0
$\begingroup$

I want to estimate a GARCH model with an exogenous variable. Data is as below:

obs return  proxy
1   0.007186644 0.000251697
2   0.00417664  0.000175223
3   -0.012423429    0.000275363
4   0.006152402 0.000211106
5   0.009684689 0.000163839
6   0.010652643 0.000177903
7   -0.007866608    6.59516E-05
8   -0.012287487    0.000125476
9   -0.000314141    0.000191536
10  0.000471175 3.25492E-05
11  -0.02088845 7.69018E-05
12  -0.014996969    0.000103732
13  0.024149265 0.000181204
14  0.004192276 9.56736E-05
15  0.017842673 6.73705E-05
16  0.003391453 0.000262908
17  0.005184803 5.70646E-05
18  0.014443275 2.80185E-05
19  -0.000454914    1.22051E-05
20  -0.012901656    3.50466E-05
21  0.010444785 0.000132914
22  0.016754761 0.000177325
23  -0.004059211    3.94445E-05
24  -0.030072964    3.51132E-05
25  -0.008228722    0.000471469
26  0.002783486 0.000144906
27  -0.009435949    0.000136806
28  -5.99102E-05    0.000140229
29  0.000996016 2.96865E-05
30  -0.000829404    0.000329365
31  0.025821873 7.2123E-05
32  0.008770559 0.000339778
33  -0.00588619 8.58032E-05
34  0.025401794 4.15771E-05
35  0.008057032 0.000115358
36  -0.019156553    9.9318E-05
37  0.015203439 0.000206373
38  -0.003635098    8.54154E-05
39  0.011747115 8.85452E-05
40  0.001858341 0.000149553
41  0.010901006 1.8419E-05
42  0.000525595 2.84284E-05
43  0.004711361 6.85203E-05
44  0.003784844 6.47293E-05
45  0.002565371 4.22289E-05
46  0.0134934   5.81467E-05
47  0.003632037 0.000106241
48  0.00448838  7.88018E-05
49  0.00916296  4.35121E-05
50  -0.013570609    4.96717E-05
51  0.004269821 9.90941E-05
52  0.024983388 7.70396E-05
53  0.019064654 5.43616E-05
54  0.005522113 0.000158796
55  -0.019817821    6.18993E-05
56  -0.017051927    0.000187971
57  0.012052545 0.000134517
58  -2.37225E-05    8.90046E-05
59  -0.000146281    1.16608E-05
60  0.004771586 4.01664E-05
61  0.01438373  3.02826E-05
62  0.004215649 2.90469E-05
63  -0.010971719    4.829E-05
64  0.018209594 6.68076E-05
65  -0.010894934    8.43702E-05
66  -0.01766645 7.98257E-05
67  -0.004261362    0.000122284
68  0.016343938 7.42675E-05
69  0.017844467 0.000154605
70  -0.003192827    0.000168825
71  0.02333846  6.97679E-05
72  0.001029615 0.000162043
73  -0.002470849    4.09404E-05
74  0.00896253  9.39789E-05
75  -0.001073962    9.47721E-05
76  -0.008157847    3.81254E-05
77  0.001408589 0.000134039
78  0.001840939 8.70011E-05
79  -0.008415848    2.98882E-05
80  0.007573817 3.71625E-05
81  -0.004467122    3.9572E-05
82  0.001213214 3.37886E-05
83  -0.001756734    4.14175E-05
84  -0.017711161    3.38932E-05
85  -0.033479254    0.000107124
86  -0.021030443    0.000613339
87  -0.008651037    0.000218423
88  -0.004211969    0.000332089
89  0.008817173 0.000150223
90  -0.00329042 4.22227E-05
91  0.002856616 6.53853E-05
92  -0.009198447    7.63505E-05
93  -0.006351589    0.000101511
94  -0.010448254    6.0489E-05
95  0.003597302 0.000135307
96  -0.000431139    0.000105024
97  -0.011538288    7.29814E-05
98  0.005330478 8.62597E-05
99  0.034174162 3.56768E-05
100 -0.010447082    0.000550323
101 -0.007321443    0.000104249
102 -8.62464E-05    5.80545E-05
103 0.00646817  2.95758E-05
104 -0.009362181    4.97202E-05
105 -0.009926305    9.93637E-05
106 -0.009951746    6.25208E-05
