Detecting Multiple Breaks in Financial Market Volatility Dynamics



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

LavielleMoulines

1000                                        1000

BIC             LWZ             BIC               LWZ

Returns

( rt )2                                                                                              |rt|

Number of Breaks

0123012301230123

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,

σu1u2)

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



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