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