107 0.024188353 8.9677E-05
108 0.005784911 0.000239764
109 -0.005552917    2.26155E-05
110 0.008599694 0.000113456
111 -0.01432104 0.00010564
112 -0.010665628    9.90417E-05
113 -0.004602492    7.51785E-05
114 -0.010173847    8.55815E-05
115 0.006287255 9.89696E-05
116 -0.020750596    1.73848E-05
117 0.010111196 0.000127497
118 0.027363727 4.89182E-05
119 0.000106801 7.75074E-05
120 -0.003409719    3.29754E-05
121 0.009306037 4.43662E-05
122 -0.034222702    7.74413E-05
123 -0.002720572    0.000147476
124 0.023251666 6.67916E-05
125 -0.002829579    9.4561E-05
126 0.001370684 6.49057E-05
127 0.014666221 4.61885E-05
128 0.005572364 3.59631E-05
129 -0.004708488    8.86167E-06
130 0.01545895  2.88229E-05
131 0.023777918 2.5547E-05
132 0.002217979 0.000200657
133 0.015472316 2.84561E-05
134 0.002848593 6.56165E-05
135 -0.073479544    1.85095E-05
136 -0.010184407    0.001902948
137 -0.016878537    0.000375819
138 -0.045166847    0.00030121
139 0.002001628 0.000480455
140 0.033387232 0.000397015
141 -0.00655445 0.000259183
142 0.018637568 0.000173402
143 0.002240026 0.000113079
144 0.002143651 6.8643E-05
145 0.017173364 8.34387E-05
146 -0.011903972    2.36702E-05
147 -0.016651126    6.83066E-05
148 0.020886253 0.000180343
149 -0.000787824    0.000223243
150 0.022275448 0.000166912
151 0.009542887 5.46484E-05
152 -0.007275569    7.30516E-05
153 0.013732624 8.52182E-05
154 -0.010237901    9.96517E-05
155 0.003114339 0.000103915
156 -0.009802121    3.7003E-05
157 0.005655145 9.55511E-05
158 -0.002266096    5.87886E-05
159 0.00223756  8.75068E-05
160 -0.002464081    5.27721E-05
161 -0.007980884    2.64197E-05
162 -0.015866095    5.48094E-05
163 0.008810426 8.72406E-05
164 0.004285121 1.9656E-05
165 -0.013062309    6.93817E-05
166 -0.001988475    4.70675E-05
167 -0.001512708    2.59074E-05
168 0.013507334 2.52971E-05
169 0.011731502 6.19496E-05
170 0.002608573 1.91895E-05
171 -0.004518314    1.44012E-05
172 0.002576557 3.96945E-05
173 -0.010199768    3.32237E-05
174 -0.013500227    3.23656E-05
175 0.02147846  9.52041E-05
176 -0.004610671    9.22141E-05
177 0.007761844 2.95602E-05
178 0.023842714 5.72984E-05
179 -0.000495135    7.14546E-05
180 -0.038740376    1.85022E-05
181 0.005652756 3.97889E-05
182 0.006679374 4.19969E-05
183 -0.007766917    2.37758E-05
184 -0.007663494    6.83551E-05
185 0.009589455 2.22313E-05
186 -0.002172889    1.64109E-05
187 0.010275382 2.5007E-05
188 0.000527389 0.000133534
189 0.001042787 3.43345E-05
190 -0.001806031    4.01943E-05
191 -0.002465931    4.00876E-05
192 -0.002350927    2.22433E-05
193 -0.008439194    5.43846E-05
194 0.0096383   5.94189E-05
195 -0.001504983    5.12875E-05
196 0.011591114 2.82467E-05
197 0.011037353 2.62092E-05
198 0.000537163 3.1208E-05
199 -0.005170918    1.32047E-05
200 0.01371625  2.2454E-05
201 -0.006265352    4.21338E-05
202 -0.000445378    4.90213E-05
203 -0.008331679    2.36981E-05
204 -0.005173434    4.18197E-05
205 0.002591972 2.59712E-05
206 -0.014203578    2.58342E-05
207 -0.003324321    0.000147459
208 -0.0063726  1.25318E-05
209 -0.031989788    5.38934E-05
210 0.018870826 0.000196547
211 0.009021187 3.0824E-05
212 -0.002081838    9.3414E-05
213 0.001984541 0.000194509
214 -0.015656025    3.42414E-05
215 -0.010095059    9.86529E-05
216 0.009780939 9.22179E-05
