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Kinh tế lượng
Đề bài:
1. Ước lượng mô hình GARCH cho một chuỗi lợi suất của một
loại cổ phiếu bất kỳ với số liệu theo tháng ( ít nhất 2 tháng)
trên HASTC hoặc HOSE.
Bài làm
Ước lượng mô hình GARCH cho chuỗi lợi suất của cổ phiếu BT6
trên HOSE.
Lựa chọn chuỗi giá của cổ phiếu BT6 với 270 quan sát ( thời gian
từ 1/8/2006 đến 31/8/2007)
Tính lợi suất của cổ phiếu BT6 với công thức:
rt= ( Pt+1 – Pt)/ Pt
trong đó :
Pt là giá cổ phiếu tại thời điểm t
Pt+1 là giá cổ phiếu tại thời điểm t+1
rt là lợi suất của cổ phiếu tại thời điểm t
Ta có chuỗi lợi suất của BT6 như sau:
1
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date
p-close
r
1
8/1/2006
38.2
2
8/2/2006
38.2
0
3
8/3/2006
40.1
0.04973822
4
8/4/2006
42.1 0.049875312
5
8/7/2006
40 -0.04988124
6
8/8/2006
41
7
8/9/2006
8
8/10/2006
42.5
9
8/11/2006
43.9 0.032941176
10
8/14/2006
46 0.047835991
11
8/15/2006
47
12
8/16/2006
48.1 0.023404255
13
8/17/2006
48.1
14
8/18/2006
47.5 -0.01247401
15
8/21/2006
47 -0.01052632
16
8/22/2006
46
0.025
42.5 0.036585366
2
0
0.02173913
0
-0.0212766
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17
8/23/2006
46
0
18
8/24/2006
46
0
19
8/25/2006
46
0
20
8/28/2006
46.5 0.010869565
21
8/29/2006
47.5 0.021505376
22
8/30/2006
48 0.010526316
23
8/31/2006
48
24
9/1/2006
25
9/5/2006
49.3
0.04893617
26
9/6/2006
49.3
0
27
9/7/2006
48.5 -0.01622718
28
9/8/2006
48.5
29
9/11/2006
48.1 -0.00824742
30
9/12/2006
47.1 -0.02079002
31
9/13/2006
32
9/14/2006
47.6 -0.00833333
33
9/15/2006
47.8 0.004201681
0
47 -0.02083333
48
3
0
0.01910828
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34
9/18/2006
48
35
9/19/2006
48.2 0.004166667
36
9/20/2006
48.5 0.006224066
37
9/21/2006
49 0.010309278
38
9/22/2006
49.4 0.008163265
39
9/25/2006
51.5 0.042510121
40
9/26/2006
54 0.048543689
41
9/27/2006
55.5 0.027777778
42
9/28/2006
54 -0.02702703
43
9/29/2006
53 -0.01851852
44
10/2/2006
55 0.037735849
45
10/3/2006
56 0.018181818
46
10/4/2006
55 -0.01785714
47
10/5/2006
53.5 -0.02727273
48
10/6/2006
54 0.009345794
49
10/9/2006
54
50 10/10/2006
0.0041841
0
53 -0.01851852
4
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51 10/11/2006
53
0
52 10/12/2006
53.5 0.009433962
53 10/13/2006
53 -0.00934579
54 10/16/2006
53.5 0.009433962
55 10/17/2006
52 -0.02803738
56 10/18/2006
52.5 0.009615385
57 10/19/2006
54 0.028571429
58 10/20/2006
53.5 -0.00925926
59 10/23/2006
53 -0.00934579
60 10/24/2006
53
61 10/25/2006
0
52.5 -0.00943396
62 10/26/2006
53
0.00952381
63 10/27/2006
53
0
64 10/30/2006
51.5 -0.02830189
65 10/31/2006
52 0.009708738
66
11/1/2006
52.5 0.009615385
67
11/2/2006
52 -0.00952381
5
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68
11/3/2006
52.5 0.009615385
69
11/6/2006
52.5
70
11/7/2006
53.5 0.019047619
71
11/8/2006
54 0.009345794
72
11/9/2006
54.5 0.009259259
73 11/10/2006
54 -0.00917431
74 11/13/2006
55 0.018518519
75 11/14/2006
55.5 0.009090909
76 11/15/2006
55 -0.00900901
77 11/16/2006
54 -0.01818182
78 11/17/2006
54
0
79 11/20/2006
54
0
80 11/21/2006
54
0
81 11/22/2006
0
54.5 0.009259259
82 11/23/2006
57
0.04587156
83 11/24/2006
59.5 0.043859649
84 11/27/2006
57 -0.04201681
6
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85 11/28/2006
