First of all, that isn't converged, so don't spend too much time analyzing the results.
I recommend using @VARLAGSELECT on the original pair of variables to pick the lag length.
It sounds like you need to review how cointegration works. The cointegrating vector can be arbitrarily rescaled---if (1,-1) is a cointegrating vector, then so is (65,-65). The estimated cointegrating vector from @JOHMLE is subject to a scaling which depends upon eigenvalues deep inside the calculation. If (as appears likely) (1,-1) is a proper cointegrating vector, then the very slight difference between the two components is due to sampling error. If you use the estimated cointegrating vector with the 65 scale, then the corresponding loadings will be smaller by (roughly) the corresponding factor of 65 relative to what you would get if you used (1,-1).
The GARCH chapter in the manual talks about diagnostics for multivariate models.
vecm - mgarch-bekk
Re: vecm - mgarch-bekk
Tom,
I adjusted the code( residuals' ditribution is assumed to be t distrubution). And var lag number is set to be 10 based on @varlagselect(crit=gtos).
here is code:
Diagnostic tests shows that there are some correlations in first residuals (I chose various lags but there were still some correlations).
Distribution of residuals are not clearly normal and so I used t distribution. ( I am not sure it is correct option to use t distribution instead of normal distribution).
But there are some questions:
1. ECT terms are positive (and very low) while one of them should be positive.
2. First variables have negative impact on the second variable while one expect that it should have positive effects.
3. Past lags of first variable have negative effects on its current value. It seems strange.
3. Overall, I am not sure about results. I think it seems there is something wrong with results.
I would be grateful if you could possibly guide me how I can improve my model.
I adjusted the code( residuals' ditribution is assumed to be t distrubution). And var lag number is set to be 10 based on @varlagselect(crit=gtos).
here is code:
Code: Select all
calendar(7) 2000:1:1
open data d:\new5.xlsx
data(org=col,format=xlsx)
@johmle(lags=10,det=constant,cv=cvector)
# lf lsb
equation(coeffs=cvector) ecteq *
# lf lsb
set dlf = lf-lf{1}
set dlsb = lsb-lf{1}
set ect = %eqnprj(ecteq,t)
*
<<obsolete code deleted by moderator>>
[code]
and output:
[code]
Likelihood Based Analysis of Cointegration
Variables: LF LSB
Estimated from 2000:01:11 to 2001:06:07
Data Points 514 Lags 10 with Constant
Unrestricted eigenvalues and -T log(1-lambda)
Rank EigVal Lambda-max Trace Trace-95% LogL
0 2638.0949
1 0.0407 21.3527 23.3820 15.4100 2648.7712
2 0.0039 2.0293 2.0293 3.8400 2649.7859
Cointegrating Vector for Largest Eigenvalue
LF LSB
-65.335498 65.301447
MV-GARCH, BEKK - Estimation by BFGS
Convergence in 216 Iterations. Final criterion was 0.0000000 <= 0.0000001
Daily(7) Data From 2000:01:12 To 2001:06:07
Usable Observations 513
Log Likelihood 2852.7465
Variable Coeff Std Error T-Stat Signif
************************************************************************************
Mean Model(DLF)
1. DLF{1} -0.072178597 0.072558986 -0.99476 0.31985421
2. DLF{2} -0.118226712 0.057778732 -2.04620 0.04073692