217 -0.005223159    2.97663E-05
218 0.005032324 6.57719E-05
219 0.006668762 4.40738E-05
220 -0.001261918    0.000105995
221 0.003546884 3.49751E-05
222 -0.010276467    4.02115E-05
223 -0.011309243    9.04096E-05
224 0.002293808 0.000199329
225 0.008393281 4.68433E-05
226 -0.010519836    1.15898E-05
227 -0.002837776    5.50531E-05
228 -0.020139909    5.68853E-05
229 0.011940177 0.000208053
230 0.002840455 0.000209741
231 0.024608403 8.89273E-05
232 0.007888906 0.000136746
233 -0.001335351    5.44581E-05
234 -0.002664442    0.000113038
235 0.006742941 2.19813E-05
236 0.009862585 0.000111834
237 -0.001487171    3.42978E-05
238 0.010322852 2.58993E-05
239 -0.00114563 0.000123249
240 -0.005581496    1.37018E-05
241 0.008390294 3.64182E-05
242 -0.002424542    5.91928E-05
243 -0.002770279    2.47364E-05
244 -0.005604351    2.27548E-05
245 0.000731426 2.84559E-05
246 -0.004281078    3.16998E-06
247 0.010999344 2.76176E-05
248 0.003708762 6.50969E-05
249 0.003882819 1.46697E-05
250 -0.004929028    2.17641E-05
251 -0.014721266    9.49338E-06
252 -0.006213747    0.000107413
253 0.003182461 8.68053E-05
254 0.00938513  8.23442E-05
255 0.003726452 6.2031E-05
256 -9.69067E-06    6.04408E-05
257 0.003519796 2.10411E-05
258 0.040678015 8.08957E-05
259 0.007798317 0.00058116
260 0.002295695 9.05216E-05
261 0.007936438 3.58499E-05
262 0.005043912 4.1798E-05
263 -0.00580243 3.18886E-05
264 0.009274321 8.77227E-05
265 -0.000232971    8.45052E-05
266 0.013872277 2.37705E-05
267 -0.012903906    9.86392E-05
268 0.008364948 0.000111196
269 1.01399E-05 6.29385E-05
270 0.028345778 3.02582E-05
271 0.000674421 0.000345453
272 0.006379001 3.03587E-05
273 0.006269801 4.07731E-05
274 0.01132438  3.47027E-05
275 -0.011740169    8.4428E-05
276 0.0013598   0.00022286
277 0.008790456 6.76557E-05
278 0.006563524 5.35171E-05
279 -0.015392848    6.19229E-05
280 0.012553073 0.000194516
281 -0.005616437    7.66618E-05
282 -0.002275919    8.65313E-05
283 0.003463308 3.07546E-05
284 0.007271074 1.00789E-05
285 -0.002736476    3.96857E-05
286 0.004252037 5.66123E-05
287 -0.004888672    1.44202E-05
288 0.006833946 0.000122692
289 -0.00992044 1.29906E-05
290 -0.005601982    8.37799E-05
291 -0.003276354    3.28652E-05
292 0.02083712  2.77345E-05
293 0.006846508 0.000133922
294 -0.002358175    1.75489E-05
295 0.014637222 1.18842E-05
296 -0.002544616    8.25134E-05
297 -0.014739268    2.79253E-05
298 -0.005404763    0.000149025
299 0.006817411 3.24694E-05
300 -0.002029367    1.61948E-05
301 -0.003283938    2.56758E-05
302 0.003460821 1.20022E-05
303 0.009156508 1.84332E-05
304 0.00246814  2.1033E-05
305 0.004528505 2.42187E-05
306 -0.0032577  2.61034E-05
307 -0.008839318    4.86838E-05
308 -0.000500966    3.66736E-05
309 0.006867759 1.56569E-05
310 -0.007637404    2.3414E-05
311 0.005411273 3.41944E-05
312 -0.010164508    1.0767E-05
313 0.000140351 2.1316E-05
314 -0.003757516    1.30653E-05
315 -0.003129548    2.13248E-05
316 -0.000642141    1.10989E-05
317 0.004783572 2.63345E-05
318 -0.004033508    3.78562E-05
319 -0.002051177    6.21969E-06
320 0.030525947 1.1012E-05
321 -0.003688935    0.000303645
322 0.000524259 4.28617E-05
323 -0.011961906    1.51135E-05
324 0.002145339 0.000105662
325 0.006530769 6.61842E-05
326 0.007910711 3.88522E-05
327 -0.006253797    0.000108987
