Vector Autoregressive Model, Impulse Response Functions and Forecast Error Decomposition

[Dmitrij Bytovan]

Good Evening everyone,

I am writing my Master Thesis and have a question regarding my programming and if I did not make a mistake somewhere.

I am using CDS data from banks from the year 2010 until the end of 2023. I am using the weighted average of the CDS of the banks based on the Total Assets value of the banks to calculate the Country index. Afterwards I calculate the logathimic return of the Country index. I also calculate the general return of the Euribor as the interest rate was negative for some time in Europe and I can not use the logarithmic return in this case.

In the following I want to create Vector Autoregressive Models with only 2 variables in each model, explicitly the logarithmic return of one Country index and the return of the Euribor. I also want to see which variables causes which, so I use Granger Causality. To analyze how one variable causes the other, I use Impulse Response Functions and Forecast Error Variance Decomposition.

In the following you will see the extract from my data. In this case you see the logarithmic return of Germany Index and the return of the Euribor as variables.

* Example generated by -dataex-. For more info, type help dataex
clear
input double(logRetGer EURIBOR_ret)
 -.0008014830285189013                     0
   -.00584418500812003 -.0014285714285714457
  -.012739185594069698  -.007153075822603716
  -.006811061390831834 -.0028818443804035088
   -.00648451575592779 -.0014450867052022698
  -.013719130225710039 -.0028943560057886897
   .008814034818116715  -.005805515239477366
   .009069609881145599 -.0014598540145985828
   .010345526811589952 -.0029239766081871066
    .00863079240874731 -.0029325513196480912
  .0038169302922630667  -.004411764705882337
  -.005042368677640866  -.002954209748892156
    .02896551084103673  -.001481481481481528
  .0013641110225295803 -.0029673590504450953
   .012289439781784843 -.0029761904761904656
  -.014296752480117872 -.0014925373134327957
 -.0030742423386257087  -.002989536621823663
    .00400158027583307 -.0029985007496251548
   .004743096737987085                     0
  .0069640995208763165                     0
  .0024376452424326486                     0
  -.005216658290761326                     0
-.00018017967925330634                     0
    .02580239606151851                     0
   .007002358654900506  -.003007518796992459
   .010371841677900773  -.003016591251885359
  -.005835596314967259                     0
   -.01074118288924797   .001512859304084735
 -.0013974243861093149                     0
   .008973370473476775  .0015105740181269312
    .00807586281750453  -.003016591251885359
   .005774222293185463    .00302571860816947
  -.011153073737283739 -.0015082956259426794
 -.0006444289101124145 -.0030211480362537513
  -.012066391649905419  .0015151515151514694
   -.01195080082200128                     0
   .014909036908611766                     0
   .010880373138635786   -.00302571860816947
   .005371140991983641 -.0015174506828528056
  -.009628323111307227  -.003039513677811523
 -.0028819914264924897 -.0015243902439023849
  -.017474910923017187                     0
  -.010138857447169036                     0
    .00814934651860331 -.0015267175572518665
   -.00918346392829665  -.001529051987767538
  -.010293038032942143 -.0015313935681470214
  -.005160373152986908                     0
   -.01193137496287989 -.0015337423312883347
    .01086081075473966  -.001536098310291889
   .003457071742120132 -.0015384615384614886
   .003626195047814202 -.0046224961479198745
   .005245166957581305                     0
  -.008012453284861137  -.003095975232198178
  .0029392998528342193 -.0015527950310558758
  .0016977529772582616 -.0015552099533436836
   .012481315082787854  -.004672897196261738
 -.0071930215364009635  -.003129890453834161
  -.008109888624258934 -.0015698587127158659
  .0037015497987476186 -.0015723270440252124
   .004245131950873587  .0015748031496063408
   -.01316382013902603 -.0015723270440252124
  -.002255699547970582                     0
    .00939025620288736 -.0015748031496063408
   .004694470243154606   .001577287066246047
 -.0054011035127074425                     0
   .004671443015811678                     0
 -.0010580185215920497     .0047244094488188
   .007237487365698195  .0015673981191222097
   .014639933326672678  .0015649452269170805
 -.0061897790054639005  .0015624999999999112
  -.019719089057449547  .0015600624024960652
  -.008519122386445565  .0031152647975078995
   .005846889976324979                     0
  .0008467025519094847                     0
    .01389685342615629                     0
   .021578501597306062 -.0015527950310558758
   -.00859383468938192 -.0015552099533436836
   .008991888047594853                     0
    .04347040290739087  .0031152647975078995
  -.009218453367740392  .0015527950310558758
   .015235561305605378                     0
     .0239521394521279  .0015503875968991832
   .024483016705930255    .01238390092879249
  -.014804824436020688   .007645259938837912
  -.011762531734938951   .006069802731411222
   .001707812283492125   .003016591251885359
     .0384144596344394   .004511278195488799
   .026065620649810013  .0059880239520957446
   .040446359745061326   .007440476190476275
   .023102563440638275   .007385524372230501
   -.08475933451141952                     0
   .025572234040501397                     0
   -.04047955305713239                     0
  -.008231716844995048  .0014662756598240456
   .029643721022751663  .0014641288433381305
   .013891693235009642  .0014619883040936088
 -.0067611949546571865   .004379562043795415
    .02212268672188685  .0029069767441860517
    .02355279349832604  .0028985507246377384
   .007230757725513529   .004335260115607031
end

Here you can see the Do-File I used to run the described mode.

import excel "C:\Users\dbyto\Desktop\Master_Studium\1. Semester\Thesis\stata\VAR_euribor.xlsx", sheet("Tabelle1") firstrow
 
* Old time variable = t
tsset t
format t %td 
* In this setting: Gaps at weekends

* Load event calendar. Caution: Event calendar file cb must be saved in the same folder and must be opened during the analyses. 
bcal load cb
* Define new time variable based on t but omit the weekendes. The start and end date musst be changes in the cb file (range). 
generate t1 = bofd("cb",t)

* Format new time variable
format t1 %tbcb
* Now tsset data using t1 rather t. This solves the gaps in the data. 
tsset t1 

dfuller logRetFr

dfuller EURIBOR_ret

var logRetFr EURIBOR_ret, lags(1,2,3)

varsoc

varstable
 
predict error, resid

summarize error

varlmar 

vargranger

irf set irf

irf create IRFlogFrEUR, step(10)

irf graph irf, irf(IRFlogFrEUR) impulse(logRetFr EURIBOR_ret) response(logRetFr EURIBOR_ret)

irf table fevd, irf(IRFlogFrEUR) impulse(logRetFr EURIBOR_ret) response(logRetFr EURIBOR_ret) noci

translate @Results mylog.txt

type mylog.txt

Hope to hear from you and will be glad to get help.

Kind Regards

Dmitrij Bytov'an