3. DLF{3} -0.153718764 0.065609963 -2.34292 0.01913359
4. DLF{4} 0.209311523 0.056701411 3.69147 0.00022296
5. DLF{5} -0.006112132 0.058226303 -0.10497 0.91639802
6. DLF{6} 0.091833606 0.054703348 1.67876 0.09319949
7. DLF{7} 0.046746488 0.055291339 0.84546 0.39785534
8. DLF{8} 0.042646325 0.058851006 0.72465 0.46866737
9. DLF{9} 0.080260404 0.048481837 1.65547 0.09782845
10. DLF{10} 0.073094931 0.052891019 1.38199 0.16697436
11. DLSB{1} -0.004076816 0.084357226 -0.04833 0.96145484
12. DLSB{2} 0.016041849 0.068788213 0.23321 0.81560116
13. DLSB{3} 0.237571202 0.077627768 3.06039 0.00221049
14. DLSB{4} -0.279371906 0.072136266 -3.87284 0.00010758
15. DLSB{5} 0.128470728 0.068381756 1.87873 0.06028162
16. DLSB{6} 0.004134627 0.068551880 0.06031 0.95190568
17. DLSB{7} -0.053489074 0.065405661 -0.81780 0.41346857
18. DLSB{8} -0.005368809 0.070291921 -0.07638 0.93911777
19. DLSB{9} -0.028509214 0.060631688 -0.47020 0.63820984
20. DLSB{10} -0.017830458 0.053289394 -0.33460 0.73792930
21. ECT{1} 0.000791657 0.000866426 0.91370 0.36087214
Mean Model(DLSB)
22. DLF{1} -0.268836246 0.069857557 -3.84835 0.00011892
23. DLF{2} -0.194837578 0.040407117 -4.82186 0.00000142
24. DLF{3} -0.157449574 0.049103277 -3.20650 0.00134361
25. DLF{4} 0.100215344 0.044132268 2.27080 0.02315938
26. DLF{5} -0.006287160 0.044078298 -0.14264 0.88657752
27. DLF{6} 0.083843963 0.040930190 2.04846 0.04051469
28. DLF{7} 0.021488616 0.044919270 0.47838 0.63237762
29. DLF{8} 0.055307810 0.042301648 1.30746 0.19105575
30. DLF{9} 0.009586137 0.035618152 0.26914 0.78782482
31. DLF{10} -0.017314549 0.036042219 -0.48040 0.63094562
32. DLSB{1} 0.361912230 0.078588595 4.60515 0.00000412
33. DLSB{2} 0.147732017 0.051324327 2.87840 0.00399696
34. DLSB{3} 0.195645295 0.056677104 3.45193 0.00055660
35. DLSB{4} -0.104149454 0.056585469 -1.84057 0.06568476
36. DLSB{5} 0.067227263 0.056153702 1.19720 0.23122826
37. DLSB{6} -0.022770540 0.052510401 -0.43364 0.66455085
38. DLSB{7} -0.037253695 0.051449746 -0.72408 0.46901706
39. DLSB{8} -0.091296362 0.051596071 -1.76944 0.07681980
40. DLSB{9} 0.008727635 0.046954122 0.18588 0.85254215
41. DLSB{10} 0.037731185 0.039067525 0.96579 0.33414723
42. ECT{1} 0.004663873 0.000886652 5.26010 0.00000014
43. C(1,1) 0.013005924 0.001961295 6.63129 0.00000000
44. C(2,1) 0.003921509 0.003065726 1.27915 0.20084591
45. C(2,2) 0.001173481 0.008710377 0.13472 0.89283150
46. A(1,1) 0.267653869 0.132479957 2.02033 0.04334867
47. A(1,2) 0.478750862 0.125250248 3.82235 0.00013218
48. A(2,1) 0.304337815 0.125439148 2.42618 0.01525875
49. A(2,2) 0.365002432 0.105487556 3.46015 0.00053988
50. B(1,1) 0.982194062 0.138722175 7.08030 0.00000000
51. B(1,2) 0.805373601 0.107892920 7.46456 0.00000000
52. B(2,1) -1.317602590 0.120181947 -10.96340 0.00000000
53. B(2,2) -0.651149972 0.107512195 -6.05652 0.00000000
54. D(1,1) 0.239252017 0.225031570 1.06319 0.28769438
55. D(1,2) -0.048327314 0.208412665 -0.23188 0.81662904
56. D(2,1) 0.464440346 0.307131254 1.51219 0.13048592
57. D(2,2) 0.237129296 0.226523300 1.04682 0.29518225
58. Shape 3.764491208 0.483643165 7.78361 0.00000000
Distribution of residuals are not clearly normal and so I used t distribution. ( I am not sure it is correct option to use t distribution instead of normal distribution).