59.5 0.043859649
86 11/29/2006
57 -0.04201681
87 11/30/2006
58.5 0.026315789
88
12/1/2006
57.5 -0.01709402
89
12/4/2006
57 -0.00869565
90
12/5/2006
55 -0.03508772
91
12/6/2006
57.5 0.045454545
92
12/7/2006
60 0.043478261
93 12/11/2006
63
0.05
94 12/12/2006
60 -0.04761905
95 12/13/2006
61 0.016666667
96 12/14/2006
60 -0.01639344
97 12/15/2006
58.5
98 12/18/2006
57.5 -0.01709402
99 12/19/2006
58 0.008695652
100 12/20/2006
55.5 -0.04310345
101 12/21/2006
53.5 -0.03603604
7
-0.025
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102 12/22/2006
53 -0.00934579
103 12/25/2006
55.5 0.047169811
104 12/26/2006
58 0.045045045
105 12/27/2006
57 -0.01724138
106 12/28/2006
56 -0.01754386
107 12/29/2006
55 -0.01785714
108
1/2/2007
54.5 -0.00909091
109
1/3/2007
56 0.027522936
110
1/4/2007
58 0.035714286
111
1/5/2007
58
112
1/8/2007
57 -0.01724138
113
1/9/2007
57
114
1/10/2007
56.5 -0.00877193
115
1/11/2007
57.5 0.017699115
116
1/12/2007
58.5 0.017391304
117
1/15/2007
60 0.025641026
118
1/16/2007
62 0.033333333
8
0
0
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119
1/17/2007
59.5 -0.04032258
120
1/18/2007
59 -0.00840336
121
1/19/2007
59.5 0.008474576
122
1/22/2007
57 -0.04201681
123
1/23/2007
59 0.035087719
124
1/24/2007
61 0.033898305
125
1/25/2007
60 -0.01639344
126
1/26/2007
60
0
127
1/29/2007
60
0
128
1/30/2007
61 0.016666667
129
1/31/2007
61
0
130
2/1/2007
61
0
131
2/2/2007
61
0
132
2/5/2007
64 0.049180328
133
2/6/2007
67
134
2/7/2007
70 0.044776119
135
2/8/2007
66.5
9
0.046875
-0.05
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136
2/9/2007
65.5 -0.01503759
137
2/12/2007
67 0.022900763
138
2/13/2007
68 0.014925373
139
2/14/2007
68
0
140
2/15/2007
68
0
141
2/26/2007
71 0.044117647
142
2/27/2007
74.5 0.049295775
143
2/28/2007
76 0.020134228
144
3/1/2007
79.5 0.046052632
145
3/2/2007
83 0.044025157
146
3/5/2007
87 0.048192771
147
3/6/2007
91 0.045977011
148
3/7/2007
88 -0.03296703
149
3/8/2007
86 -0.02272727
150
3/9/2007
85 -0.01162791
151
3/12/2007
86 0.011764706
152
3/13/2007
87 0.011627907
10
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153
3/14/2007
83 -0.04597701
154
3/15/2007
80 -0.03614458
155
3/16/2007
82
156
3/19/2007
84 0.024390244
157
3/20/2007
83 -0.01190476
158
3/21/2007
80 -0.03614458
159
3/22/2007
77
-0.0375
160
3/23/2007
77
0
161
3/26/2007
75 -0.02597403
162
3/27/2007
71.5 -0.04666667
163
3/28/2007
69 -0.03496503
164
3/29/2007
72 0.043478261
165
3/30/2007
75.5 0.048611111
166
4/2/2007
72 -0.04635762
167
4/3/2007
70 -0.02777778
168
4/4/2007
72 0.028571429
169
4/5/2007
72
11
0.025
0
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170
4/6/2007
71 -0.01388889
171
4/7/2007
74 0.042253521
172
4/9/2007
69 -0.06756757
173
4/10/2007
69
0
174
4/11/2007
69
0
175
4/12/2007
66 -0.04347826
176
4/13/2007
63.5 -0.03787879
177
4/16/2007
60.5 -0.04724409
178
4/17/2007
57.5 -0.04958678
179
4/18/2007
60 0.043478261
180
4/19/2007
63
181
4/20/2007
62 -0.01587302
182
4/23/2007
61.5 -0.00806452
183
4/24/2007
60 -0.02439024
184
5/2/2007
62 0.033333333
185
5/3/2007
62
0
186
5/4/2007
62
0
12
0.05
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187
5/7/2007
65 0.048387097
188
5/8/2007
66 0.015384615
189
5/9/2007
65 -0.01515152
