Table 5: 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 of the
sample in the GARCH process.
|
Samples, T Lavielle & Moulines |
1000 1000 BIC LWZ BIC LWZ |
|
Returns |
( rt )2 |rt| |
|
Number of Breaks |
012≥3012≥3012≥3012≥3 |
|
Segments tk |
HA : Break in the dynamics of volatility with parameters (β0, β1, β2) |
DGP1:
|
(0.5,0.6,0.8) |
5 |
0.00 |
0.95 |
0.05 |
0.00 |
0.01 |
0.99 |
0.00 |
0.00 |
0.00 |
0.98 |
0.02 |
0.00 |
0.06 |
0.94 |
0.00 |
0.00 |
|
3 |
0.00 |
1.00 |
0.00 |
0.00 |
0.01 |
0.99 |
0.00 |
0.00 |
0.00 |
0.97 |
0.03 |
0.00 |
0.02 |
0.98 |
0.00 |
0.00 | |
|
(0.5,0.6,0.3) |
5 |
0.14 |
0.47 |
0.39 |
0.00 |
0.94 |
0.04 |
0.02 |
0.00 |
0.16 |
0.56 |
0.28 |
0.00 |
0.93 |
0.07 |
0.00 |
0.00 |
|
3 |
0.20 |
0.50 |
0.28 |
0.00 |
0.97 |
0.03 |
0.00 |
0.00 |
0.19 |
0.62 |
0.19 |
0.00 |
0.96 |
0.04 |
0.00 |
0.00 | |
|
DGP2: | |||||||||||||||||
|
(0.8,0.5,0.8) |
5 |
0.00 |
0.03 |
0.90 |
0.06 |
0.70 |
0.19 |
0.11 |
0.00 |
0.01 |
0.00 |
0.99 |
0.36 |
0.06 |
0.58 |
0.00 |
0.00 |
|
3 |
0.03 |
0.97 |
0.00 |
0.00 |
0.68 |
0.32 |
0.00 |
0.00 |
0.00 |
0.01 |
0.99 |
0.00 |
0.51 |
0.08 |
0.41 |
0.00 |
HB : Break in the constant of volatility with parameters (ω0, ω 1, ω2)
DGP1:
|
(0.4,0.5,0.8) |
5 3 |
0.05 0.02 |
0.91 0.97 |
0.04 0.01 |
0.00 0.00 |
0.66 0.52 |
0.34 0.48 |
0.00 0.00 |
0.00 0.00 |
0.04 0.05 |
0.94 0.94 |
0.02 0.01 |
0.00 0.00 |
0.63 0.69 |
0.37 0.31 |
0.00 0.00 |
0.00 0.00 |
|
(0.4,0.8,0.4) |
5 |
0.09 |
0.00 |
0.90 |
0.01 |
0.92 |
0.00 |
0.08 |
0.00 |
0.09 |
0.02 |
0.89 |
0.00 |
0.92 |
0.00 |
0.08 |
0.00 |
|
3 |
0.02 |
0.00 |
0.98 |
0.00 |
0.90 |
0.00 |
0.10 |
0.00 |
0.09 |
0.01 |
0.90 |
0.00 |
0.97 |
0.00 |
0.03 |
0.00 | |
|
DGP2: | |||||||||||||||||
|
(0.1,0.2,0.5) |
5 |
0.00 |
0.82 |
0.18 |
0.00 |
0.01 |
0.99 |
0.00 |
0.00 |
0.00 |
0.67 |
0.30 |
0.03 |
0.00 |
1.00 |
0.00 |
0.00 |
|
3 |
0.00 |
0.91 |
0.09 |
0.00 |
0.00 |
1.00 |
0.00 |
0.00 |
0.00 |
0.72 |
0.28 |
0.00 |
0.00 |
1.00 |
0.00 |
0.00 | |
|
(0.1,0.5,0.8) |
5 |
0.00 |
0.18 |
0.79 |
0.03 |
0.00 |
0.99 |
0.01 |
0.00 |
0.00 |
0.36 |
0.60 |
0.04 |
0.00 |
0.96 |
0.04 |
0.00 |
|
3 |
0.00 |
0.20 |
0.80 |
0.00 |
0.00 |
1.00 |
0.00 |
0.00 |
0.00 |
0.34 |
0.66 |
0.00 |
0.00 |
0.91 |
0.09 |
0.00 | |
|
(0.1,0.5,0.1) |
5 |
0.00 |
0.00 |
0.95 |
0.05 |
0.01 |
0.00 |
0.99 |
0.00 |
0.00 |
0.00 |
0.94 |
0.06 |
0.00 |
0.00 |
1.00 |
0.00 |
|
3 |
0.00 |
0.00 |
1.00 |
0.00 |
0.01 |
0.00 |
0.99 |
0.00 |
0.00 |
0.00 |
1.00 |
0.00 |
0.02 |
0.00 |
0.98 |
0.00 | |
|
(0.1,0.3,0.1) |
5 |
0.00 |
0.00 |
0.99 |
0.01 |
0.77 |
0.00 |
0.23 |
0.00 |
0.02 |
0.02 |
0.93 |
0.03 |
0.75 |
0.02 |
0.23 |
0.00 |
|
3 |
0.01 |
0.02 |
0.97 |
0.00 |
0.68 |
0.00 |
0.32 |
0.00 |
0.04 |
0.00 |
0.96 |
0.00 |
0.71 |
0.02 |
0.27 |
0.00 | |
|
H1C |
: Break in the variance of the error with parameters (σu0, |
σu1,σu2) | |||||||||||||||
|
DGP1: | |||||||||||||||||
|
(0,1.5,3) |
5 |
0.00 |
0.78 |
0.22 |
0.00 |
0.00 |
0.98 |
0.02 |
0.00 |
0.00 |
0.37 |
0.56 |
0.07 |
0.00 |
0.96 |
0.04 |
0.00 |
|
3 |
0.00 |
0.97 |
0.03 |
0.00 |
0.00 |
1.00 |
0.00 |
0.00 |
0.00 |
0.53 |
0.47 |
0.00 |
0.00 |
1.00 |
0.00 |
0.00 | |
|
(0,3,5) |
5 |
0.00 |
0.76 |
0.24 |
0.00 |
0.00 |
0.96 |
0.04 |
0.00 |
0.00 |
0.00 |
0.81 |
0.19 |
0.00 |
0.00 |
0.98 |
0.02 |
|
3 |
0.00 |
0.96 |
0.04 |
0.00 |
0.00 |
1.00 |
0.00 |
0.00 |
0.00 |
0.00 |
1.00 |
0.00 |
0.00 |
0.00 |
1.00 |
0.00 | |
28