But there are some questions:
1. ECT terms are positive (and very low) while one of them should be positive.
2. First variables have negative impact on the second variable while one expect that it should have positive effects.
3. Past lags of first variable have negative effects on its current value. It seems strange.
3. Overall, I am not sure about results. I think it seems there is something wrong with results.
I would be grateful if you could possibly guide me how I can improve my model.
Re: vecm - mgarch-bekk
- Why are you using 7 day a week data? Won't that have large numbers of non-trading days? Didn't you ask about that earlier, and I told you to go to weekly data? With several non-trading days in a row repeated throughout the sample, you will get serially correlated residuals. I guarantee it.
- You also clearly didn't read what I wrote about scale and cointegrating vectors---you're using the estimated ones with the scale on the order of 65, so the alpha's will be scaled down by 65.
- I would never recommend using GTOS as the method for selection in a VAR. Use BIC or AIC. However, if you want the lag coefficients to all have the correct sign, you'll be waiting for a long time---it doesn't happen.
Re: vecm - mgarch-bekk
I really appreciat your reply Tom.
But:
1- My first question is that: can someone rely on the sign of the parameters of the model. For example, it seems that futures price (DLF) have a negative effect on spot price (DLSB) that is counter intuitive. So, does it undermine my model?(I know that parameters' of VAR model sometimes have unexpected sign).
2. What about residuals' distribution? I chose t distribution because J-B test rejects normality of the residuals. Did I select a true distribution?
I have excluded non trading days from my sample. So, There are not any zero returns in my data. I selected 7 day a week calendar JUST to estimate model, it dose not mean that there are zero mean returns in data ( I could select other formats of calendar like 5 day but, I think, it dose not make a difference regarding parameters estimation).Why are you using 7 day a week data? Won't that have large numbers of non-trading days?
I really apologize about this point. I used to use Eviews that automatically normalize coefficient vector. I got the point and I try to fix this one.You also clearly didn't read what I wrote about scale and cointegrating vectors-
I used AIC for lag selection in VAR (AIC suggested 3 lags). And here is results:would never recommend using GTOS as the method for selection in a VAR. Use BIC or AIC.
Code: Select all
MV-GARCH, BEKK - Estimation by BFGS
Convergence in 109 Iterations. Final criterion was 0.0000000 <= 0.0000001
Daily(7) Data From 2000:01:05 To 2001:06:07
Usable Observations 520
Log Likelihood 2867.9030
Variable Coeff Std Error T-Stat Signif
************************************************************************************
Mean Model(DLF)
1. DLF{1} -0.104726463 0.076517261 -1.36866 0.17110416
2. DLF{2} -0.071853419 0.063030787 -1.13997 0.25429740
3. DLF{3} -0.141595628 0.062019173 -2.28309 0.02242481
4. DLSB{1} 0.015576869 0.087828064 0.17736 0.85922845
5. DLSB{2} -0.123496758 0.073570002 -1.67863 0.09322432
6. DLSB{3} 0.145195159 0.068783172 2.11091 0.03477996
7. ECT{1} 0.000392793 0.001196126 0.32839 0.74261874
Mean Model(DLSB)
