Table 4: Size, Power and Frequency Distribution of the number of change-points obtained
with the Kokoszka and Leipus (2000) test when there are two breaks at 0.33T and 0.67T of the
sample in the GARCH process.
|
Samples, T Returns Number of Breaks |
0 |
( rt ) 2 12 |
1000 ≥30 |
|rt| 12 |
≥3 |
0 |
( rt ) 2 12 |
3000 ≥30 |
|rt| 12 |
≥3 | ||||||
|
HA : Break in the dynamics of volatility with parameters (β0, β1, β2) | ||||||||||||||||
|
DGP1: | ||||||||||||||||
|
(0.5,0.6,0.8) |
0.00 |
0.88 |
0.01 |
0.11 |
0.00 |
0.00 |
0.87 |
0.13 |
0.00 |
0.87 |
0.13 |
0.00 |
0.00 |
0.00 |
1.00 |
0.00 |
|
(0.5,0.6,0.3) |
0.00 |
0.60 |
0.39 |
0.01 |
0.00 |
0.00 |
0.99 |
0.01 |
0.00 |
0.00 |
0.99 |
0.01 |
0.00 |
0.00 |
1.00 |
0.00 |
|
DGP2: | ||||||||||||||||
|
(0.8,0.5,0.8) |
0.00 |
0.00 |
1.00 |
0.00 |
0.00 |
0.00 |
1.00 |
0.00 |
0.00 |
0.00 |
1.00 |
0.00 |
0.00 |
0.00 |
1.00 |
0.00 |
|
HB : Break in the constant of volatility with parameters (ω 0, ω 1, ω 2) | ||||||||||||||||
|
DGP1: | ||||||||||||||||
|
(0.4,0.5,0.8) |
0.00 |
0.39 |
0.61 |
0.00 |
0.00 |
0.00 |
0.71 |
0.29 |
0.00 |
0.00 |
1.00 |
0.00 |
0.00 |
0.00 |
1.00 |
0.00 |
|
(0.4,0.8,0.4) |
0.00 |
0.53 |
0.39 |
0.08 |
0.00 |
0.00 |
0.77 |
0.23 |
0.00 |
0.30 |
0.66 |
0.04 |
0.00 |
0.00 |
0.99 |
0.01 |
|
DGP2: | ||||||||||||||||
|
(0.1,0.2,0.5) |
0.00 |
0.01 |
0.99 |
0.00 |
0.00 |
0.00 |
0.99 |
0.01 |
0.00 |
0.00 |
0.99 |
0.01 |
0.00 |
0.00 |
1.00 |
0.00 |
|
(0.1,0.5,0.8) |
0.00 |
0.00 |
1.00 |
0.00 |
0.00 |
0.00 |
1.00 |
0.00 |
0.00 |
0.00 |
1.00 |
0.00 |
0.00 |
0.00 |
1.00 |
0.00 |
|
(0.1,0.5,0.1) |
0.00 |
0.06 |
0.94 |
0.00 |
0.00 |
0.00 |
0.98 |
0.02 |
0.00 |
0.00 |
1.00 |
0.00 |
0.00 |
0.00 |
1.00 |
0.00 |
|
(0.1,0.3,0.1) |
0.00 |
0.20 |
0.78 |
0.02 |
0.00 |
0.00 |
0.97 |
0.03 |
0.00 |
0.00 |
0.99 |
0.01 |
0.00 |
0.00 |
0.99 |
0.00 |
|
H1C : Break in |
the variance |
of the |
error |
with parameters (σ |
u0,σu |
1, σ U 2 ) | ||||||||||
|
DGP1: | ||||||||||||||||
|
(0,1.5,3) |
0.00 |
0.00 |
1.00 |
0.00 |
0.00 |
0.00 |
1.00 |
0.00 |
0.00 |
0.00 |
1.00 |
0.00 |
0.00 |
0.00 |
1.00 |
0.00 |
|
(0,3,5) |
0.00 |
1.00 |
0.00 |
0.00 |
0.00 |
0.00 |
1.00 |
0.00 |
0.00 |
0.00 |
1.00 |
0.00 |
0.00 |
0.00 |
1.00 |
0.00 |
Notes: The K&L test (see notes in Table 1) is applied following a sequential sample segmentation approach and the frequency
distribution of the change-points is reported. The highlighted numbers refer to the true number of breaks in the simulated process.
27
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