question about NO CONVERGENCE

[jingran]

I am running a multivariate asymmetric dynamic covariance model.

The code is as follows,
OPEN DATA d:\study\newdataus.XLS

ALL 4959
DATA(FORMAT=XLS,ORG=COLUMNS)


******************************************
COMPUTE GSTART=2 , GEND=4959

* n = the number of equations:
******************************************
compute n=5


* definition

dec vect[series] y(n) u(n)
dec vect[frml] resid(n)
dec symm hx(n,n) uux(n,n)
dec vect ux(n)
dec symm[series] h(n,n)
dec symm[series] uu(n,n)
declare frml[symm] hf
dec vect b(n)

* set regressors
******************************************
set y(1) = US
set y(2) = UK
set y(3) = JP
set y(4) = HK
set y(5) = SG

set st11 = US1
set st13 = US3
set st21 = UK1
set st23 = UK3
set st31 = JP1
set st33 = JP3
set st41 = HK1
set st42 = HK2
set st51 = SG1
set st52 = SG2


* mean equation

*dec vect bm(n)
*dec rect ba(n,n)
dec rect ba(n,n)


nonlin(parmset=meanparms) b ba
*********************************************************************************************

frml resid(1) = y(1)-b(1)-ba(1,1)*y(1){1}-ba(1,2)*y(2){1}-ba(1,3)*y(3){1}-ba(1,4)*y(4){1}-ba(1,5)*y(5){1}
frml resid(2) = y(2)-b(2)-ba(2,1)*y(1){1}-ba(2,2)*y(2){1}-ba(2,3)*y(3){1}-ba(2,4)*y(4){1}-ba(2,5)*y(5){1}
frml resid(3) = y(3)-b(3)-ba(3,1)*y(1){1}-ba(3,2)*y(2){1}-ba(3,3)*y(3){1}-ba(3,4)*y(4){1}-ba(3,5)*y(5){1}
frml resid(4) = y(4)-b(4)-ba(4,1)*y(1){1}-ba(4,2)*y(2){1}-ba(4,3)*y(3){1}-ba(4,4)*y(4){1}-ba(4,5)*y(5){1}
frml resid(5) = y(5)-b(5)-ba(5,1)*y(1){1}-ba(5,2)*y(2){1}-ba(5,3)*y(3){1}-ba(5,4)*y(4){1}-ba(5,5)*y(5){1}





* Initialization

*compute bm=%const(0.0)
compute ba=%const(0.0)
compute b=%const(0.0)

do i=1,n
linreg(noprint) y(i) / u(i)
# constant
compute b(i)=%beta(1)
end do i

vcv(matrix=rr,noprint)
# u

do i=1,n
do j=1,i
set h(i,j) = rr(i,j)
set uu(i,j) = 0.0
end do j
end do i

* Logliklihood function

frml logl = $
hx = hf(t) , $
%do(i,1,n,u(i)=resid(i)),$
ux = %xt(u,t) , uux = %outerxx(ux),$
%pt(h,t,hx),%pt(uu,t,%outerxx(ux)),$
%logdensity(hx,ux)



***********ADC Variance*************


dec rect vbr(n,n) vgv(n,n)
dec symm vcr(n,n) vav(n,n)
dec real rho12 rho13 rho14 rho15 rho23 rho24 rho25 rho34 rho35 rho45
dec real huai12 huai13 huai14 huai15 huai23 huai24 huai25 huai34 huai35 huai45
dec real s11 s13 s21 s23 s31 s33 s41 s42 s51 s52



nonlin(parmset=garchparms1) vav vbr vcr vgv rho12 rho13 rho14 rho15 rho23 rho24 rho25
nonlin(parmset=garchparms2) rho34 rho35 rho45 huai12 huai13 huai14
nonlin(parmset=garchparms3) huai15 huai23 huai24 huai25 huai34 huai35 huai45
nonlin(parmset=garchparms4) s11 s13 s21 s23 s31 s33 s41 s42 s51 s52


