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Econ 101: Appendix 2 - Statistical Distributions & Critical Values | Môn Econometrics with Financial Application - Trường Đại học Quốc tế, Đại học Quốc gia Thành phố Hồ Chí Minh

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Môn: Econometrics with Financial Application (BA174IU) 10 tài liệu

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Appendix 2
Tables of Stascal Distribuons
Table A2.1 Normal crical values for dierent values of α
α
0.4
0.25
0.2
0.15
0.1
0.05
0.025
0.0
Z
α
.2533
.6745
.8416
1.0364
1.2816
1.6449
1.9600
2.3
Source: Author’s computaon using the NORMDIST funcon in Excel.
Table A2.2 Crical values of Student’s t-distribuon for dierent probability
levels, α and degrees of freedom, ν
α
0.25
0.1
0.025
0.01
ν
1
1.000
0
3.077
7
12.706
2
31.820
5
2
0.816
5
1.885
6
4.3027
6.9646
3
0.764
9
1.637
7
3.1824
4.5407
4
0.740
7
1.533
2
2.7764
3.7469
5
0.726
7
1.475
9
2.5706
3.3649
6
0.717
6
1.439
8
2.4469
3.1427
7
0.711
1
1.414
9
2.3646
2.9980
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8
0.706
4
1.396
8
2.3060
2.8965
9
0.702
7
1.383
0
2.2622
2.8214
1
0
0.699
8
1.372
2
2.2281
2.7638
1
1
0.697
4
1.363
4
2.2010
2.7181
1
2
0.695
5
1.356
2
2.1788
2.6810
13
0.2586
0.6938
1.0795
1.3502
1.7709
2.1604
2.6503
14
0.2582
0.6924
1.0763
1.3450
1.7613
2.1448
2.6245
15
0.2579
0.6912
1.0735
1.3406
1.7531
2.1314
2.6025
16
0.2576
0.6901
1.0711
1.3368
1.7459
2.1199
2.5835
17
0.2573
0.6892
1.0690
1.3334
1.7396
2.1098
2.5669
18
0.2571
0.6884
1.0672
1.3304
1.7341
2.1009
2.5524
19
0.2569
0.6876
1.0655
1.3277
1.7291
2.0930
2.5395
20
0.2567
0.6870
1.0640
1.3253
1.7247
2.0860
2.5280
21
0.2566
0.6864
1.0627
1.3232
1.7207
2.0796
2.5176
22
0.2564
0.6858
1.0614
1.3212
1.7171
2.0739
2.5083
23
0.2563
0.6853
1.0603
1.3195
1.7139
2.0687
2.4999
24
0.2562
0.6848
1.0593
1.3178
1.7109
2.0639
2.4922
25
0.2561
0.6844
1.0584
1.3163
1.7081
2.0595
2.4851
26
0.2560
0.6840
1.0575
1.3150
1.7056
2.0555
2.4786
27
0.2559
0.6837
1.0567
1.3137
1.7033
2.0518
2.4727
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28
0.2558
0.6834
1.0560
1.3125
1.7011
2.0484
2.4671
29
0.2557
0.6830
1.0553
1.3114
1.6991
2.0452
2.4620
30
0.2556
0.6828
1.0547
1.3104
1.6973
2.0423
2.4573
35
0.2553
0.6816
1.0520
1.3062
1.6896
2.0301
2.4377
40
0.2550
0.6807
1.0500
1.3031
1.6839
2.0211
2.4233
45
0.2549
0.6800
1.0485
1.3006
1.6794
2.0141
2.4121
50
0.2547
0.6794
1.0473
1.2987
1.6759
2.0086
2.4033
60
0.2545
0.6786
1.0455
1.2958
1.6706
2.0003
2.3901
70
0.2543
0.6780
1.0442
1.2938
1.6669
1.9944
2.3808
80
0.2542
0.6776
1.0432
1.2922
1.6641
1.9901
2.3739
90
0.2541
0.6772
1.0424
1.2910
1.6620
1.9867
2.3685
100
0.2540
0.6770
1.0418
1.2901
1.6602
1.9840
2.3642
120
0.2539
0.6765
1.0409
1.2886
1.6577
1.9799
2.3578
150
0.2538
0.6761
1.0400
1.2872
1.6551
1.9759
2.3515
200
0.2537
0.6757
1.0391
1.2858
1.6525
1.9719
2.3451
300
0.2536
0.6753
1.0382
1.2844
1.6499
1.9679
2.3388
∞
0.2533
0.6745
1.0364
1.2816
1.6449
1.9600
2.3263
Source: Author’s own computaon using the TINV funcon in Excel.
