Detecting Multiple Breaks in Financial Market Volatility Dynamics



Table 7: Testing for multiple change-points in the volatility of daily Stock Market Indices
(SMI) over the period 1989-2001

Lavielle and Moulines Test

SMI

Process

Selection Criterion

Number & Location of Breaks

FTSE

|rt|

BIC -2.616(2), -2.610(1)

LWZ -2.599(1), -2.549(0)

2

1

3/11/92, 1/8/97

1/8/97

( rt )2

BIC -2.123(1), -2.070(0)

LWZ -2.112(1), -2.069(0)

1

1

10/7/98

10/7/98

HSI

|rt|

BIC -1.121(3), -1.117(2)

LWZ -1.108(1), -1.074(0)

3

1

3/7/92, 24/1/95, 15/8/97

15/8/97

( rt )2

BIC 2.005(1), 2.009(0)

LWZ 2.010(0)

1

0

15/8/97

NIKKEI

|rt|

BIC -1.874(2), -1.867(1)

LWZ -1.857(1), -1.851(0)

2

1

15/9/92, 30/7/97

20/8/98

( rt )2

BIC -0.457(2), -0.452(1)

LWZ -0.448(0)

2

0

15/9/92, 14/10/97

S&P500

|rt|

BIC -2.525(3), -2.513(2)

LWZ -2.492(2), -2.491(1)

3

2

27/12/91, 5/1/96, 28/7/98

20/8/91, 3/2/97

( rt )2

BIC -1.602(1), -1.559(0)

LWZ -1.591(1), -1.559(0)

1

1

14/10/97

14/10/97

Notes: For brief data description refer to note 1, Table 6. The Lavielle and Moulines test is described in section 1.2. The number of
segments for multiple breaks denoted by
m is set equal to 3. The selection criteria BIC and LWZ refer to the Bayesian or Schwarz
Information Criterion and modified BIC proposed in Liu et al. (1997).

31



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