FRML HF = $
(HX=%XT(H,T-1)),(UUX=%XT(UU,T-1)),$
ETAXX=||(%if(u(1){1}<0.0,uu(1,1){1},0.0)),(%if(u(1){1}<0.0.and.u(2){1}<0.0,uu(1,2){1},0.0)),(%if(u(1){1}<0.0.and.u(3){1}<0.0,uu(1,3){1},0.0)),$
(%if(u(1){1}<0.0.and.u(4){1}<0.0,uu(1,4){1},0.0)),(%if(u(1){1}<0.0.and.u(5){1}<0.0,uu(1,5){1},0.0))|$
(%if(u(1){1}<0.0.and.u(2){1}<0.0,uu(1,2){1},0.0)),(%if(u(2){1}<0.0,uu(2,2){1},0.0)),(%if(u(2){1}<0.0.and.u(3){1}<0.0,uu(2,3){1},0.0)),$
(%if(u(2){1}<0.0.and.u(4){1}<0.0,uu(2,4){1},0.0)),(%if(u(2){1}<0.0.and.u(5){1}<0.0,uu(2,5){1},0.0))|$
(%if(u(1){1}<0.0.and.u(3){1}<0.0,uu(1,3){1},0.0)),(%if(u(2){1}<0.0.and.u(3){1}<0.0,uu(2,3){1},0.0)),(%if(u(3){1}<0.0,uu(3,3){1},0.0)),$
(%if(u(3){1}<0.0.and.u(4){1}<0.0,uu(3,4){1},0.0)),(%if(u(3){1}<0.0.and.u(5){1}<0.0,uu(3,5){1},0.0))|$
(%if(u(1){1}<0.0.and.u(4){1}<0.0,uu(1,4){1},0.0)),(%if(u(2){1}<0.0.and.u(4){1}<0.0,uu(2,4){1},0.0)),(%if(u(3){1}<0.0.and.u(4){1}<0.0,uu(3,4){1},0.0)),$
(%if(u(4){1}<0.0,uu(4,4){1},0.0)),(%if(u(4){1}<0.0.and.u(5){1}<0.0,uu(4,5){1},0.0))|$
(%if(u(1){1}<0.0.and.u(5){1}<0.0,uu(1,5){1},0.0)),(%if(u(2){1}<0.0.and.u(5){1}<0.0,uu(2,5){1},0.0)),(%if(u(3){1}<0.0.and.u(5){1}<0.0,uu(3,5){1},0.0)),$
(%if(u(4){1}<0.0.and.u(5){1}<0.0,uu(4,5){1},0.0)),(%if(u(5){1}<0.0,uu(5,5){1},0.0))||,$
STT=||1+s11*st11+s13*st13,sqrt((1+s11*st11+s13*st13)*(1+s21*st21+s23*st23)),sqrt((1+s11*st11+s13*st13)*(1+s31*st31+s33*st33)),sqrt((1+s11*st11+s13*st13)*$
(1+s41*st41+s42*st42)),sqrt((1+s11*st11+s13*st13)*(1+s51*st51+s52*st52))|$
sqrt((1+s11*st11+s13*st13)*(1+s21*st21+s23*st23)),1+s21*st21+s23*st23,sqrt((1+s21*st21+s23*st23)*(1+s31*st31+s33*st33)),sqrt((1+s21*st21+s23*st23)*$
(1+s41*st41+s42*st42)),sqrt((1+s21*st21+s23*st23)*(1+s51*st51+s52*st52))|$
sqrt((1+s11*st11+s13*st13)*(1+s31*st31+s33*st33)),sqrt((1+s21*st21+s23*st23)*(1+s31*st31+s33*st33)),1+s31*st31+s33*st33,sqrt((1+s31*st31+s33*st33)*$
(1+s41*st41+s42*st42)),sqrt((1+s31*st31+s33*st33)*(1+s51*st51+s52*st52))|$
sqrt((1+s11*st11+s13*st13)*(1+s41*st41+s42*st42)),sqrt((1+s21*st21+s23*st23)*(1+s41*st41+s42*st42)),sqrt((1+s31*st31+s33*st33)*(1+s41*st41+s42*st42)),$
1+s41*st41+s42*st42,sqrt((1+s41*st41+s42*st42)*(1+s51*st51+s52*st52))|$
sqrt((1+s11*st11+s13*st13)*(1+s51*st51+s52*st52)),sqrt((1+s21*st21+s23*st23)*(1+s51*st51+s52*st52)),sqrt((1+s31*st31+s33*st33)*(1+s51*st51+s52*st52)),$
sqrt((1+s41*st41+s42*st42)*(1+s51*st51+s52*st52)),1+s51*st51+s52*st52||,$
FY=STT.*(%INNERXX(VCR)+VAV.*HX+%MQFORM(UUX./STT,VBR)+%MQFORM(ETAXX./STT,VGV)),$
DD=%diag(||sqrt(FY(1,1)),sqrt(FY(2,2)),sqrt(FY(3,3)),sqrt(FY(4,4)),sqrt(FY(5,5))||),$
RRHO=||1.0,rho12,rho13,rho14,rho15|rho12,1.0,rho23,rho24,rho25|rho13,rho23,1.0,rho34,rho35|$
rho14,rho24,rho34,1.0,rho45|rho15,rho25,rho35,rho45,1.0||,$
HHI=||0.0,huai12,huai13,huai14,huai15|huai12,0.0,huai23,huai24,huai25|huai13,huai23,0.0,huai34,huai35|$
huai14,huai24,huai34,0.0,huai45|huai15,huai25,huai35,huai45,0.0||,$
(DD*RRHO*DD+HHI.*FY)

