Table 6: Testing for a single change-point in the volatility of daily Stock Market Indices (SMI)
over the period 1989-2001
Change-point Statistics
SMI Returns
Change-point k * |
Kokoszka & Leipus Test |
Inclan & Tiao Tests | |||||
max Uk * |
max Uk* ^ HAC |
max Uk* GARMA |
IT |
Bt ( C ) | |||
FTSE |
|rt| |
05/06/97 |
1.917 |
5.862* |
6.665* |
4.414* |
0.599 |
( rt )2 |
04/08/97 |
2.238 |
5.266* |
3.511* |
9.195* |
1.249 | |
HSI |
|rt| |
14/08/97 |
3.460 |
4.619* |
5.828* |
4.954* |
0.321 |
( rt )2 |
18/08/97 |
7.104 |
2.181* |
1.291 |
8.583* |
0.556 | |
NIKKEI |
|rt| |
31/07/97 |
1.521 |
3.091* |
3.806* |
2.905* |
0.449 |
( rt )2 |
21/10/97 |
1.836 |
1.972* |
1.305 |
4.427* |
0.684 | |
S&P500 |
|rt| |
04/02/97 |
2.395 |
6.882* |
7.181* |
5.837* |
0.356 |
( rt )2 |
26/03/97 |
2.718 |
4.888* |
1.665* |
11.103* |
0.678 |
Notes: (1) The Stock Market Index (SMI) series refer to the Financial Times Stock Exchange index 100 (FTSE100), the Hang-Seng
Index (HSI), the Nikkei 500 (NIKKEI), the Standards and Poors 500 index (S&P500). The daily sample over the period 4/1/1989 to
19/10/2001 yields T = 3338 observations. The series rt := logpt - log p t-1 represents the returns on each index. The change-point tests
are applied to the (rt)2 and ∣rt∣ transformations as well as (ut)2 where ut is the residual from the GARCH. (2) The Kokoszka and Leipus
(1998, 2000) reported max Uk∙ is the maximum of the statistic, Uk =( ɪ ∑k r2 - ɪ ɪ ∑T, r2 ) which is standardized by
' ' ' ‘ ∖, TT l=1 j ' TT l =k+1 lJ j
nonparametric estimators, Heteroskedastic Consistent (σHAC) and ARMA estimators (σARMA) of squared and absolute returns. The
normalized statistic max Uk∙ /σ converges to the sup of a Brownian Bridge. (3) The Inclan and Tiao (1994) statistic
Dk = (∑j=1 l∑j= 1 r2) - "r specified for iid processes normalized as IT = 1∕T/2 max(Dk ∣also converges to the sup of a Brownian
Bridge and is extended in Kim et al. (2000) for GARCH processes to be Bt(C) = CJT max|.Dk∣ where C2and κ are constants that are
estimated by substituting the quasi-MLEs of the GARCH(1,1) ω, Й, β and T-1 ∑j=1 r4 to ω, α, β and E(rj). (4) k* refers to the
location of the break and the * symbol attached to statistics denotes that the null hypothesis of no structural change is rejected using the
asymptotic critical value of 1.36.
30
More intriguing information
1. THE EFFECT OF MARKETING COOPERATIVES ON COST-REDUCING PROCESS INNOVATION ACTIVITY2. Bridging Micro- and Macro-Analyses of the EU Sugar Program: Methods and Insights
3. Sex-gender-sexuality: how sex, gender, and sexuality constellations are constituted in secondary schools
4. The name is absent
5. Testing for One-Factor Models versus Stochastic Volatility Models
6. Social Cohesion as a Real-life Phenomenon: Exploring the Validity of the Universalist and Particularist Perspectives
7. Tobacco and Alcohol: Complements or Substitutes? - A Statistical Guinea Pig Approach
8. Large-N and Large-T Properties of Panel Data Estimators and the Hausman Test
9. Innovation Trajectories in Honduras’ Coffee Value Chain. Public and Private Influence on the Use of New Knowledge and Technology among Coffee Growers
10. The name is absent