190
5/10/2007
63 -0.03076923
191
5/11/2007
65 0.031746032
192
5/14/2007
65.5 0.007692308
193
5/15/2007
66.5 0.015267176
194
5/16/2007
65.5 -0.01503759
195
5/17/2007
65 -0.00763359
196
5/18/2007
64 -0.01538462
197
5/21/2007
64
0
198
5/22/2007
64.5
0.0078125
199
5/23/2007
64.5
0
200
5/24/2007
201
5/25/2007
63.5
-0.0078125
202
5/28/2007
63.5
0
203
5/30/2007
62.5 -0.01574803
64 -0.00775194
13
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204
5/31/2007
63
205
6/1/2007
61.5 -0.02380952
206
6/4/2007
61 -0.00813008
207
6/5/2007
59.5 -0.02459016
208
6/6/2007
60 0.008403361
209
6/7/2007
60.5 0.008333333
210
6/8/2007
61 0.008264463
211
6/11/2007
61.5 0.008196721
212
6/12/2007
61 -0.00813008
213
6/13/2007
61.5 0.008196721
214
6/14/2007
60.5 -0.01626016
215
6/15/2007
60.5
216
6/18/2007
60 -0.00826446
217
6/19/2007
59.5 -0.00833333
218
6/20/2007
59.5
219
6/21/2007
58.5 -0.01680672
220
6/22/2007
57.5 -0.01709402
14
0.008
0
0
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221
6/25/2007
55 -0.04347826
222
6/26/2007
56.5 0.027272727
223
6/27/2007
56.5
224
6/28/2007
55.5 -0.01769912
225
6/29/2007
56 0.009009009
226
7/2/2007
55.5 -0.00892857
227
7/3/2007
53.5 -0.03603604
228
7/4/2007
55.5 0.037383178
229
7/5/2007
54.5 -0.01801802
230
7/6/2007
54.5
0
231
7/9/2007
57
0.04587156
232
7/10/2007
59.5 0.043859649
233
7/11/2007
62 0.042016807
234
7/12/2007
65 0.048387097
235
7/13/2007
64.5 -0.00769231
236
7/16/2007
61.5 -0.04651163
237
7/17/2007
64 0.040650407
15
0
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238
7/18/2007
62.5
-0.0234375
239
7/19/2007
61.5
-0.016
240
7/20/2007
61.5
0
241
7/23/2007
61.5
0
242
7/24/2007
60 -0.02439024
243
7/25/2007
59 -0.01666667
244
7/26/2007
58 -0.01694915
245
7/27/2007
57.5 -0.00862069
246
7/30/2007
57 -0.00869565
247
7/31/2007
56 -0.01754386
248
8/1/2007
58.5 0.044642857
249
8/2/2007
57.5 -0.01709402
250
8/3/2007
57.5
251
8/6/2007
59 0.026086957
252
8/7/2007
59
0
253
8/8/2007
59
0
254
8/9/2007
0
59.5 0.008474576
16
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255
8/10/2007
60 0.008403361
256
8/13/2007
60.5 0.008333333
257
8/14/2007
62 0.024793388
258
8/15/2007
64 0.032258065
259
8/16/2007
62.5
-0.0234375
260
8/17/2007
61.5
-0.016
261
8/20/2007
62 0.008130081
262
8/21/2007
62
0
263
8/22/2007
62
0
264
8/23/2007
62
0
265
8/24/2007
62.5 0.008064516
266
8/27/2007
62.5
0
267
8/28/2007
62.5
0
268
8/29/2007
62
-0.008
269
8/30/2007
270
8/31/2007
62.5 0.008064516
63
17
0.008
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18
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I, MỘT SỐ QUAN SÁT VỀ CHUỖI LỢI SUẤT CỦA GIÁ CỔ
PHIẾU BT6.
1, đồ thị của chuỗi lợi suất:
a) kiểm định tính dừng của chuỗi lợi suất, ta có kết quả:
ADF Test
-
1% Critical
Statistic
14.298 Value*
2.573
96
3
5% Critical
Value
1.940
8
19
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10% Critical
-
Value
1.616
3
*MacKinnon critical values for rejection of
hypothesis of a unit root.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(R)
Method: Least Squares
Date: 11/22/04 Time: 18:08
Sample(adjusted): 3 270
Included observations: 268 after adjusting
endpoints
Variable
Coeffic
ient
R(-1)
Std.
t- Prob.
Error Statistic
- 0.0606
20
- 0.000