*
* Initialize c's from the decomp of the covariance matrix
*
COMPUTE vcr = %decomp(rr)
compute vav = %mscalar(.50) ,vbr = %mscalar(.50) , vgv = %const(.30)
compute rho12 = 0.05, rho13 = 0.05, rho14 = 0.05, rho15 = 0.05, rho23 = 0.05
compute rho24 = 0.05, rho25 = 0.05, rho34 = 0.05, rho35 = 0.05
compute rho45 = 0.05, huai12 = 0.60, huai13 = 0.60, huai14 = 0.60, huai15 = 0.60
compute huai23 = 0.60, huai24 = 0.60, huai25 = 0.60
compute huai34 = 0.60, huai35 = 0.60, huai45 = 0.60
compute s11=0.05, s13=0.05, s21=0.05, s23=0.05, s31=0.05, s33=0.05, s41=0.05, s42=0.05, s51=0.05, s52=0.05



*
*MAXIMIZE(parmset=meanparms+garchparms1+garchparms2+garchparms3+garchparms4,METHOD=SIMPLEX,ITERS=50) LOGL GSTART GEND
NLPAR(subiters=500)
MAXIMIZE(parmset=meanparms+garchparms1+garchparms2+garchparms3+garchparms4,METHOD=Bfgs,ITERS=1800) LOGL GSTART GEND



But the result appears to be like this,


MAXIMIZE - Estimation by BFGS
NO CONVERGENCE IN 1126 ITERATIONS
LAST CRITERION WAS 0.0000046
ESTIMATION POSSIBLY HAS STALLED OR MACHINE ROUNDOFF IS MAKING FURTHER PROGRESS DIFFICULT.
TRY HIGHER SUBITERATIONS LIMIT, TIGHTER CVCRIT, DIFFERENT SETTING FOR EXACTLINE OR ALPHA ON NLPAR.
RESTARTING ESTIMATION FROM LAST ESTIMATES OR DIFFERENT INITIAL GUESSES MIGHT ALSO WORK
Usable Observations 4958
Function Value -40744.01025850