8. DLF{1} -0.714298504 0.059958635 -11.91319 0.00000000
9. DLF{2} -0.179074268 0.047891179 -3.73919 0.00018461
10. DLF{3} -0.164494619 0.046597437 -3.53012 0.00041537
11. DLSB{1} 0.802595289 0.065548091 12.24437 0.00000000
12. DLSB{2} 0.072093244 0.056417636 1.27785 0.20130253
13. DLSB{3} 0.153945927 0.049887444 3.08587 0.00202961
14. ECT{1} -0.002562251 0.000920760 -2.78276 0.00538992
15. C(1,1) 0.015714644 0.001676188 9.37523 0.00000000
16. C(2,1) 0.009090535 0.002385918 3.81008 0.00013892
17. C(2,2) -0.002061536 0.004557052 -0.45238 0.65099251
18. A(1,1) 0.383826688 0.120564084 3.18359 0.00145461
19. A(1,2) 0.468368420 0.085248367 5.49416 0.00000004
20. A(2,1) 0.185636912 0.105673698 1.75670 0.07896908
21. A(2,2) 0.322066736 0.088505709 3.63894 0.00027377
22. B(1,1) 0.283213131 0.254071372 1.11470 0.26497939
23. B(1,2) 0.604049678 0.163487186 3.69478 0.00022007
24. B(2,1) -0.959097172 0.253767246 -3.77944 0.00015718
25. B(2,2) -0.722222415 0.156886045 -4.60348 0.00000415
26. D(1,1) 0.762798697 0.232117188 3.28627 0.00101525
27. D(1,2) 0.335393132 0.177015828 1.89471 0.05813123
28. D(2,1) -0.201395359 0.292885380 -0.68763 0.49168885
29. D(2,2) -0.166987461 0.228220600 -0.73169 0.46435585
30. Shape 4.187630202 0.551848383 7.58837 0.00000000
1- My first question is that: can someone rely on the sign of the parameters of the model. For example, it seems that futures price (DLF) have a negative effect on spot price (DLSB) that is counter intuitive. So, does it undermine my model?(I know that parameters' of VAR model sometimes have unexpected sign).
2. What about residuals' distribution? I chose t distribution because J-B test rejects normality of the residuals. Did I select a true distribution?
Re: vecm - mgarch-bekk
If the data aren't daily (or weekly or whatever), don't use a CALENDAR that labels them as such.
I'm always suspect of any GARCH model with a t distribution with estimated degrees of freedom that's that small. That's usually an indication that you have a few very large outliers that can't be explained by the GARCH process.
I'm always suspect of any GARCH model with a t distribution with estimated degrees of freedom that's that small. That's usually an indication that you have a few very large outliers that can't be explained by the GARCH process.
Re: vecm - mgarch-bekk
Thank you for your help.
Do you mean I should remove outliers from the data?
Do you mean I should remove outliers from the data?
Re: vecm - mgarch-bekk
Not necessarily. An outlier in a GARCH model is a natural "experiment" in whether the GARCH variance process describes the data. If you have a big outlier, it should be followed by a fairly lengthy period of elevated volatility. If it isn't, then you need to figure out why the outlier is present. If it's due to (for instance) a change in law or policy, you may need to exclude a larger period than just one data point. Remember that when you estimate one of these GARCH models, you're saying that one process is supposed to provide a reasonable approximation to the volatility dynamics for the entire data set.COMI wrote:Thank you for your help.
Do you mean I should remove outliers from the data?
VECM-MGARCH-BEKK
Dear tom,COMI wrote:Thank you very much for the insightful and informative guidance you gave me here in RATS forums. I learned so much from you.