328 0.01351176  9.18024E-05
329 0.004169399 4.02917E-05
330 0.014808885 1.42813E-05
331 0.008831623 4.41488E-05
332 -0.001190227    8.56026E-05
333 -0.002540826    2.29176E-05
334 0.003946595 3.93726E-05
335 -0.003168069    4.19972E-05
336 -0.005240407    4.39409E-05
337 -0.008820224    4.1481E-05
338 0.009519405 4.74929E-05
339 -0.001019274    4.05891E-05
340 0.015761702 2.69529E-05
341 0.009093954 0.000113189
342 -0.011292262    5.92875E-05
343 -0.001238333    8.56545E-05
344 0.006206204 4.45389E-05
345 0.005984396 1.49225E-05
346 -0.004550095    1.60844E-05
347 -0.006052338    5.94261E-05
348 0.013079875 6.39321E-05
349 0.013573945 1.46647E-05
350 0.006083641 0.000102352
351 -0.006130102    4.47366E-05
352 -0.001840343    2.58808E-05
353 0.00197348  2.48884E-05
354 -0.003878746    1.95443E-05
355 0.001990362 2.4942E-05
356 -0.001803832    3.99731E-05
357 0.015309699 3.43341E-05
358 -0.006860176    2.84969E-05
359 0.00142039  7.47012E-05
360 -0.007298089    2.49582E-05
361 0.003691527 6.49491E-05
362 0.009804344 9.35877E-06
363 0.005033053 2.81441E-05
364 -0.001433418    2.38018E-05
365 0.003384007 4.51645E-05
366 -0.009066404    2.48154E-05
367 -0.005529504    2.19133E-05
368 0.011538737 4.43311E-05
369 -0.000633027    1.30708E-05
370 0.001216655 2.39958E-05
371 0.006838713 3.16211E-05
372 -0.004341284    1.29898E-05
373 0.009777946 1.59502E-05
374 -0.00425651 5.18424E-05
375 0.00249284  3.43933E-05
376 0.000815176 3.25317E-05
377 0.006796137 9.59277E-06
378 -0.004588618    2.25045E-05
379 -0.001166402    1.59048E-05
380 -0.00540718 3.63041E-05
381 0.010068504 2.03327E-05
382 0.020418587 1.24317E-05
383 0.006059564 0.000221613
384 0.003850019 5.08066E-05
385 0.009222365 4.32005E-05
386 0.009851601 2.62095E-05
387 -0.004706067    4.67219E-05
388 0.015945193 1.39483E-05
389 -0.006368924    6.36885E-05
390 0.001004128 3.94712E-05
391 -0.001238754    4.09317E-05
392 0.003089108 2.74252E-05
393 0.001544854 9.9223E-06
394 0.0109979   1.05318E-05
395 -0.006404626    1.9603E-05
396 -0.001563714    1.61168E-05
397 -0.012954293    1.96554E-05
398 0.003554853 0.000114403
399 0.005881169 2.37332E-05
400 0.012902691 7.92573E-06
401 0.011320967 5.73721E-05
402 -0.001294411    2.13555E-05
403 -0.008468329    2.35349E-05
404 -0.008444361    2.04452E-05
405 -0.007797639    7.97305E-05
406 0.023781763 6.72201E-05
407 -0.024247827    8.82488E-05
408 -0.000479663    0.000337149
409 -0.000343118    0.000283764
410 0.003523846 5.02492E-05
411 0.013089406 5.75935E-05
412 -0.000188021    0.000133885
413 0.003293817 2.59028E-05
414 0.001844786 1.10308E-05
415 0.00549298  3.6719E-05
416 0.005314533 4.0998E-05
417 0.000753024 1.06603E-05
418 -0.003743717    2.85704E-05
419 -0.010393751    9.42987E-06
420 0.006762968 8.71485E-05
421 0.001195871 4.61529E-05
422 -0.0118359  2.68857E-05
423 0.009236093 0.000107175
424 -0.00300438 2.48112E-05
425 -0.008966341    3.29822E-05
426 0.000819687 5.51938E-05
427 -0.004653275    5.57699E-05
428 -0.011266881    1.93909E-05
429 -0.015292915    7.42236E-05
430 0.00386128  0.000144181
431 -0.012635743    3.3571E-05
432 0.001169014 8.32441E-05
433 -0.017953415    5.64578E-05
434 0.016093112 0.000126656
435 -0.026431578    0.000100961
436 0.014056289 0.000271855
437 0.002496902 0.000131901