Variable Coeff Std Error T-Stat Signif
*******************************************************************************
1. B(1) 0.0295901 0.0092865 3.18637 0.00144071
2. B(2) 0.0150669 0.0140820 1.06994 0.28464609
3. B(3) -0.0365186 0.0288780 -1.26458 0.20602211
4. B(4) 0.0308491 0.0486810 0.63370 0.52627746
5. B(5) 0.0182589 0.0250838 0.72792 0.46666519
6. BA(1,1) 0.1533076 0.0151565 10.11498 0.00000000
7. BA(2,1) 0.1861083 0.0186784 9.96380 0.00000000
8. BA(3,1) 0.3059336 0.0264881 11.54983 0.00000000
9. BA(4,1) 0.3341442 0.0207432 16.10861 0.00000000
10. BA(5,1) 0.2991329 0.0245128 12.20311 0.00000000
11. BA(1,2) 0.0084914 0.0084001 1.01087 0.31208005
12. BA(2,2) 0.0646633 0.0160958 4.01740 0.00005884
13. BA(3,2) 0.1329602 0.0260043 5.11301 0.00000032
14. BA(4,2) 0.0975813 0.0235262 4.14777 0.00003357
15. BA(5,2) 0.0802209 0.0424778 1.88854 0.05895385
16. BA(1,3) -0.0080922 0.0040817 -1.98255 0.04741804
17. BA(2,3) 0.0001024 0.0066105 0.01549 0.98764181
18. BA(3,3) 0.0649158 0.0156347 4.15203 0.00003295
19. BA(4,3) -0.0351948 0.0180049 -1.95474 0.05061404
20. BA(5,3) -0.0205978 0.0136002 -1.51452 0.12989352
21. BA(1,4) -0.0056328 0.0061526 -0.91551 0.35992147
22. BA(2,4) 0.0032012 0.0098301 0.32566 0.74468475
23. BA(3,4) 0.0272430 0.0240570 1.13244 0.25745133
24. BA(4,4) 0.0983870 0.0916199 1.07386 0.28288513
25. BA(5,4) 0.0484242 0.0291046 1.66380 0.09615275
26. BA(1,5) 0.0073565 0.0050045 1.46997 0.14156954
27. BA(2,5) -0.0156963 0.0080301 -1.95467 0.05062152
28. BA(3,5) 0.0213645 0.0212526 1.00527 0.31476898
29. BA(4,5) 0.0025431 0.0457991 0.05553 0.95571870
30. BA(5,5) 0.0387715 0.0254261 1.52487 0.12729219
31. VAV(1,1) 0.7744627 0.0319129 24.26804 0.00000000
32. VAV(2,1) 5.0608202 1.6578956 3.05256 0.00226901
33. VAV(2,2) 0.8855390 0.0205808 43.02737 0.00000000
34. VAV(3,1) 0.8925902 1.2126924 0.73604 0.46170632
35. VAV(3,2) -53.8973519 7.5326897 -7.15513 0.00000000
36. VAV(3,3) 0.8595711 0.0160713 53.48501 0.00000000
37. VAV(4,1) 2.5958129 1.9716726 1.31655 0.18798826
38. VAV(4,2) -5.6270621 0.5703438 -9.86609 0.00000000
39. VAV(4,3) -2.2832977 1.4441841 -1.58103 0.11387128
40. VAV(4,4) 0.8612437 0.0134951 63.81879 0.00000000
41. VAV(5,1) 22.2758563 5.0486926 4.41220 0.00001023
42. VAV(5,2) -324.4338501 42.0109827 -7.72260 0.00000000
43. VAV(5,3) 1.0325796 0.4220237 2.44673 0.01441573
44. VAV(5,4) 1.0493052 0.1051323 9.98080 0.00000000
45. VAV(5,5) 0.8716735 0.0148190 58.82150 0.00000000
46. VBR(1,1) 0.2936619 0.0264452 11.10453 0.00000000
47. VBR(2,1) 0.0195581 0.0150478 1.29973 0.19369406
48. VBR(3,1) 0.0028222 0.0064964 0.43442 0.66398532
49. VBR(4,1) -0.0127419 0.0079742 -1.59789 0.11006650
50. VBR(5,1) 0.0053597 0.0066466 0.80638 0.42002182
51. VBR(1,2) -0.0020790 0.0247978 -0.08384 0.93318514