lOMoARcPSD| 58583460
Table A2.3 Upper 5% crical values for F-distribuon
Source: Author’s own computaon using the Excel FINV funcon.
lOMoARcPSD| 58583460
Table A2.4 Upper 1% crical values for F-distribuon
Source: Author’s own computaon using the Excel CHIINV funcon.
lOMoARcPSD| 58583460
Table 2.5 Chi-squared crical values for dierent values of α and degrees of
freedom, ν
Source: Author’s own computaon using the Excel CHIINV funcon.
Table A2.6 Lower and upper 1% crical values for the Durbin–Watson
stasc
k′ = 1
k′ = 2
k′ = 3
k′ = 4
k′ = 5
lOMoARcPSD| 58583460
T
d
L
d
U
d
L
d
U
d
L
d
U
d
L
d
U
d
L
d
U
15
0.8
1
1.0
7
0.7
0
1.2
5
0.5
9
1.4
6
0.4
9
1.7
0
0.3
9
1.9
6
16
0.8
4
1.0
9
0.7
4
1.2
5
0.6
3
1.4
4
0.5
3
1.6
6
0.4
4
1.9
0
17
0.8
7
1.1
0
0.7
7
1.2
5
0.6
7
1.4
3
0.5
7
1.6
3
0.4
8
1.8
5
18
0.9
0
1.1
2
0.8
0
1.2
6
0.7
1
1.4
2
0.6
1
1.6
0
0.5
2
1.8
0
19
0.9
3
1.1
3
0.8
3
1.2
6
0.7
4
1.4
1
0.6
5
1.5
8
0.5
6
1.7
7
20
0.9
5
1.1
5
0.8
6
1.2
7
0.7
7
1.4
1
0.6
8
1.5
7
0.6
0
1.7
4
21
0.9
7
1.1
6
0.8
9
1.2
7
0.8
0
1.4
1
0.7
2
1.5
5
0.6
3
1.7
1
22
1.0
0
1.1
7
0.9
1
1.2
8
0.8
3
1.4
0
0.7
5
1.5
4
0.6
6
1.6
9
23
1.0
2
1.1
9
0.9
4
1.2
9
0.8
6
1.4
0
0.7
7
1.5
3
0.7
0
1.6
7
24
1.0
4
1.2
0
0.9
6
1.3
0
0.8
8
1.4
1
0.8
0
1.5
3
0.7
2
1.6
6
25
1.0
5
1.2
1
0.9
8
1.3
0
0.9
0
1.4
1
0.8
3
1.5
2
0.7
5
1.6
5
26
1.0
7
1.2
2
1.0
0
1.3
1
0.9
3
1.4
1
0.8
5
1.5
2
0.7
8
1.6
4
27
1.0
9
1.2
3
1.0
2
1.3
2
0.9
5
1.4
1
0.8
8
1.5
1
0.8
1
1.6
3
28
1.1
0
1.2
4
1.0
4
1.3
2
0.9
7
1.4
1
0.9
0
1.5
1
0.8
3
1.6
2
29
1.1
2
1.2
5
1.0
5
1.3
3
0.9
9
1.4
2
0.9
2
1.5
1
0.8
5
1.6
1
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30
1.1
3
1.2
6
1.0
7
1.3
4
1.0
1
1.4
2
0.9
4
1.5
1
0.8
8
1.6
1
31
1.1
5
1.2
7
1.0
8
1.3
4
1.0
2
1.4
2
0.9
6
1.5
1
0.9
0
1.6
0
32
1.1
6
1.2
8
1.1
0
1.3
5
1.0
4
1.4
3
0.9
8
1.5
1
0.9
2
1.6
0
33
1.1
7
1.2
9
1.1
1
1.3
6
1.0
5
1.4
3
1.0
0
1.5
1
0.9
4
1.5
9
34
1.1
8
1.3
0
1.1
3
1.3
6
1.0
7
1.4
3
1.0
1
1.5
1
0.9
5
1.5
9
35
1.1
9
1.3
1
1.1
4
1.3
7
1.0
8
1.4
4
1.0
3
1.5
1
0.9
7
1.5
9
36
1.2
1
1.3
2
1.1
5
1.3
