Integrated GARCH

[Dario Maimone Ansaldo Patti]

Dear All,

I posted a similar thread some time ago but I did not get any reply. I would like to estimate an integrated garch model, since the sum of the arch and the garch terms in my model is larger than 1.

My data:

* Example generated by -dataex-. To install: ssc install dataex
clear
input float wpi int t float ln_wpi
 30.7  0  3.424263
 30.8  1 3.4275146
 30.7  2  3.424263
 30.7  3  3.424263
 30.8  4 3.4275146
 30.5  5  3.417727
 30.5  6  3.417727
 30.6  7     3.421
 30.7  8  3.424263
 30.6  9     3.421
 30.7 10  3.424263
 30.7 11  3.424263
 30.6 12     3.421
 30.5 13  3.417727
 30.6 14     3.421
 30.7 15  3.424263
 30.7 16  3.424263
 30.6 17     3.421
 30.7 18  3.424263
 30.7 19  3.424263
 30.9 20  3.430756
 31.2 21  3.440418
 31.4 22  3.446808
 31.6 23  3.453157
 32.1 24  3.468856
 32.2 25 3.4719665
 32.6 26  3.484312
 32.4 27 3.4781585
 32.3 28  3.475067
 32.3 29  3.475067
 32.4 30 3.4781585
 32.5 31   3.48124
 32.9 32  3.493473
 33.1 33  3.499533
 33.3 34  3.505557
 33.4 35  3.508556
 33.9 36  3.523415
 34.4 37 3.5380566
 34.7 38   3.54674
   35 39  3.555348
 35.5 40 3.5695326
 35.7 41  3.575151
 35.9 42  3.580737
 35.9 43  3.580737
 36.5 44  3.597312
 36.9 45 3.6082115
 37.2 46  3.616309
 37.2 47  3.616309
 37.9 48  3.634951
 38.3 49   3.64545
 38.8 50   3.65842
 39.2 51  3.668677
 41.1 52  3.716008
 43.1 53  3.763523
 44.9 54  3.804438
 45.3 55  3.813307
 48.3 56 3.8774316
   50 57  3.912023
 53.6 58  3.981549
 55.4 59   4.01458
 55.4 60   4.01458
   56 61 4.0253515
 57.2 62  4.046554
 57.8 63 4.0569887
 58.1 64 4.0621657
   59 65 4.0775375
 59.7 66  4.089332
 60.2 67 4.0976725
 61.6 68 4.1206617
   63 69 4.1431346
 63.1 70 4.1447206
 63.9 71 4.1573195
 65.4 72 4.1805224
 67.4 73  4.210645
 68.4 74  4.225373
   70 75  4.248495
 72.5 76 4.2835865
 75.1 77 4.3188205
 77.4 78 4.3489866
 80.2 79 4.3845234
 83.9 80 4.4296255
 85.6 81  4.449685
 88.4 82  4.481872
 90.4 83 4.5042443
 93.1 84 4.5336742
 95.2 85 4.5559797
 95.9 86  4.563306
 95.8 87 4.5622625
 96.6 88 4.5705786
 96.7 89 4.5716133
 97.1 90 4.5757413
 97.2 91  4.576771
 97.3 92  4.577799
 97.6 93 4.5808773
 98.6 94  4.591071
 99.1 95 4.5961294
100.2 96  4.607168
100.8 97  4.613138
100.6 98  4.611152
100.3 99 4.6081657
end
format %tq t

Unfortunately, I cannot find any specific command in Stata to estimate an Integrated GARCH. However, since such a model poses a constraint on the values of the arch and garch model (i.e. their sum cannot be larger than 1), I though I could estimate the model as follows:

constraint 1 [ARCH]l1.arch+[ARCH]l1.garch=1

arch D.ln_wpi, arch(1) garch(1) constraints(1)

Nonetheless, I am not sure if this is the correct way to proceed. Could someone help? Thanks in advance.

Dari

[Justin Niakamal]

The response here is a bit late, but I had this same question.

It appears you can estimate an Integrated GARCH as

webuse "wpi1.dta", clear 
constraint 1 _b[ARCH:L.garch] + _b[ARCH:L.arch] = 1
arch D.ln_wpi, arch(1) garch(1) constraints(1)

[Dario Maimone Ansaldo Patti]

Justin Blasongame thanks for your feedback. Even if late, still really appreciated.

[Hessel Bouwman]

Dear Justin Niakamal , Dario Maimone Ansaldo Patti ,

In my search to estimate an IGARCH model in STATA, I came across your discussion. Similar to the case of Dario, I am also dealing with ARCH and GARCH terms that in sum exceed 1.

The code posted above seems a solution to estimate an IGARCH manually. However, I was wondering where I can find more documentation/discussion on estimating an IGARCH in STATA (using this particular code).

Can any of you help me with this or point me in the right direction?

I would highly appreciate your help.

Kind regards,

Hessel

[Dario Maimone Ansaldo Patti]

Hi,

I did not find yet any resources, using a code similar to the one above. It is based on the functioning of an IGARCH. So starting from the idea that charactirrse the iGARCH, the command above solves the issue

[Glaucia Grellmann]

Dear all,
I am estimating a panel IGARCH model, but I wonder how to test the heteroskedasticity and autocorrelation (the diagnostic tests after the estimation). I saw that the Stata doesn't allow the use of these tests for panel data.
Is there another way to test the diagnosis of IGARCH for panel data?

Thanks in advance.