I just excluded first half of the data set and this is the final results from bekk vecm:Code: Select all
MV-GARCH, BEKK - Estimation by BFGS Convergence in 79 Iterations. Final criterion was 0.0000000 <= 0.0000100 With Heteroscedasticity/Misspecification Adjusted Standard Errors Usable Observations 478 Log Likelihood -905.3081 Variable Coeff Std Error T-Stat Signif ************************************************************************************ Mean Model(DLX) 1. DLX{1} -0.469852739 0.072277425 -6.50068 0.00000000 2. DLX{2} -0.042194519 0.071854942 -0.58722 0.55705727 3. DLY{1} 0.479989991 0.077901431 6.16150 0.00000000 4. DLY{2} 0.152567368 0.076116500 2.00439 0.04502800 5. Constant 0.032005787 0.042540470 0.75236 0.45183405 6. ECT{1} 0.120494298 0.042808179 2.81475 0.00488153 Mean Model(DLY) 7. DLX{1} -0.135971624 0.073779143 -1.84295 0.06533561 8. DLX{2} -0.095986609 0.071252789 -1.34713 0.17793909 9. DLY{1} -0.015456804 0.080778746 -0.19135 0.84825342 10. DLY{2} 0.052187982 0.079427821 0.65705 0.51114932 11. Constant -0.002793417 0.039845889 -0.07011 0.94410967 12. ECT{1} 0.049129260 0.035825619 1.37134 0.17026764 13. C(1,1) 0.264537030 0.064302940 4.11392 0.00003890 14. C(2,1) 0.282051310 0.074770615 3.77222 0.00016180 15. C(2,2) -0.000010973 0.009857068 -0.00111 0.99911180 16. A(1,1) 0.585947112 0.193703812 3.02496 0.00248662 17. A(1,2) 0.539532404 0.161717423 3.33627 0.00084912 18. A(2,1) -0.181957025 0.317154379 -0.57372 0.56615897 19. A(2,2) -0.388020645 0.280421673 -1.38370 0.16644905 20. B(1,1) 0.845819877 0.103034135 8.20912 0.00000000 21. B(1,2) -0.084104770 0.100658332 -0.83555 0.40340978 22. B(2,1) 0.016585319 0.076773077 0.21603 0.82896405 23. B(2,2) 0.956960775 0.070549791 13.56433 0.00000000 Multivariate Q(10)= 40.30750 Significance Level as Chi-Squared(34)= 0.21130 Test for Multivariate ARCH Statistic Degrees Signif 31.31 27 0.25863
I have a question about the above results.
According the mean models, we can see that LX variable (futures market) reacts to deviation from long run relationship but DY variable (spot market) dose not react to the deviation from this relationship.
But according to the variance models, LX's squared returns (A(1,2)) has a positive and significant effect on the the current volatility of
LY (shocks to futures market lag-one returns has a significant effect on the current conditional volatility of spot market returns). And meanwhile, LY's squared returns dose not have a significant effect on the the current volatility of LX ((A(2,1)).
I mean, when futures market reacts to the deviation from long run relationship and spot market dose not, then, the results that shocks to the futures market has a statistically significant effect on the spot market volatility and shocks to the spot market dose not have a statistically significant effect on the futures market are somehow counter intuitive. In this regards, one expects that shocks to the spot market also has a statistically significant effect.
Do you think that the results are logical?
Re: vecm - mgarch-bekk
That would be the interpretation of the results. This is your data---you're supposed to understand how the markets work. However, it's not unreasonable for a market to be the major source of uncertainty (risk) without driving the level. After all, the whole point of GARCH models is that you can have predictability in the volatility, even if you don't have predictability in the level.
Re: vecm - mgarch-bekk
Thank you very much for your kind relply;
I don't know why univariate arch test cannot reject heteroscedasticity but multivariate arch test rejects heteroscedasticity (bekk model):
And when I estimate cc model results change in comparison with bekk model:
I don't know which model is better.
