## Almon/PDL in MiDaS

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KrilleJ
Posts: 40
Joined: Fri Feb 20, 2015 6:15 am

### Almon/PDL in MiDaS

We have recently been exploring MiDaS in EViews, it is a really great feature. Also, the MiDaS webinar was superb.

However, I have a minor problem with the Almon/PDL weighting in the MiDaS estimation. The issue is described in the attached PDF.

Also, when determining the degree of the Almon polynomial, I miss an estimated parameter. Suppose that I choose polynomial degree 3. Then I would expect to get 4 estimated parameters (the a_i:s) for the polynomial: a_0+a_1*X+a_2*X^2+a_3*X^3. But only three estimated parameters are presented in the output. I suspect that a second degree polynomial is estimated when setting polynomial degree to 3: a_0+a_1*X+a_2*X^2. Is this so or is it a restricted (a_0=0) third degree polynomial (a_1*X+a_2*X^2+a_3*X^3) that is estimated?

Best,
Kristian
Attachments
AlmonLagsEViews.pdf

EViews Gareth
Fe ddaethom, fe welon, fe amcangyfrifon
Posts: 11983
Joined: Tue Sep 16, 2008 5:38 pm

### Re: Almon/PDL in MiDaS

Here's an EViews program that manually computes an example MIDAS model, and shows the weighting calculations:

Code: Select all

!xlags = 4
!ylags=1
!horizon=2
!polyorder = 3 ' matlab order +1

wfopen(wf=midas, page=quarterly) .\mydata.xlsx range="Sheet1"
series x1 = dlog(value(-!horizon))*100
for !i=2 to !xlags
series x!i = x1(-!i+1)
next
for !i=1 to !xlags
series z!i=x!i(-2)
next

pageselect quarterly
series y = dlog(value)*100
smpl 1985 2009/1/1

for !i=1 to !xlags
copy(c=l) monthly\z!i x!i
next

for !i=1 to !polyorder
series z!i=0
next

for !i=1 to !xlags
for !j=1 to !polyorder
z!j = z!j + !i^(!j-1)*x!i
next
next

group xlags z*

group ylags
for !i=1 to !ylags
next

equation eq2.ls y c xlags ylags

show eq2

equation eq1.midas(freq=first) y c y(-1) @ monthly\x1

show eq1
Attachments
mydata.xlsx

KrilleJ
Posts: 40
Joined: Fri Feb 20, 2015 6:15 am

### Re: Almon/PDL in MiDaS

It is exectly this I am after.

Estimations in EViews and the MiDaS toolbox for Matlab use the weighting

for !i=1 to !xlags
for !j=1 to !polyorder
z!j = z!j + !i^(!j-1)*x!i
next
next

In the documentation for the MiDaS Matlab toolbox (see equation 2.10 in the documentation for version 2.1 as of August 3, 2016), in the documentation for EViews 9.5 (Equation 28.6) and in Intriligator (1978) Econometric models, techniques, and applications, page 183, equation 6.7.28, the weighting described for the Almon/PDL case is

for !i=1 to !xlags
for !j=1 to !polyorder
z!j = z!j + (!i-1)^(!j-1)*x!i
next
next

This might of course be a minor difference (although the curvature of the estimated parameters seems to be affected), but if I understand you correctly it is the documentation that is the candidate to be changed and not the estimation routine?

EViews Gareth
Fe ddaethom, fe welon, fe amcangyfrifon
Posts: 11983
Joined: Tue Sep 16, 2008 5:38 pm

### Re: Almon/PDL in MiDaS

Yes

Acrobatcr
Posts: 1
Joined: Mon Oct 08, 2018 3:38 pm

### Re: Almon/PDL in MiDaS

Hi.

I post my question here as it seems the most appropiate thread.

I am using MiDaS in Eviews 10.

With PDL/ALmon weighting, if I use equation 28.5 in the Eviews documention (which is consistent with all Ghysels papers and his Matlab toolbox documentation), I cannot replicate the lag weights in the output. Please see Excel file. In order to obtain the reported lag weights I have to divide the estimates according to equation 28.5 (column (1) ) by the lag number. I cannot find a reference to this variation of Almon weighting. Is this correct and should the documentation be modified?

Thanks.
Attachments
Example_Midas.xlsx