Jump GARCH Replication of Q stats

[spollard777]

Hi

I have some questions about jump garch. I downloaded the program and associated files. I run them with no problem. I know that for the jump garch models, that u is the residuals and h is the variance. I follow the formulas on UG-290 and UG-291 to get the standardized and squared standardized residuals. However, I can't seem to replicate the Q2 stats in Table 2. It seems that the standardized Q is closer to what they report? Are these not the right residuals to use.

Also, is there a way to calculate the other Q statistic of the innovations of the application of the filter as discussed on page 379 eq 5.

Thanks for any help.

For example
set ustd end1969+1 end1984 = u/sqrt(h)
set ustdsq end1969+1 end1984 = ustd(t)^2
For @regcorrs(report) ustdsq end1969+1 end1984
I get:

Lag Corr Partial LB Q Q Signif
1 0.009 0.009 0.66396 0.4152
2 -0.003 -0.003 0.73342 0.6930
3 -0.002 -0.002 0.76142 0.8587
4 0.002 0.002 0.78214 0.9408
5 0.003 0.003 0.86033 0.9730
6 -0.012 -0.012 2.09142 0.9111
7 -0.004 -0.004 2.22564 0.9463
8 -0.003 -0.003 2.31126 0.9700
9 0.006 0.006 2.64319 0.9768
10 0.010 0.010 3.47823 0.9678
11 -0.002 -0.003 3.53070 0.9817
12 0.003 0.003 3.61393 0.9894
13 0.004 0.004 3.72922 0.9937
14 -0.005 -0.005 3.91105 0.9960
15 -0.006 -0.006 4.19508 0.9970
and for
@regcorrs(report) ustd end1969+1 end1984
I get


Lag Corr Partial LB Q Q Signif
1 0.010 0.010 0.93374 0.3339
2 0.009 0.009 1.59371 0.4507
3 0.025 0.025 7.10706 0.0686
4 0.013 0.013 8.65494 0.0703
5 0.013 0.012 10.06799 0.0733
6 -0.018 -0.019 12.72879 0.0476
7 0.001 0.001 12.73783 0.0788
8 0.015 0.014 14.61935 0.0670
9 -0.003 -0.003 14.69930 0.0995
10 0.009 0.009 15.39571 0.1183
11 -0.014 -0.015 17.11087 0.1046
12 0.007 0.007 17.54590 0.1302
13 -0.006 -0.007 17.90478 0.1612
14 -0.003 -0.002 18.00020 0.2068
15 0.001 0.001 18.01749 0.2617

[TomDoan]

They're using a modified Q test. I've just posted a procedure for this at:

http://www.estima.com/forum/viewtopic.php?f=7&t=1375

[spollard777]

Hi,

This is an edited post based on my more discovery on my part.

I am trying to reproduce more of their paper. I believe that xi is the series of jump density residuals/shocks. lam is the series of lambda over time. Both from the ARJI models

Remaining questions: Are the standardized residuals found by u/sqrt(h) for these models? When I check the modified Q stats for the standardized squared residuals for the ARJI-ht model they are not close to what is in the table.

And, can one get xi for the Constant intensity jump model? I have and idea how to add this based on the ARJI models, but wanted to get it right.

As for the evaluation of the density of the forecasts, I found that discussion elsewhere on the forum, so ignore any earlier posts about that.


Thanks.

Stephen Pollard

[TomDoan]

Hi,

This is an edited post based on my more discovery on my part.

I am trying to reproduce more of their paper. I believe that xi is the series of jump density residuals/shocks. lam is the series of lambda over time. Both from the ARJI models

Remaining questions: Are the standardized residuals found by u/sqrt(h) for these models? When I check the modified Q stats for the standardized squared residuals for the ARJI-ht model they are not close to what is in the table.

And, can one get xi for the Constant intensity jump model? I have and idea how to add this based on the ARJI models, but wanted to get it right.

The standardized residuals that they are using are the one-step normalized errors taking into account the jump process (their formulas (18) and (19)). The updated programs (http://www.estima.com/forum/viewtopic.php?f=8&t=1578) include this.