I don't know why univariate arch test cannot reject heteroscedasticity but multivariate arch test rejects heteroscedasticity (bekk model):
Code: Select all
Independence Tests for Series Z1
Test Statistic P-Value
Ljung-Box Q(10) 14.552596 0.1492
McLeod-Li(10) 27.750828 0.0020
Turning Points -0.253600 0.7998
Difference Sign 0.870534 0.3840
Rank Test -1.925204 0.0542
Independence Tests for Series Z2
Test Statistic P-Value
Ljung-Box Q(10) 12.600122 0.2469
McLeod-Li(10) 27.741655 0.0020
Turning Points 0.181143 0.8563
Difference Sign 0.079139 0.9369
Rank Test -1.917752 0.0551
Multivariate Q(10)= 40.30750
Significance Level as Chi-Squared(34)= 0.21130
Test for Multivariate ARCH
Statistic Degrees Signif
100.40 90 0.21299Code: Select all
MV-CC GARCH with Spillover Variances - Estimation by BFGS
Convergence in 47 Iterations. Final criterion was 0.0000036 <= 0.0000100
With Heteroscedasticity/Misspecification Adjusted Standard Errors
Usable Observations 478
Log Likelihood -901.3928
Variable Coeff Std Error T-Stat Signif
************************************************************************************
Mean Model(DLF)
1. DLF{1} -0.451901300 0.075309402 -6.00060 0.00000000
2. DLF{2} -0.044341994 0.077438011 -0.57261 0.56690691
3. DLSB{1} 0.507481398 0.083692029 6.06368 0.00000000
4. DLSB{2} 0.127622864 0.082471956 1.54747 0.12174999
5. Constant 0.014118626 0.025963130 0.54380 0.58658240
6. ECT{1} 0.101421006 0.022728447 4.46229 0.00000811
Mean Model(DLSB)
7. DLF{1} -0.105257521 0.068630646 -1.53368 0.12510814
8. DLF{2} -0.083795663 0.069491691 -1.20584 0.22788029
9. DLSB{1} -0.011470864 0.079574296 -0.14415 0.88537975
10. DLSB{2} 0.019374760 0.082987820 0.23347 0.81540026
11. Constant -0.021143137 0.027052883 -0.78155 0.43448002
12. ECT{1} 0.032831195 0.022697681 1.44646 0.14804936
13. C(1) 0.012459757 0.011531237 1.08052 0.27990976
14. C(2) 0.011548422 0.016423858 0.70315 0.48196281
15. A(1,1) 0.068480820 0.040593817 1.68698 0.09160785
16. A(1,2) 0.106251519 0.043092234 2.46568 0.01367547
17. A(2,1) 0.005141506 0.016330426 0.31484 0.75288154
18. A(2,2) 0.080033841 0.041831718 1.91323 0.05571817
19. B(1) 0.837806202 0.045326241 18.48391 0.00000000
20. B(2) 0.907741914 0.051314802 17.68967 0.00000000
21. R(2,1) 0.818844071 0.018481913 44.30516 0.00000000
Independence Tests for Series Z1
Test Statistic P-Value
Ljung-Box Q(10) 15.147859 0.1268
McLeod-Li(10) 28.732833 0.0014
Turning Points 0.181143 0.8563
Difference Sign 0.553976 0.5796
Rank Test -1.615085 0.1063
Independence Tests for Series Z2
Test Statistic P-Value
Ljung-Box Q(10) 14.576261 0.1483
McLeod-Li(10) 13.355187 0.2045
Turning Points 0.398514 0.6903
Difference Sign 0.870534 0.3840
Rank Test -1.885078 0.0594
Multivariate Q(10)= 39.77825
Significance Level as Chi-Squared(34)= 0.22831
Test for Multivariate ARCH
Statistic Degrees Signif
107.52 90 0.10048Re: vecm - mgarch-bekk
First of all, you are describing the result backwards---they reject homoscedasticity since that's the null hypothesis. That may be a power issue---the univariate tests are looking at just own with own, while the multivariate are doing all cross combinations, so they are testing 90 things rather than 10. I would look at the specific correlations of the squared univariate residuals to see if the failure is on the short lags or one "random" lags. If it's the latter (and it usually is), then there's nothing to fix.COMI wrote:Thank you very much for your kind relply;
I don't know why univariate arch test cannot reject heteroscedasticity but multivariate arch test rejects heteroscedasticity (bekk model):Code: Select all
Independence Tests for Series Z1 Test Statistic P-Value Ljung-Box Q(10) 14.552596 0.1492 McLeod-Li(10) 27.750828 0.0020 Turning Points -0.253600 0.7998 Difference Sign 0.870534 0.3840 Rank Test -1.925204 0.0542 Independence Tests for Series Z2 Test Statistic P-Value Ljung-Box Q(10) 12.600122 0.2469 McLeod-Li(10) 27.741655 0.0020 Turning Points 0.181143 0.8563 Difference Sign 0.079139 0.9369 Rank Test -1.917752 0.0551 Multivariate Q(10)= 40.30750 Significance Level as Chi-Squared(34)= 0.21130 Test for Multivariate ARCH Statistic Degrees Signif 100.40 90 0.21299
The CC-Spillover has a higher log likelihood on fewer parameters with better diagnostics. Seems like an obvious choice. Note that all GARCH models are approximations at best. None is actually "correct" and in many cases people choose a particular model out of inertia in the literature (I use a BEKK because papers A, B and C did a BEKK even if there was no strong reason to prefer the BEKK).COMI wrote: And when I estimate cc model results change in comparison with bekk model:
I don't know which model is better.