8
1.1
0
1.4
4
1.0
4
1.5
1
0.9
9
1.5
9
37
1.2
2
1.3
2
1.1
6
1.3
8
1.1
1
1.4
5
1.0
6
1.5
1
1.0
0
1.5
9
38
1.2
3
1.3
3
1.1
8
1.3
9
1.1
2
1.4
5
1.0
7
1.5
2
1.0
2
1.5
8
39
1.2
4
1.3
4
1.1
9
1.3
9
1.1
4
1.4
5
1.0
9
1.5
2
1.0
3
1.5
8
40
1.2
5
1.3
4
1.2
0
1.4
0
1.1
5
1.4
6
1.1
0
1.5
2
1.0
5
1.5
8
45
1.2
9
1.3
8
1.2
4
1.4
2
1.2
0
1.4
8
1.1
6
1.5
3
1.1
1
1.5
8
50
1.3
2
1.4
0
1.2
8
1.4
5
1.2
4
1.4
9
1.2
0
1.5
4
1.1
6
1.5
9
55
1.3
6
1.4
3
1.3
2
1.4
7
1.2
8
1.5
1
1.2
5
1.5
5
1.2
1
1.5
9
60
1.3
8
1.4
5
1.3
5
1.4
8
1.3
2
1.5
2
1.2
8
1.5
6
1.2
5
1.6
0
65
1.4
1
1.4
7
1.3
8
1.5
0
1.3
5
1.5
3
1.3
1
1.5
7
1.2
8
1.6
1
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70
1.4
3
1.4
9
1.4
0
1.5
2
1.3
7
1.5
5
1.3
4
1.5
8
1.3
1
1.6
1
75
1.4
5
1.5
0
1.4
2
1.5
3
1.3
9
1.5
6
1.3
7
1.5
9
1.3
4
1.6
2
80
1.4
7
1.5
2
1.4
4
1.5
4
1.4
2
1.5
7
1.3
9
1.6
0
1.3
6
1.6
2
85
1.4
8
1.5
3
1.4
6
1.5
5
1.4
3
1.5
8
1.4
1
1.6
0
1.3
9
1.6
3
90
1.5
0
1.5
4
1.4
7
1.5
6
1.4
5
1.5
9
1.4
3
1.6
1
1.4
1
1.6
4
95
1.5
1
1.5
5
1.4
9
1.5
7
1.4
7
1.6
0
1.4
5
1.6
2
1.4
2
1.6
4
10
0
1.5
2
1.5
6
1.5
0
1.5
8
1.4
8
1.6
0
1.4
6
1.6
3
1.4
4
1.6
5
Note: T, number of observaons; k′, number of explanatory variables (excluding a
constant term).
Source: Durbin and Watson (1951): 159–77. Reprinted with the permission of Oxford
University Press.
Table A2.7 Dickey–Fuller crical values for dierent signicance levels, α
Sample
size T
0.01
0.025
0.05
0.10
τ
25
−2.66
−2.26
−1.95
−1.60
50
−2.62
−2.25
−1.95
−1.61
100
−2.60
−2.24
−1.95
−1.61
250
−2.58
−2.23
−1.95
−1.62
500
−2.58
−2.23
−1.95
−1.62
∞
−2.58
−2.23
−1.95
−1.62
lOMoARcPSD| 58583460
τ
μ
25
−3.75
−3.33
−3.00
−2.63
50
−3.58
−3.22
−2.93
−2.60
100
−3.51
−3.17
−2.89
−2.58
250
−3.46
−3.14
−2.88
−2.57
500
−3.44
−3.13
−2.87
−2.57
∞
−3.43
−3.12
−2.86
−2.57
τ
τ
25
−4.38
−3.95
−3.60
−3.24
50
−4.15
−3.80
−3.50
−3.18
100
−4.04
−3.73
−3.45
−3.15
250
−3.99
−3.69
−3.43
−3.13
500
−3.98
−3.68
−3.42
−3.13
∞
−3.96
−3.66
−3.41
−3.12
Source: Fuller (1976). Reprinted with the permission of John Wiley and Sons.
