VECM-GARCH Model

[faaequah13]

MV-GARCH, BEKK - Estimation by BFGS
Convergence in 80 Iterations. Final criterion was 0.0000032 <= 0.0000100

With Heteroscedasticity/Misspecification Adjusted Standard Errors
Usable Observations 4544
Log Likelihood -15002.7789

Variable Coeff Std Error T-Stat Signif
************************************************************************************
Mean Model(RITC)
1. RITC{5} 0.014171412 0.015869322 0.89301 0.37185352
2. RIND{5} 0.114807655 0.146229108 0.78512 0.43238218
3. Constant -0.025138834 0.062641921 -0.40131 0.68819184
Mean Model(RIND)
4. RITC{5} 0.000681188 0.002079070 0.32764 0.74318326
5. RIND{5} 0.026549952 0.016746460 1.58541 0.11287393
6. Constant 0.003580589 0.003114716 1.14957 0.25032033

7. C(1,1) 2.713493996 0.437193036 6.20663 0.00000000
8. C(2,1) -0.035145786 0.014254174 -2.46565 0.01367654
9. C(2,2) -0.000012592 0.014748386 -8.53819e-04 0.99931875
10. A(1,1) 0.021359765 0.032256754 0.66218 0.50785613
11. A(1,2) 0.000685967 0.001097622 0.62496 0.53199896
12. A(2,1) -0.259154876 0.091460361 -2.83352 0.00460382
13. A(2,2) 0.366881785 0.065551088 5.59688 0.00000002
14. B(1,1) 0.798965203 0.068231509 11.70962 0.00000000
15. B(1,2) 0.005712736 0.004236554 1.34844 0.17751710
16. B(2,1) -0.081382745 0.061126799 -1.33138 0.18306537
17. B(2,2) 0.937636451 0.021022358 44.60187 0.00000000

HI, TOM DOAN SIR
I Am attaching me results of bekk, can u help me out by taking the look, is it okay? and what we mean about positive definitness of conditional covariance?

[TomDoan]

The BEKK model, by construction, will always give a positive definite covariance matrix at every time period, no matter what the data look like and no matter what the parameters are. That's not true with a DVECH or VECH model, though the "advantage" of the BEKK in that sense is greatly overstated---if you estimate a DVECH model, it will always produce positive definite covariance matrices in sample (the log likelihood would be undefined otherwise), and if you have estimated such a model it is almost impossible to feed it any alternative data that will not also produce positive definite covariance matrices.

[faaequah13]

A IS representing arch term and B representing GARCH term and C is representing constant term. now my question is, which term represent covariance matrix?
C12,A12,A21,B12,B21- Only these term represent as covariance term as per my understanding, Am i right? if yes than in the previous post i have attached result in which one of the parameter is negative. what it mean. is my result not true after convergence.
can u suggest me a detailed literature on bekk model?

[TomDoan]

The A's and B's are the coefficients in the GARCH recursion---they are NOT supposed to be positive definite; in fact, you can change the signs of all elements of A or B without changing the model. See

https://estima.com/ratshelp/garchmvrpf. ... utput_BEKK

[faaequah13]

You mean the results of arch and garch coefficients are not appropriate, I need to multiply by -1 to A or B, if I do so my positive elements become negative and negative become positive, now in that case how it is said positive definite. Actually I am non mathematician and econometric background, and I am trying to learn and I have to submit thesis very soon.

[TomDoan]

You mean the results of arch and garch coefficients are not appropriate, I need to multiply by -1 to A or B, if I do so my positive elements become negative and negative become positive, now in that case how it is said positive definite. Actually I am non mathematician and econometric background, and I am trying to learn and I have to submit thesis very soon.

No. It's just that there is no need for those to be positive definite. The A and B come in through quadratic forms: A'uu'A is always positive semi-definite no matter what A and u are; B'HB is positive semi-definite if H is, no matter what the B's are. B'HB is exactly the same as (-B')H(-B) for any H (same for the terms involving A), that is, you can flip the signs of all elements of B and get exactly the same model, so you should not focus on the signs of elements of A and B (or their determinants or their eigenvalues).

There doesn't seem to be anything obviously wrong with your GARCH estimates. The only concern I would have is why you are using lag 5 only in your mean model. Why just 5 and not 1, 2, 3 and 4? (Lag 1 by itself is fairly normal. 5 by itself isnt').

[faaequah13]

MV-GARCH, BEKK - Estimation by BFGS
Convergence in 80 Iterations. Final criterion was 0.0000032 <= 0.0000100

With Heteroscedasticity/Misspecification Adjusted Standard Errors
Usable Observations 4544
Log Likelihood -15002.7789

Variable Coeff Std Error T-Stat Signif
************************************************************************************
Mean Model(RITC)
1. RITC{5} 0.014171412 0.015869322 0.89301 0.37185352
2. RIND{5} 0.114807655 0.146229108 0.78512 0.43238218
3. Constant -0.025138834 0.062641921 -0.40131 0.68819184
Mean Model(RIND)
4. RITC{5} 0.000681188 0.002079070 0.32764 0.74318326
5. RIND{5} 0.026549952 0.016746460 1.58541 0.11287393
6. Constant 0.003580589 0.003114716 1.14957 0.25032033