52. VBR(2,2) 0.2378404 0.0227828 10.43949 0.00000000
53. VBR(3,2) 0.0159426 0.0087656 1.81877 0.06894601
54. VBR(4,2) -0.0075311 0.0099038 -0.76042 0.44700288
55. VBR(5,2) -0.0091755 0.0090256 -1.01661 0.30934020
56. VBR(1,3) 0.0032558 0.0352896 0.09226 0.92649097
57. VBR(2,3) -0.0872003 0.0318850 -2.73484 0.00624104
58. VBR(3,3) 0.2294823 0.0180851 12.68904 0.00000000
59. VBR(4,3) -0.0834304 0.0288116 -2.89572 0.00378285
60. VBR(5,3) -0.0412891 0.0265933 -1.55261 0.12051566
61. VBR(1,4) -0.0517271 0.0244415 -2.11636 0.03431426
62. VBR(2,4) 0.0183327 0.0294983 0.62148 0.53428140
63. VBR(3,4) -0.0711544 0.0181243 -3.92591 0.00008640
64. VBR(4,4) 0.2833757 0.0167772 16.89048 0.00000000
65. VBR(5,4) -0.1080659 0.0205040 -5.27048 0.00000014
66. VBR(1,5) -0.0092582 0.0271072 -0.34154 0.73269656
67. VBR(2,5) -0.0392821 0.0225021 -1.74571 0.08086126
68. VBR(3,5) 0.0066397 0.0169905 0.39079 0.69595462
69. VBR(4,5) -0.1118555 0.0204454 -5.47093 0.00000004
70. VBR(5,5) 0.2513801 0.0184505 13.62459 0.00000000
71. VCR(1,1) 0.0413183 0.0731464 0.56487 0.57216143
72. VCR(2,1) -0.0532768 0.0832686 -0.63982 0.52229039
73. VCR(2,2) 0.0688667 0.1182101 0.58258 0.56017714
74. VCR(3,1) 0.0820945 0.0879364 0.93357 0.35052722
75. VCR(3,2) -0.1007940 0.1294352 -0.77872 0.43614373
76. VCR(3,3) 0.2824937 0.0811836 3.47969 0.00050200
77. VCR(4,1) 0.0620565 0.0602993 1.02914 0.30341359
78. VCR(4,2) -0.0833778 0.0762507 -1.09347 0.27418779
79. VCR(4,3) 0.0444727 0.1102857 0.40325 0.68676440
80. VCR(4,4) 0.1451980 0.0624495 2.32505 0.02006945
81. VCR(5,1) -0.0693860 0.0628346 -1.10426 0.26947829
82. VCR(5,2) 0.0931351 0.0847586 1.09883 0.27184341
83. VCR(5,3) -0.0508504 0.1034200 -0.49169 0.62293953
84. VCR(5,4) -0.1615948 0.0496104 -3.25727 0.00112488
85. VCR(5,5) 0.1797943 0.0638636 2.81529 0.00487338
86. VGV(1,1) -0.1922157 0.0328565 -5.85015 0.00000000
87. VGV(2,1) -0.0972182 0.0160754 -6.04762 0.00000000
88. VGV(3,1) -0.0114384 0.0097482 -1.17338 0.24064189
89. VGV(4,1) -0.0499082 0.0087016 -5.73555 0.00000001
90. VGV(5,1) 0.0407034 0.0101914 3.99390 0.00006500
91. VGV(1,2) 0.1297255 0.0297644 4.35842 0.00001310
92. VGV(2,2) 0.0597363 0.0451159 1.32406 0.18548192
93. VGV(3,2) -0.0065508 0.0197434 -0.33180 0.74004094
94. VGV(4,2) 0.0468568 0.0165073 2.83855 0.00453193
95. VGV(5,2) -0.0250280 0.0184745 -1.35473 0.17550343
96. VGV(1,3) -0.0557146 0.0388464 -1.43423 0.15150698
97. VGV(2,3) -0.0286324 0.0416190 -0.68796 0.49147529
98. VGV(3,3) -0.2397077 0.0287096 -8.34938 0.00000000
99. VGV(4,3) -0.0160313 0.0378408 -0.42365 0.67181941
100.VGV(5,3) -0.1097008 0.0313367 -3.50071 0.00046402
101.VGV(1,4) -0.0851039 0.0338924 -2.51100 0.01203887
102.VGV(2,4) -0.0718320 0.0420696 -1.70745 0.08773770
