Intervention Modeling

[ac_1]

Hi Tom,


Questions based on the following example from the User's Guide, Section 6.4.3., https://estima.com/ratshelp/index.html? ... ction.html (Note: for PERM the results on UG-202 and the intervention.rpf link are different. Running the program file I get N_PERM{0} 0.1284936068 and N_PERM{1} 0.1379586480, not negative coeffs as in UG-202)

Modelling a series with a large increase in the mean level at a specific point in time e.g. a 240% increase.

I get results like

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boxjenk(diff=1,constant,inputs=1,ar=1) series
# perm 1

Variable                        Coeff      Std Error      T-Stat      Signif
************************************************************************************
1.  CONSTANT                      0.004880935  0.000422505     11.55238  0.00000000
2.  AR{1}                         0.288520147  0.038839065      7.42861  0.00000000
3.  N_PERM{0}                    -1.182720875  0.008725208   -135.55217  0.00000000
4.  N_PERM{1}                     1.177920073  0.008754546    134.54953  0.00000000

or

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boxjenk(diff=1,constant,inputs=1,ar=1) series
# temp 1 1

Variable                        Coeff      Std Error      T-Stat      Signif
************************************************************************************
1.  CONSTANT                      0.004872733  0.000417972     11.65804  0.00000000
2.  AR{1}                         0.280859613  0.039655939      7.08241  0.00000000
3.  N_TEMP{0}                     1.184484584  0.008989514    131.76292  0.00000000
4.  N_TEMP{1}                    -1.111213683  0.086284220    -12.87853  0.00000000
5.  D_TEMP{1}                     0.945505494  0.070280984     13.45322  0.00000000

as I am already differencing the series I have not used the APPLYDIFFS option. These appear reasonable. Correct?


And, for a series with a 14% decrease, i.e. let's say a temporary drop in the mean, and then back to 'normal' levels.

If specified similar as above, and without APPLYDIFFS

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    Variable                        Coeff      Std Error      T-Stat      Signif
************************************************************************************
1.  CONSTANT                      0.001497142  0.000396097      3.77974  0.00016635
2.  AR{1}                         0.884178851  0.024865579     35.55835  0.00000000
3.  MA{1}                        -0.586593602  0.042356423    -13.84899  0.00000000
4.  N_PERM{0}                     0.149402878  0.003414694     43.75293  0.00000000
5.  N_PERM{1}                    -0.159008357  0.003442834    -46.18531  0.00000000

and as a temp

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    Variable                        Coeff      Std Error      T-Stat      Signif
************************************************************************************
1.  CONSTANT                      0.001667754  0.000361307      4.61589  0.00000443
2.  AR{1}                         0.883954710  0.025024540     35.32351  0.00000000
3.  MA{1}                        -0.609878494  0.042512854    -14.34574  0.00000000
4.  N_TEMP{0}                    -0.144644152  0.003415858    -42.34490  0.00000000
5.  N_TEMP{1}                     0.137009282  0.007880181     17.38657  0.00000000
6.  D_TEMP{1}                     0.759636356  0.055720977     13.63286  0.00000000

Are these reasonable?

thanks,
Amarjit

[TomDoan]

I am already differencing the series I have not used the APPLYDIFFS option.

What does that mean? I see a BOXJENK with a DIFFS option which is very much not "already differencing the series". APPLYDIFFERENCES is used when the shift is in the level of series (which seems to be what you're describing happened). It means that the difference operator is also applied to the shift dummy (or a better way to look at it, the dummy is taken off the level before differencing is done). If you pass an already differenced series to BOXJENK (so there is no DIFFS option), you need a completely different type of dummy to model a level shift since differencing the data has eliminated the level in the data itself.

[ac_1]

Apologies, I have not used good examples!

From INTERVENTION.RPF, if

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dummy(ao=1987:10) temp 1947:1 1993:12

TEMP has 0's everywhere, except for 1987:10 where it's a 1.

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boxjenk(diff=1,applydiff,constant,inputs=1,ma=1) logsp_500 $
   1980:1 1993:12 tresids
# temp 1 1

    Variable                        Coeff      Std Error      T-Stat      Signif
************************************************************************************
1.  CONSTANT                      0.008715909  0.003419433      2.54893  0.01172839
2.  MA{1}                         0.317061758  0.074340267      4.26501  0.00003377
3.  N_TEMP{0}                     0.001909992  0.020301010      0.09408  0.92515830
4.  N_TEMP{1}                    -0.002947065  0.021264954     -0.13859  0.88994688
5.  D_TEMP{1}                    -0.952734786  0.072001530    -13.23215  0.00000000

and if I estimate

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boxjenk(diff=1,constant,ma=1,regressors) logsp_500 1980:1 1993:12
# temp

    Variable                        Coeff      Std Error      T-Stat      Signif
************************************************************************************
1.  CONSTANT                      0.009288393  0.003129933      2.96760  0.00344796
2.  MA{1}                         0.230195541  0.076654291      3.00304  0.00308932
3.  TEMP                         -0.094441083  0.032510365     -2.90495  0.00417695

The latter is easier to understand: it's a 'constant' dummy, i.e. independent of the MA term, if the date is not 1987:10 the value of logsp_500 is 0.009288393; if the date is 1987:10 the value of logsp_500 is 0.009288393+(-0.094441083), i.e. reduced due to the significant events of October 1987.

What do the N_STEP{0}, N_STEP{0}, D_STEP{1}, coeffs represent? And how to interpret?

[TomDoan]

If you are really interested, you should find a book which goes into this in some depth. As described in the user's guide and the description of BOXJENK, the numerator terms handle specific delayed responses while the denominator handles geometric responses. In this case

effect(t)=(n0+n1L)/(1+d1L) I(t)

where I is the intervention variable. d1=-1 is basically an "integrator" which would mean that I really should have been a level shift rather than a point shock. So -.9 means it's close to that. As described in the User's Guide, because the data are monthly averages, the data itself will not show the full effect for a period anyway (since the October data that are averaged in are largely before the shock), hence the need for a lag in the numerator.

Note that some descriptions of this will pull the n0 factor out, so both the numerator and denominator lag polynomials have a lead unit coefficient. (That is

effect(t)=n0 x (1 + (n1/n0)L)/(1+d1L) I(t)

That obviously has no effect on the statistics and n0 doesn't even have any real economic significance since the overall effect depends upon all the coefficients. You might also find different signing conventions in both polynomials.