Table A2.8 Crical values for the Engle–Granger cointegraon test on
regression residuals with no constant in test regression
Number
of
variables in
system
Sample
size T
0.01
0.05
0.10
50
−4.32
−3.67
−3.28
2
100
−4.07
−3.37
−3.03
lOMoARcPSD| 58583460
200
−4.00
−3.37
−3.02
50
−4.84
−4.11
−3.73
3
100
−4.45
−3.93
−3.59
200
−4.35
−3.78
−3.47
50
−4.94
−4.35
−4.02
4
100
−4.75
−4.22
−3.89
200
−4.70
−4.18
−3.89
50
−5.41
−4.76
−4.42
5
100
−5.18
−4.58
−4.26
200
−5.02
−4.48
−4.18
Source: Engle and Granger (1987). Reprinted with the permission of Elsevier.
lOMoARcPSD| 58583460
Table A2.9 Quanles of the asymptoc distribuon of the Johansen
cointegraon rank test stascs (constant in cointegrang vectors only)
Source: Osterwald-Lenum (1992, Table 1
*
). Reprinted with the permission of Blackwell
Publishers.
lOMoARcPSD| 58583460
Table A2.10 Quanles of the asymptoc distribuon of the Johansen
cointegraon rank test stascs (constant, i.e., a dri only in VAR and in
cointegrang vector)
Source: Osterwald-Lenum (1992, Table 1). Reprinted with the permission of Blackwell
Publishers.
lOMoARcPSD| 58583460
Table A2.11 Quanles of the asymptoc distribuon of the Johansen
cointegraon rank test stascs (constant in cointegrang vector and VAR,
trend in cointegrang vector)
Source: Osterwald-Lenum (1992, Table 2
*
). Reprinted with the permission of Blackwell
Publishers.

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lOMoAR cPSD| 58583460 Appendix 2
Tables of Statistical Distributions
Table A2.1 Normal critical values for different values of α α 0.4 0.25 0.2 0.15 0.1 0.05 0.025 0.0 Zα
.2533 .6745 .8416 1.0364 1.2816 1.6449 1.9600 2.3
Source: Author’s computation using the NORMDIST function in Excel.
Table A2.2 Critical values of Student’s t-distribution for different probability
levels, α and degrees of freedom, ν α 0.4 0.25 0.15 0.1 0.05 0.025 0.01 ν 1 0.324 1.000 1.962 3.077 6.313 12.706 31.820 9 0 6 7 8 2 5 2 0.288 0.816 1.386 1.885 2.920 4.3027 6.9646 7 5 2 6 0 3 0.276 0.764 1.249 1.637 2.353 3.1824 4.5407 7 9 8 7 4 4 0.270 0.740 1.189 1.533 2.131 2.7764 3.7469 7 7 6 2 8 5 0.267 0.726 1.155 1.475 2.015 2.5706 3.3649 2 7 8 9 0 6 0.264 0.717 1.134 1.439 1.943 2.4469 3.1427 8 6 2 8 2 7 0.263 0.711 1.119 1.414 1.894 2.3646 2.9980 2 1 2 9 6 lOMoAR cPSD| 58583460 8 0.261 0.706 1.108 1.396 1.859 2.3060 2.8965 9 4 1 8 5 9 0.261 0.702 1.099 1.383 1.833 2.2622 2.8214 0 7 7 0 1 1 0.260 0.699 1.093 1.372 1.812 2.2281 2.7638 0 2 8 1 2 5 1 0.259 0.697 1.087 1.363 1.795 2.2010 2.7181 1 6 4 7 4 9 1 0.259 0.695 1.083 1.356 1.782 2.1788 2.6810 2 0 5 2 2 3 13
