A researcher models the Chinese stock returns series, Yt, as an AR(1) process and obtains the follow

  

A researcher models the Chinese stock returns series, Yt, as an AR(1) process and obtains the following results.The standard errors are given in parentheses (see attachment), Use statistical tables, (see attachment), answer the following questions, (see attachment)
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Question 2
A researcher models the Chinese stock returns series, Yt, as an AR(1) process and obtains the
following results. The standard errors are given in parentheses.
Yˆt =
0.826
(0.595)

0.569 Yt-1
(0.113)
R 2 = 0.79 ; n = 185
a. Is the intercept term significant to the model? Conduct a relevant hypothesis test to answer this
question.
b. Is the slope significant to the model? Conduct a relevant hypothesis test to answer this question.
c. What is the necessary condition that needs to be satisfied to achieve covariance stationarity? Is
that condition satisfied in this model? Conduct a relevant hypothesis test to answer this question.
d. Compute the mean-reverting level  for the Chinese stock returns series and interpret what this
number means.
Suppose the true underlying data generating process for the stock returns series is in fact the AR(1)
process shown above.
e. What does the correlogram for the AutoCorrelation Function (ACF) of Yt look like up to 8 lags?
f. Suppose the process is currently at  . Then, in time period t a shock occurs to the system. In
other words,  t  0 . For simplicity, assume that there are no other shocks prior to or after this
shock. Use relevant equations to trace the impact of this shock from period (t-1) to (t+k).
g. Using your equations in part (f), show that the above AR(1) process will eventually get back to its
mean-reverting level  as k approaches infinity.
1
– – _.— – – – – – — – – _
B -8
. .. _ –

Appendix B
Table 3
Normal Probabilities
z
.00
.01
.02
.03
.04
.05
.06
.07
.08
.09
0.0
.0000
.0040
.0080
.0239
.0279
.0319
.0398
.0793
.0438
.0478
.0160
.0557
.0199
0.1
0.2
.0120
.0517
.0636
.0675
.0714
.0832
.0871
.0948
.11 03
.1141
0.3
0.4
.1179
.1554
.1255
.1331
.1368
.1026
.1406
.1064
.1217
.0910
.1293
.0596
.0987
.0359
.0753
.1443
.1480
.1517
.1591
.1664
.1700
.1772
.1808
.1844
.1879
05
0.6
.1915
.2257
.1628
.1985
.2123
.2157
.2190
.2224
.2454
.2486
.2517
.2549
0.7
0.8
.2054
.2324
.2389
.2422
.2580
.2291
.2611
.2019
.2357
.1736
.2088
.2642
.2673
.2704
.2734
.2764
.2794
.2823
.2881
.2910
.2967
.2995
.3023
.3051
.3078
.3106
.2852
.3133
0.9
.3159
.3186
.2939
.3212
.3238
.3264
.3289
.3365
.3389
.3413
.3461
.3485
.3508
.3531
.3577
.3599
.3621
1.1
:3686
.3708
.3729
.3749
.3770
.3790
.3810
1.2
.3643
.3849
.3438
.3665
.3315
.3554
.3340
1.0
.3869
.3888
.3907
.3925
.3944
.3962
.3980
.3997
.3830
.4015
1.3
.4032
.4082
.4131
.4147
.4162
.4177
.4222
.4236
.4099
.4251
.4115
.4192
.4049
.4207
.4066
1.4
.4292
.4306
.4319
1.5
.4332
.4345
.4463
.4429
.4535
.4564
.4573
.4599
.4608
.4649
.4656
.4664
.4591
.4671
.4418
.4525
.4616
.4441
.4452
.4554
.4641
.4370
.4484
.4582
.4406
1.6
1.7
1.8
.4357
.4474
.4265
.4394
.4505 ‘
.4279
.4678
.4713
.4726
.4732
.4738
.4744
,4767
2.0
.4772
.4719
.4778
.4686
.4750
.4633
.4706
1.9
.4625
.4699
.4761
.4783
.4788
.4821
.4861
.4826
.4830
.4834
.4793
.4838
.4798
2.1
2.2
.4812
.4854
.4817
.4857
.4864
.4893
.4918
.4896
.4920
.4868
.4898
.4922
.4871
.4901
.4887
.4913
.4890
.4916
.4936
2.5
2.6
.4938
.4953
.4940
.4941
.4955
.4956
.4943
.4957
2.7
.4965
.4966
.4967
.4968
2.8
2.9
.4974
.4981
.4975
.4982
.4976
.4982
.4977
_’l 8i S
.4904
.4927
.4945
.4959
.4969
.4977
.4878
2.3
2.4
.4983
.4984
.4984
3.0
.4987
.4987
.4987
.4988
.4988
.4989
.1950
.4925
.4382
.4495
.45 15
.4693
,4756
.4545
.4906
.4803
.4846
.4881
,4909
.4850
.4884
.4911
.4929
.4931
.4932
.4946
.4948
.4949
.4934
.4951
.4960
.4961
.4962
.4963
.4964
.4970
.4978
.4971
.4972
.4979
.4974
.4985
.4973
.4980
.4986
.4989
.4990
.4990
.4842
.4979
.4985
.4989
.4808
.4952
.4981
.4986
SOURCE: Abridged from Table 1 of A. Hald, Statistical Tables and Formulas (New York: Wiley & Sons. Inc.), 1952. Reproduced by
permission of A. Hald and the publisher, John Wiley & Sons. Inc.
Appendix B
8-9
Table 4 Critical Values of t
~
.’ ~.:’-:….
r”
DEGREES OF
PREEOOM
DEGREES OF
FREEDOM
1.100
t.05O
t.Q2S
t.010
t.oos
24
q18
1.711
~.p64
2.492
2.797
9.925
25
1.316
1.708
2.060

