Detecting Multiple Breaks in Financial Market Volatility Dynamics



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

LavielleMoulines

BIC             LWZ

BIC               LWZ

Returns

( rt )2

|rt|

Number of Breaks

012301230

1230123

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



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