return is the stock's return and proxy is the exogenous variable. Data is in incresing time order.

Using EVIEWS, I get the below result:

Dependent Variable: RETURN              
Method: ML ARCH - Normal distribution (BFGS / Marquardt steps)              
Date: 11/20/17   Time: 21:02                
Sample: 1 437               
Included observations: 437              
Convergence achieved after 50 iterations                
Coefficient covariance computed using outer product of gradients                
Presample variance: backcast (parameter = 0.7)              
GARCH = C(1) + C(2)*RESID(-1)^2 + C(3)*GARCH(-1) + C(4)*PROXY               

Variable    Coefficient Std. Error  z-Statistic Prob.  

C           5.54E-07    9.08E-07    0.610485    0.5415
RESID(-1)^2 0.008037    0.008162    0.984716    0.3248
GARCH(-1)   0.967734    0.010998    87.99007    0.0000
PROXY       0.034338    0.016815    2.042116    0.0411

R-squared           -0.005534       Mean dependent var      0.000859
Adjusted R-squared  -0.003233       S.D. dependent var      0.011565
S.E. of regression  0.011584        Akaike info criterion   -6.106682
Sum squared resid   0.058639        Schwarz criterion       -6.069337

The STATA results are as below:

Sample: 1 - 437                                   Number of obs   =        437
Distribution: Gaussian                            Wald chi2(.)    =          .
Log likelihood =  1338.603                        Prob > chi2     =          .

------------------------------------------------------------------------------
             |                 OPG
      return |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
HET          |
       proxy |   644.7733    7821.37     0.08   0.934    -14684.83    15974.38
       _cons |  -13.44454   .7684806   -17.49   0.000    -14.95073   -11.93835
-------------+----------------------------------------------------------------
ARCH         |
        arch |
         L1. |   .0244042   .0079479     3.07   0.002     .0088267    .0399818
             |
       garch |
         L1. |   .9638913   .0127278    75.73   0.000     .9389452    .9888373
------------------------------------------------------------------------------

STATA code is as below:

arch return, noconstant arch(1/1) garch(1/1) het(proxy)

I am both new in EVIEWS and STATA.

There are some big differences between the estimates. The proxy's coefficient is very different in two models. In EVIEWS its estimate is 0.034338, in STATA its estimate is 644.7733. There is big difference also in constant term.

Am I doing something wrong?

$\endgroup$
  • $\begingroup$ This is precariously poised as what syntax to use in particular software is off-topic; yet why different programs don't agree is on-topic when the aim is statistical. I am no expert on GARCH, yet for any regression problem, including or excluding a constant term is a big deal. The way you include a constant in Stata is by not specifying noconstant. In short, it's the default. $\endgroup$ – Nick Cox Nov 20 '17 at 18:33
  • $\begingroup$ For STATA read Stata throughout. $\endgroup$ – Nick Cox Nov 20 '17 at 18:34
  • $\begingroup$ @NickCox, I edited the question. I stated it wrong before. Both models include the constant term. $\endgroup$ – oercim Nov 20 '17 at 18:39
  • $\begingroup$ Your Stata code says the the exact opposite. The question is pointless if there is confusion on such details. $\endgroup$ – Nick Cox Nov 20 '17 at 18:42
  • $\begingroup$ @NickCox, noconstant term refers to mean function. $\endgroup$ – oercim Nov 20 '17 at 18:44

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