0.2586 0.6938 1.0795 1.3502 1.7709 2.1604 2.6503 14
0.2582 0.6924 1.0763 1.3450 1.7613 2.1448 2.6245 15
0.2579 0.6912 1.0735 1.3406 1.7531 2.1314 2.6025 16
0.2576 0.6901 1.0711 1.3368 1.7459 2.1199 2.5835 17
0.2573 0.6892 1.0690 1.3334 1.7396 2.1098 2.5669 18
0.2571 0.6884 1.0672 1.3304 1.7341 2.1009 2.5524 19
0.2569 0.6876 1.0655 1.3277 1.7291 2.0930 2.5395 20
0.2567 0.6870 1.0640 1.3253 1.7247 2.0860 2.5280 21
0.2566 0.6864 1.0627 1.3232 1.7207 2.0796 2.5176 22
0.2564 0.6858 1.0614 1.3212 1.7171 2.0739 2.5083 23
0.2563 0.6853 1.0603 1.3195 1.7139 2.0687 2.4999 24
0.2562 0.6848 1.0593 1.3178 1.7109 2.0639 2.4922 25
0.2561 0.6844 1.0584 1.3163 1.7081 2.0595 2.4851 26
0.2560 0.6840 1.0575 1.3150 1.7056 2.0555 2.4786 27
0.2559 0.6837 1.0567 1.3137 1.7033 2.0518 2.4727 lOMoAR cPSD| 58583460 28
0.2558 0.6834 1.0560 1.3125 1.7011 2.0484 2.4671 29
0.2557 0.6830 1.0553 1.3114 1.6991 2.0452 2.4620 30
0.2556 0.6828 1.0547 1.3104 1.6973 2.0423 2.4573 35
0.2553 0.6816 1.0520 1.3062 1.6896 2.0301 2.4377 40
0.2550 0.6807 1.0500 1.3031 1.6839 2.0211 2.4233 45
0.2549 0.6800 1.0485 1.3006 1.6794 2.0141 2.4121 50
0.2547 0.6794 1.0473 1.2987 1.6759 2.0086 2.4033 60
0.2545 0.6786 1.0455 1.2958 1.6706 2.0003 2.3901 70
0.2543 0.6780 1.0442 1.2938 1.6669 1.9944 2.3808 80
0.2542 0.6776 1.0432 1.2922 1.6641 1.9901 2.3739 90
0.2541 0.6772 1.0424 1.2910 1.6620 1.9867 2.3685
100 0.2540 0.6770 1.0418 1.2901 1.6602 1.9840 2.3642
120 0.2539 0.6765 1.0409 1.2886 1.6577 1.9799 2.3578
150 0.2538 0.6761 1.0400 1.2872 1.6551 1.9759 2.3515
200 0.2537 0.6757 1.0391 1.2858 1.6525 1.9719 2.3451
300 0.2536 0.6753 1.0382 1.2844 1.6499 1.9679 2.3388 ∞
0.2533 0.6745 1.0364 1.2816 1.6449 1.9600 2.3263
Source: Author’s own computation using the TINV function in Excel. lOMoAR cPSD| 58583460
Table A2.3 Upper 5% critical values for F-distribution
Source: Author’s own computation using the Excel FINV function. lOMoAR cPSD| 58583460
Table A2.4 Upper 1% critical values for F-distribution
Source: Author’s own computation using the Excel CHIINV function. lOMoAR cPSD| 58583460
Table 2.5 Chi-squared critical values for different values of α and degrees of freedom, ν
Source: Author’s own computation using the Excel CHIINV function.