2.485
4.541
5.841
26
1.315
1.706
2.056
2.479
2.779
3.747
4.604
27
1.314
1.703
2.052
2.473
2.771
3.365
4.032
28
1.313
1.701
2.048
2.467
2.763
3.143
3.707
29
1.311
1.699
2.045
2.462
2.756
t.100
t.oso
t.02S
t.01.O
t.oos
1
3.078
6.314
12.706
31.821
63.657
2
1.886
2.920
4.303
6.965
3
1.638
2.353
3.182
4
1.533
2.132
2.776
5
1.476
2.015
2.571
6
1.440
1.943
2.447
2.787
7
1.415
1.895
2.365
2.998
3.499
30
1.310
1.697
2.042
2.457
2.750
8
1.397
1.860
2.306
2.896
3.355
1.690
2.030
2.438
2.724
9
1.383
1.833
2.262
2.821
3.250
35
4D
1.306
1.303
1.684
2.021
2.423
2.705
10
1.372
1.812
2.228
2.764
3.169
45
1.301
1.679
2.014
2.412
2.690
11
1.363
1.796
2.201
2.718
3.106
50
1.299
1.676
2.009
2.403
2.678
12
1.356
1.782
2.179
2.681
3.055
60
1296
1.671
2.000
2.390
2.660
13
1.350
1.771
2.160
2.650
3.012
70
1.294
1.667
1.994
2.381
2.648
14
1.345
1.761
2.145
2.624
2.977
80
1.292
1.664
1.990
2.374
2.639
15
1.341
1.753
2.131
2.602
2.947
90
1.291
1.662
1.987
2.369
16
1.337
1.746
2.120
2.583
2.921
100
1.290
1.660
1.984
2.364 ‘
2.626
17
1.333
1.740
2.110
2.567
2.898
120
1.289
1.658
1.980
2.358
2.617
18
1.330
1.734
2.101
2.552
2.878
140
1.288
1.656
1.977
2.353
2.611
1.287
1.654
1.975
2.350
2.607
2.632
t’
19
1.328
1.729
2.093
2.539
2.861
160
20
1.325
1.725
2.086
2.528
2.845
180
1.286
1.653
1.973
2.347
2.603
21
1.323
1.721
2.080
2.518
2.831
200
1.286
1.653
1.972
2.345
2.601
22
1.321
1.717
2.074
2.508
2.819

7

8

9

4,052
98.50
34.12
21.20
16.26
13.75
12.25
11.26
10.56
10.04
9.65
9.33
9.07
8:86
8.68
8.53
8.40
8.29
8.18
8.10
8.02
7.95
7.88
7.82
7.77
7.72
7.68
7.64
7.60
7.56
7.31
7.08
6.85
6.63

4,999.5
99.00
30.82
18.00
13 .27
10.92
9.55
8.65
8.02
7.56
7.21
6.93
6.70
6.51
6.36
6.23
6.11
6.01
5.93
5.85
5.78
5.72
5.66
5.61
5.57
5.53
5.49
5.45
5.42
5.39
5.18
4.98
4.79
4.61

5,403
99.17
29.46
16.69
12.06
9.78
8.45
7.59
6.99
6.55
6.22
5.95
5.74
5.56
5.42
5.29
5.18
5.09
5.01
4.94
4.87
4.82
4.76
4.72
4.68
4.64
4.60
4.57
4.54
4.51
4.31
4.13
3.95
3.78

5,625
99.25
28.71
15.98
11.39
9.15
7.85
7.01
6.42
5.99
5.67
5.41
5.21
5.04
4.89
4.77
4.67
4.58
4.50
4.43
4.37
4.31
4.26
4.22
4.18
4.14
4.11
4.07
4.04
4.02
3.83
3.65
3.48
3.32

5,764
99.30
28.24
15.52
10.97
8.75
7.46
6.63
6.06
5.64
5.32
5.06
4.86
4.69
4.56
4.44
4.34
4.25
4.17
4.10
4.04
3.99
3.94
3.90
3.85
3.82
3.78
3.75
3.73
3.70
3.51
3.34
3.17
3.02

5,859
99.33
27.91
15.21
10.67
8.47
7.19
6.37
5.80
5.39
5.07
4.82
4.62
4.46
4.32
4.20
4.10
4.01
3.94
3.87
3.81
3.76
3.71
3.67
3.63
3.59
3.56
3.53
3.50
3.47
3.29
3.12
2.96
2.80

5,928
99.36
27.67
14.98
10.46
8.26
6.99
6.18
5.61
5.20
4.89
4.64
4.44
4.28
4.14
4.03
3.93
3.84

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