103.VGV(3,4) 0.0778987 0.0505483 1.54107 0.12329873
104.VGV(4,4) -0.1668094 0.0369393 -4.51577 0.00000631
105.VGV(5,4) -0.1502988 0.0247374 -6.07576 0.00000000
106.VGV(1,5) -0.1021508 0.0246927 -4.13688 0.00003521
107.VGV(2,5) -0.0074190 0.0341694 -0.21712 0.82811156
108.VGV(3,5) 0.0129068 0.0375661 0.34358 0.73116485
109.VGV(4,5) -0.1078158 0.0281891 -3.82474 0.00013091
110.VGV(5,5) -0.1823908 0.0325331 -5.60632 0.00000002
111.RHO12 0.0245523 0.0058882 4.16976 0.00003049
112.RHO13 0.0144504 0.0213065 0.67822 0.49763440
113.RHO14 0.0340616 0.0250969 1.35720 0.17471707
114.RHO15 0.0101460 0.0052202 1.94362 0.05194158
115.RHO23 0.1553291 0.0881533 1.76203 0.07806360
116.RHO24 0.0519647 0.0125876 4.12825 0.00003655
117.RHO25 0.3040043 0.0255881 11.88069 0.00000000
118.RHO34 0.3365446 0.0383254 8.78125 0.00000000
119.RHO35 0.0752398 0.0429806 1.75055 0.08002275
120.RHO45 0.1397431 0.0183121 7.63121 0.00000000
121.HUAI12 0.1665040 0.0475990 3.49806 0.00046866
122.HUAI13 0.3082177 0.1527786 2.01741 0.04365230
123.HUAI14 0.2048667 0.1114018 1.83899 0.06591676
124.HUAI15 0.0384741 0.0078375 4.90895 0.00000092
125.HUAI23 0.0010283 0.0128386 0.08009 0.93616185
126.HUAI24 -0.1076104 0.0192189 -5.59919 0.00000002
127.HUAI25 0.0027882 0.0003255 8.56687 0.00000000
128.HUAI34 0.3411000 0.1436977 2.37373 0.01760931
129.HUAI35 0.5582597 0.1294736 4.31176 0.00001620
130.HUAI45 0.6523826 0.0527309 12.37193 0.00000000
131.S11 0.0903534 0.0232804 3.88109 0.00010399
132.S13 0.1445893 0.0400919 3.60645 0.00031042
133.S21 0.0417952 0.0147342 2.83662 0.00455945
134.S23 0.0352719 0.0119971 2.94003 0.00328179
135.S31 0.0273229 0.0096115 2.84273 0.00447296
136.S33 0.0188099 0.0089099 2.11113 0.03476105
137.S41 0.0297955 0.0090884 3.27841 0.00104394
138.S42 0.0006827 0.0065353 0.10446 0.91680551
139.S51 0.0515045 0.0107068 4.81043 0.00000151
140.S52 0.0159575 0.0072221 2.20954 0.02713707



So, although the coeffecient is significant, I still could not use it.
I have adjusted the subiterations but still similar result.
What else could I adjust, please give some suggestions.
For, there is 4959 obs, I need two days to run the program one time.
Plus, I have tried weekly frequency instead of daily frequency data, the convergence seems to be alright.

[TomDoan]

It's possible that this is actually converged. I hope you put the TRACE option on so you can tell more easily. If the norm of the gradient is small, you're probably fine. Sometimes it helps with very large parameter sets like this to use the NLPAR(EXACTLINESEARCH) command before doing the MAXIMIZE.

Is there something unusual about this model that won't allow you to use GARCH? GARCH might still require a couple of hours, but it wouldn't be two days.