Table A2.6 Lower and upper 1% critical values for the Durbin–Watson statistic k′ = 1 k′ = 2 k′ = 3 k′ = 4 k′ = 5 lOMoAR cPSD| 58583460 T dL dU dL dU dL dU dL dU dL dU 15 0.8 1.0 0.7 1.2 0.5 1.4 0.4 1.7 0.3 1.9 1 7 0 5 9 6 9 0 9 6 16 0.8 1.0 0.7 1.2 0.6 1.4 0.5 1.6 0.4 1.9 4 9 4 5 3 4 3 6 4 0 17 0.8 1.1 0.7 1.2 0.6 1.4 0.5 1.6 0.4 1.8 7 0 7 5 7 3 7 3 8 5 18 0.9 1.1 0.8 1.2 0.7 1.4 0.6 1.6 0.5 1.8 0 2 0 6 1 2 1 0 2 0 19 0.9 1.1 0.8 1.2 0.7 1.4 0.6 1.5 0.5 1.7 3 3 3 6 4 1 5 8 6 7 20 0.9 1.1 0.8 1.2 0.7 1.4 0.6 1.5 0.6 1.7 5 5 6 7 7 1 8 7 0 4 21 0.9 1.1 0.8 1.2 0.8 1.4 0.7 1.5 0.6 1.7 7 6 9 7 0 1 2 5 3 1 22 1.0 1.1 0.9 1.2 0.8 1.4 0.7 1.5 0.6 1.6 0 7 1 8 3 0 5 4 6 9 23 1.0 1.1 0.9 1.2 0.8 1.4 0.7 1.5 0.7 1.6 2 9 4 9 6 0 7 3 0 7 24 1.0 1.2 0.9 1.3 0.8 1.4 0.8 1.5 0.7 1.6 4 0 6 0 8 1 0 3 2 6 25 1.0 1.2 0.9 1.3 0.9 1.4 0.8 1.5 0.7 1.6 5 1 8 0 0 1 3 2 5 5 26 1.0 1.2 1.0 1.3 0.9 1.4 0.8 1.5 0.7 1.6 7 2 0 1 3 1 5 2 8 4 27 1.0 1.2 1.0 1.3 0.9 1.4 0.8 1.5 0.8 1.6 9 3 2 2 5 1 8 1 1 3 28 1.1 1.2 1.0 1.3 0.9 1.4 0.9 1.5 0.8 1.6 0 4 4 2 7 1 0 1 3 2 29 1.1 1.2 1.0 1.3 0.9 1.4 0.9 1.5 0.8 1.6 2 5 5 3 9 2 2 1 5 1 lOMoAR cPSD| 58583460 30 1.1 1.2 1.0 1.3 1.0 1.4 0.9 1.5 0.8 1.6 3 6 7 4 1 2 4 1 8 1 31 1.1 1.2 1.0 1.3 1.0 1.4 0.9 1.5 0.9 1.6 5 7 8 4 2 2 6 1 0 0 32 1.1 1.2 1.1 1.3 1.0 1.4 0.9 1.5 0.9 1.6 6 8 0 5 4 3 8 1 2 0 33 1.1 1.2 1.1 1.3 1.0 1.4 1.0 1.5 0.9 1.5 7 9 1 6 5 3 0 1 4 9 34 1.1 1.3 1.1 1.3 1.0 1.4 1.0 1.5 0.9 1.5 8 0 3 6 7 3 1 1 5 9 35 1.1 1.3 1.1 1.3 1.0 1.4 1.0 1.5 0.9 1.5 9 1 4 7 8 4 3 1 7 9 36 1.2 1.3 1.1 1.3 1.1 1.4 1.0 1.5 0.9 1.5 1 2 5 8 0 4 4 1 9 9 37 1.2 1.3 1.1 1.3 1.1 1.4 1.0 1.5 1.0 1.5 2 2 6 8 1 5 6 1 0 9 38 1.2 1.3 1.1 1.3 1.1 1.4 1.0 1.5 1.0 1.5 3 3 8 9 2 5 7 2 2 8 39 1.2 1.3 1.1 1.3 1.1 1.4 1.0 1.5 1.0 1.5 4 4 9 9 4 5 9 2 3 8 40 1.2 1.3 1.2 1.4 1.1 1.4 1.1 1.5 1.0 1.5 5 4 0 0 5 6 0 2 5 8 45 1.2 1.3 1.2 1.4 1.2 1.4 1.1 1.5 1.1 1.5 9 8 4 2 0 8 6 3 1 8 50 1.3 1.4 1.2 1.4 1.2 1.4 1.2 1.5 1.1 1.5 2 0 8 5 4 9 0 4 6 9 55 1.3 1.4 1.3 1.4 1.2 1.5 1.2 1.5 1.2 1.5 6 3 2 7 8 1 5 5 1 9 60 1.3 1.4 1.3 1.4 1.3 1.5 1.2 1.5 1.2 1.6 8 5 5 8 2 2 8 6 5 0 65 1.4 1.4 1.3 1.5 1.3 1.5 1.3 1.5 1.2 1.6 1 7 8 0 5 3 1 7 8 1 lOMoAR cPSD| 58583460 70 1.4 1.4 1.4 1.5 1.3 1.5 1.3 1.5 1.3 1.6 3 9 0 2 7 5 4 8 1 1 75 1.4 1.5 1.4 1.5 1.3 1.5 1.3 1.5 1.3 1.6 5 0 2 3 9 6 7 9 4 2 80 1.4 1.5 1.4 1.5 1.4 1.5 1.3 1.6 1.3 1.6 7 2 4 4 2 7 9 0 6 2 85 1.4 1.5 1.4 1.5 1.4 1.5 1.4 1.6 1.3 1.6 8 3 6 5 3 8 1 0 9 3 90 1.5 1.5 1.4 1.5 1.4 1.5 1.4 1.6 1.4 1.6 0 4 7 6 5 9 3 1 1 4 95 1.5 1.5 1.4 1.5 1.4 1.6 1.4 1.6 1.4 1.6 1 5 9 7 7 0 5 2 2 4 10 1.5 1.5 1.5 1.5 1.4 1.6 1.4 1.6 1.4 1.6 0 2 6 0 8 8 0 6 3 4 5
Note: T, number of observations; k′, number of explanatory variables (excluding a constant term).
