state trend=c(1) + trend(-1) + [var=exp(c(5))/lambda] @state cycle=c(3) * cycle(-1) + c(4) *lcycle(-1) + [var=exp(c(5))/lambda] @state lcycle=cycle(-1) @signal dhouse_p=c(6)*dhouse_p(-1) + c(7)*cycle+ [var=exp(c(5))] param c(1)0.66 c(3) 1.17 c(4) -0.31 c(5) -8.767 c(6) 0.86 c(7) -0.11 @mprior a0 @vprior v0

I feel like my model is mispecified. Especially since in the unconstrained SSPACE model (the 1st one) I did not include an error term in the first signal equation. Also, I am a bit confused by the fact that here I have two signal equations, and I'm not sure if I should impose the same coefficient for variance.
I'd be very grateful for any help

Regards