7. C(1,1) 2.713493996 0.437193036 6.20663 0.00000000
8. C(2,1) -0.035145786 0.014254174 -2.46565 0.01367654
9. C(2,2) -0.000012592 0.014748386 -8.53819e-04 0.99931875
10. A(1,1) 0.021359765 0.032256754 0.66218 0.50785613
11. A(1,2) 0.000685967 0.001097622 0.62496 0.53199896
12. A(2,1) -0.259154876 0.091460361 -2.83352 0.00460382
13. A(2,2) 0.366881785 0.065551088 5.59688 0.00000002
14. B(1,1) 0.798965203 0.068231509 11.70962 0.00000000
15. B(1,2) 0.005712736 0.004236554 1.34844 0.17751710
16. B(2,1) 0.081382745 0.061126799 -1.33138 0.18306537
17. B(2,2) 0.937636451 0.021022358 44.60187 0.00000000

i have flip the sign of B(2,1) as you can see in previous result that B(2,1) was negative, now is it correct? i have taken five lags due to AIC criteria.

[TomDoan]

NO.NO.NO. Do not change the signs of any of the coefficients. There is no reason the B's and A's can't be negative. Period. That's the only point I'm trying to make.

If you want five lags in the VAR, use LAGS 1 to 5; not LAGS 5.

[faaequah13]

MV-GARCH, BEKK - Estimation by BFGS
Convergence in 59 Iterations. Final criterion was 0.0000061 <= 0.0000100

With Heteroscedasticity/Misspecification Adjusted Standard Errors
Usable Observations 4544
Log Likelihood -14984.5280

Variable Coeff Std Error T-Stat Signif
************************************************************************************
Mean Model(RITC)
1. RITC{1} -0.006394160 0.015047694 -0.42493 0.67089044
2. RITC{2} -0.026800489 0.014688685 -1.82457 0.06806641
3. RITC{3} -0.019161004 0.005909614 -3.24234 0.00118551
4. RITC{4} -0.001386251 0.008761138 -0.15823 0.87427770
5. RITC{5} 0.006832066 0.009650703 0.70793 0.47898594
6. RIND{1} -0.052426683 0.081942197 -0.63980 0.52230211
7. RIND{2} -0.094867975 0.071690193 -1.32330 0.18573404
8. RIND{3} 0.043928110 0.073698161 0.59605 0.55113892
9. RIND{4} -0.117674560 0.091565448 -1.28514 0.19874283
10. RIND{5} 0.117996209 0.140375152 0.84058 0.40058461
11. Constant -0.015611995 0.044877841 -0.34788 0.72793212
Mean Model(RIND)
12. RITC{1} -0.002834884 0.003278583 -0.86467 0.38722142
13. RITC{2} -0.003758668 0.003091325 -1.21588 0.22403219
14. RITC{3} -0.000385656 0.000911914 -0.42291 0.67236232
15. RITC{4} 0.000848833 0.002289792 0.37070 0.71085872
16. RITC{5} 0.001087069 0.001384066 0.78542 0.43220913
17. RIND{1} -0.060782493 0.015036502 -4.04233 0.00005292
18. RIND{2} -0.001429565 0.014617746 -0.09780 0.92209386
19. RIND{3} 0.004776242 0.016415467 0.29096 0.77108200
20. RIND{4} 0.027714436 0.015042705 1.84238 0.06541903
21. RIND{5} 0.031297296 0.014587836 2.14544 0.03191785
22. Constant 0.002994589 0.003692138 0.81107 0.41732441

23. C(1,1) 3.263999855 0.480811543 6.78852 0.00000000
24. C(2,1) -0.018437511 0.010296273 -1.79070 0.07334185
25. C(2,2) 0.029790857 0.013240709 2.24994 0.02445248
26. A(1,1) -0.017053725 0.015810280 -1.07865 0.28074473
27. A(1,2) -0.003135119 0.003241337 -0.96723 0.33342890
28. A(2,1) -0.268564925 0.076731205 -3.50007 0.00046513
29. A(2,2) 0.360366812 0.030802094 11.69943 0.00000000
30. B(1,1) 0.689848340 0.105567048 6.53469 0.00000000
31. B(1,2) 0.004077235 0.000960257 4.24598 0.00002176
32. B(2,1) -0.164466231 0.107903052 -1.52420 0.12745783
33. B(2,2) 0.939020800 0.009723545 96.57185 0.00000000
now, is it okay? i have changed the lags to 1 to 5. is it okay?

[TomDoan]

Yes. That's fine. What's the RITC variable? It seems to have somewhat odd properties (the own lag VAR coefficients are mainly negative and the GARCH properties are a bit weak).

[faaequah13]

log return of ITC company.

[faaequah13]

Hello Sir, can u help me in interpretation of Johansen's countertraction test?

[TomDoan]

Cointegration? If you show me the output, I can help.

[faaequah13]

sorry, yes cointegration- yes i can share the output below:

Code: Select all

@johmle(lags=5,det=constant,cv=cv)
# rcoal rind

Likelihood Based Analysis of Cointegration
Variables:  RCOAL RIND
Estimated from 6 to 1938
Data Points 1933 Lags 5 with Constant

Unrestricted eigenvalues and -T log(1-lambda)
  Rank    EigVal  Lambda-max  Trace  Trace-95%    LogL
       0                                       -5304.1966
       1   0.0043     8.3202 13.1618   15.4100 -5300.0365
       2   0.0025     4.8416  4.8416    3.8400 -5297.6157

Cointegrating Vector for Largest Eigenvalue
RCOAL    RIND
0.083548 0.050923

here it is.

[faaequah13]

i think the above result showing no cointegration