HELENA CHULIÁ ET AL. 307Table 16.1Summary statisticsR1,t p-value R2,t p-valueMean −0.00015 −0.00013
Variance 0.00014 0.00019
Skewness 0.11161 [0.0927] −0.06255 [0.3461]
Kurtosis 5.97705 [0.0000] 4.90041 [0.0000]
Bera–Jarque 506.536 [0.0000] 206.146 [0.0000]
Q(6) 6.34085 [0.3861] 2.93234 [0.8172]
Q^2 (6) 214.134 [0.0000] 230.674 [0.0000]
ARCH(6) 126.292 [0.0000] 125.215 [0.0000]
ADF(4) −1.86827 [0.3476] −1.72608 [0.4179]
PP(6) −1.89895 [0.3330] −1.74016 [0.4107]Notes:p-values displayed as [.].R1,tandR2,trepresent the log-returns of the S&P500 and
the IBEX35 indices. The Bera–Jarque statistic tests for the normal distribution hypothesis
and has an asymptotic distributionX^2 (2). Q(6) and Q^2 (6) are Ljung-Box tests for sixth-
order serial correlation in the returns and squared returns. ARCH(6) is Engle’s test for sixth
order ARCH, distributed asX^2 (6). The ADF (number of lags) and PP (truncation lag) refer to
the Augmented Dickey–Fuller (1981) and Phillips and Perron (1988) unit-root tests. Critical
value at 5% significance level of Mackinnon (1991) for the ADF and PP tests (process with
intercept but without trend) is−2.86.returns exhibit conditional heteroskedasticity, while the Ljung–Box test (of
sixth order) indicates significant autocorrelation in both markets in squared
returns but not in levels. Fat tails and non-normal distributions are common
features of financial data. Finally, both the augmented Dickey–Fuller (ADF)
and Philips and Perron (PP) tests indicate that both series have a single
unit root.
The sample has been divided into two similar-length sub-samples in
order to separately analyze the volatility patterns before (18 January 2000–10
September 2001) and after (11 October 2001–11 October 2003) the terrorist
attack. There is one month excluded between the pre- and post- sub-samples
because during the crisis period other events, such as the attack of the USA
on Afghanistan, affected stock market returns making them more unstable.
Moreover, US financial markets were closed until 17 September. Finally, it
took one month for the S&P500 index to recover to the original level it had
before the tragic event occurred.
Table 16.2 displays returns, correlations and volatilities, period by period,
for both stock indexes, the S&P500 and the IBEX35. Three facts can be high-
lighted from these panels. Firstly, in all periods, means equality test can not
be rejected. Secondly, the IBEX35 is more volatile than the S&P500 and the
Levene’s test rejects variance equality in all periods except before September
- This last result is significant, since it may suggest a change in volatility