Table 2: Sizes and local powers of tests of the cointegration rank
|
(a) Empirical sizes | ||||
|
Я = |
10 |
Я = |
20 | |
|
T |
REG |
LLL |
REG |
LLL |
|
20 |
0.012 |
0.000 |
0.010 |
0.000 |
|
30 |
0.033 |
0.000 |
0.033 |
0.000 |
|
50 |
0.053 |
0.004 |
0.050 |
0.002 |
|
100 |
0.056 |
0.030 |
0.068 |
0.033 |
|
(b) Local powers (size adjusted) | ||||
|
Я = |
10 |
Я = |
20 | |
|
T |
REG |
LLL |
REG |
LLL |
|
20 |
0.242 |
0.150 |
0.240 |
0.143 |
|
30 |
0.221 |
0.150 |
0.227 |
0.148 |
|
50 |
0.186 |
0.141 |
0.206 |
0.153 |
|
100 |
0.164 |
0.146 |
0.169 |
0.166 |
Note: Rejection frequency for tests of the null hypothesis r = 1. “REG” indi-
cates the regression based test suggested in Theorem 2 and “LLL” denotes the
LR-bar statistic suggested by Lyhagen et al. (2001). The local power is com-
puted by simulating the data under the local alternative VNT = —10/ (T∖N).
The critical values are used that yield tests with an exact size of 0.05 under the
null hypothesis (size adjusted power). 5000 replications are used to compute
the rejection frequencies.
23