Table 5: Continued. Size, Power and Frequency Distribution of the number of change-points
obtained with the Lavielle and Moulines (2000) test when there are two breaks at 0.33T and
0.67T, (T = 3000) of the sample in the GARCH.
|
Samples, T |
3000 |
3000 |
|
Lavielle & Moulines |
BIC LWZ |
BIC LWZ |
|
Returns |
( rt )2 |
|rt| |
|
Number of Breaks |
012≥3012≥30 |
12≥3012≥3 |
Segments tk
HA : Break in the dynamics of volatility with parameters (30, β1, β2)
DGP1:
|
(0.5,0.6,0.8) |
5 |
0.00 |
0.92 |
0.08 |
0.00 |
0.00 |
1.00 |
0.00 |
0.00 |
0.00 |
0.79 |
0.21 |
0.00 |
0.00 |
1.00 |
0.00 |
0.00 |
|
(0.5,0.6,0.3) |
5 |
0.00 |
0.91 |
0.09 |
0.00 |
0.00 |
1.00 |
0.00 |
0.00 |
0.00 |
0.77 |
0.22 |
0.01 |
0.00 |
1.00 |
0.00 |
0.00 |
|
DGP2: | |||||||||||||||||
|
(0.8,0.5,0.8) |
5 |
0.00 |
0.00 |
0.96 |
0.04 |
0.00 |
0.00 |
1.00 |
0.00 |
0.00 |
0.00 |
0.94 |
0.06 |
0.00 |
0.00 |
1.00 |
0.00 |
|
H1B |
: Break in the constant of volatility with parameters (ω0. |
, ω1, ω2) | |||||||||||||||
|
DGP1: | |||||||||||||||||
|
(0.4,0.5,0.8) |
5 |
0.00 |
0.90 |
0.10 |
0.00 |
0.01 |
0.99 |
0.00 |
0.00 |
0.00 |
0.92 |
0.08 |
0.00 |
0.03 |
0.97 |
0.00 |
0.00 |
|
(0.4,0.8,0.4) |
5 |
0.00 |
0.00 |
0.99 |
0.01 |
0.09 |
0.00 |
0.91 |
0.00 |
0.00 |
0.09 |
0.91 |
0.00 |
0.00 |
0.98 |
0.02 |
0.00 |
|
DGP2: | |||||||||||||||||
|
(0.1,0.2,0.5) |
5 |
0.00 |
0.45 |
0.54 |
0.01 |
0.00 |
1.00 |
0.00 |
0.00 |
0.00 |
0.16 |
0.82 |
0.02 |
0.00 |
0.98 |
0.02 |
0.00 |
|
(0.1,0.5,0.8) |
5 |
0.00 |
0.01 |
0.99 |
0.00 |
0.00 |
0.35 |
0.65 |
0.00 |
0.00 |
0.01 |
0.94 |
0.05 |
0.00 |
0.39 |
0.61 |
0.00 |
|
(0.1,0.5,0.1) |
5 |
0.00 |
0.00 |
0.99 |
0.01 |
0.01 |
0.00 |
0.99 |
0.00 |
0.00 |
0.00 |
0.96 |
0.04 |
0.00 |
0.00 |
1.00 |
0.00 |
|
(0.1,0.3,0.1) |
5 |
0.00 |
0.00 |
0.99 |
0.01 |
0.01 |
0.00 |
0.99 |
0.00 |
0.00 |
0.00 |
0.97 |
0.03 |
0.01 |
0.00 |
0.99 |
0.00 |
Hɑ : Break in the variance of the error with parameters (σu0, σu 1, σu2)
DGP1:
|
(0,1.5,3) |
5 |
0.00 |
0.74 |
0.26 |
0.00 |
0.00 |
0.98 |
0.02 |
0.00 |
0.00 |
0.00 |
0.75 |
0.25 |
0.00 |
0.87 |
0.13 |
0.00 |
|
(0,3,5) |
5 |
0.00 |
0.64 |
0.34 |
0.02 |
0.00 |
0.99 |
0.01 |
0.00 |
0.00 |
0.00 |
0.83 |
0.17 |
0.00 |
0.00 |
0.99 |
0.00 |
Notes: Please refer to the notes in Table 3.
29