Re: vecm - mgarch-bekk
Something that is really strange is the changing of results from bekk to cc model:
In bekk model A(1,2) is statistically significant meaning that residuals of first variable (futures market) has a positive effect on volatility of the other variable (spot market) not vice versa.
But in the cc model it is the residuals of spot market (A(1,2) please correct me if I am wrong) that have a statistically positive effect on the spot market volatility not vice versa. I think the results of cc model are more consistent with the error correction terms.
I think that stability of results are really fragile.
So, I follow your insightful recommendation and choose cc model for studying the relationship between spot and futures market.
In bekk model A(1,2) is statistically significant meaning that residuals of first variable (futures market) has a positive effect on volatility of the other variable (spot market) not vice versa.
But in the cc model it is the residuals of spot market (A(1,2) please correct me if I am wrong) that have a statistically positive effect on the spot market volatility not vice versa. I think the results of cc model are more consistent with the error correction terms.
I think that stability of results are really fragile.
So, I follow your insightful recommendation and choose cc model for studying the relationship between spot and futures market.
Re: vecm - mgarch-bekk
The two models aren't easily compared. However, also, see the last sentence before the output in
https://estima.com/ratshelp/garchmvrpf. ... utput_BEKK
https://estima.com/ratshelp/garchmvrpf. ... utput_BEKK
VARLAGSELECT - Automatic lag selection in a VAR
Dear Tom,COMI wrote: Usable Observations 478
Log Likelihood -905.3081
Variable Coeff Std Error T-Stat Signif
************************************************************************************
Mean Model(DLX)
1. DLX{1} -0.469852739 0.072277425 -6.50068 0.00000000
2. DLX{2} -0.042194519 0.071854942 -0.58722 0.55705727
3. DLY{1} 0.479989991 0.077901431 6.16150 0.00000000
4. DLY{2} 0.152567368 0.076116500 2.00439 0.04502800
5. Constant 0.032005787 0.042540470 0.75236 0.45183405
6. ECT{1} 0.120494298 0.042808179 2.81475 0.00488153
Mean Model(DLY)
7. DLX{1} -0.135971624 0.073779143 -1.84295 0.06533561
8. DLX{2} -0.095986609 0.071252789 -1.34713 0.17793909
9. DLY{1} -0.015456804 0.080778746 -0.19135 0.84825342
10. DLY{2} 0.052187982 0.079427821 0.65705 0.51114932
11. Constant -0.002793417 0.039845889 -0.07011 0.94410967
12. ECT{1} 0.049129260 0.035825619 1.37134 0.17026764
.
I have a question about the above results.
As you can see, coefficients of DLY equation are all insignificant in conventional level (diagnostic tests show that the model is ok). Therefore F test for this equation will be insignificant probably. Is anything wrong about this model? I mean if in a VECM model like this one that all of the coefficients of one of the equations are insignificant statistically, can anyone rely on the model's results? Can anyone criticize the model as a whole?
Thank you very much in advance.
Re: vecm - mgarch-bekk
There's nothing necessarily wrong with those results. Y and X can be cointegrated even if Y is a simple random walk, as all the adjustment to keep the two together can be done by changes to X.