Source: Durbin and Watson (1951): 159–77. Reprinted with the permission of Oxford University Press.
Table A2.7 Dickey–Fuller critical values for different significance levels, α Sample 0.01 0.025 0.05 0.10 size T τ 25 −2.66 −2.26 −1.95 −1.60 50 −2.62 −2.25 −1.95 −1.61 100 −2.60 −2.24 −1.95 −1.61 250 −2.58 −2.23 −1.95 −1.62 500 −2.58 −2.23 −1.95 −1.62 ∞ −2.58 −2.23 −1.95 −1.62 lOMoAR cPSD| 58583460 τμ 25 −3.75 −3.33 −3.00 −2.63 50 −3.58 −3.22 −2.93 −2.60 100 −3.51 −3.17 −2.89 −2.58 250 −3.46 −3.14 −2.88 −2.57 500 −3.44 −3.13 −2.87 −2.57 ∞ −3.43 −3.12 −2.86 −2.57 ττ 25 −4.38 −3.95 −3.60 −3.24 50 −4.15 −3.80 −3.50 −3.18 100 −4.04 −3.73 −3.45 −3.15 250 −3.99 −3.69 −3.43 −3.13 500 −3.98 −3.68 −3.42 −3.13 ∞ −3.96 −3.66 −3.41 −3.12
Source: Fuller (1976). Reprinted with the permission of John Wiley and Sons.
Table A2.8 Critical values for the Engle–Granger cointegration test on
regression residuals with no constant in test regression Number of variables in Sample system size T 0.01 0.05 0.10 50 −4.32 −3.67 −3.28 2 100 −4.07 −3.37 −3.03 lOMoAR cPSD| 58583460 200 −4.00 −3.37 −3.02 50 −4.84 −4.11 −3.73 3 100 −4.45 −3.93 −3.59 200 −4.35 −3.78 −3.47 50 −4.94 −4.35 −4.02 4 100 −4.75 −4.22 −3.89 200 −4.70 −4.18 −3.89 50 −5.41 −4.76 −4.42 5 100 −5.18 −4.58 −4.26 200 −5.02 −4.48 −4.18
Source: Engle and Granger (1987). Reprinted with the permission of Elsevier. lOMoAR cPSD| 58583460
Table A2.9 Quantiles of the asymptotic distribution of the Johansen
cointegration rank test statistics (constant in cointegrating vectors only)
Source: Osterwald-Lenum (1992, Table 1*). Reprinted with the permission of Blackwell Publishers. lOMoAR cPSD| 58583460
Table A2.10 Quantiles of the asymptotic distribution of the Johansen
cointegration rank test statistics (constant, i.e., a drift only in VAR and in cointegrating vector)
Source: Osterwald-Lenum (1992, Table 1). Reprinted with the permission of Blackwell Publishers. lOMoAR cPSD| 58583460
Table A2.11 Quantiles of the asymptotic distribution of the Johansen
cointegration rank test statistics (constant in cointegrating vector and VAR,
trend in cointegrating vector)
Source: Osterwald-Lenum (1992, Table 2*). Reprinted with the permission of Blackwell Publishers.

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