Advances in Risk Management

308 VOLATILITY TRANSMISSION PATTERNS BETWEEN THE USA AND SPAIN

Table 16.2 Returns, correlations and volatilities

Panel A: returns and correlations

Period μ 1 μ 2 Mean Test ρ1,2
Ho:μ 1 =μ 2

Total −0.00015 −0.00013 0.05543 0.6945

Pre-09/11 −0.00069 −0.00087 0.19266 0.6165
Post-09/11 −0.00004 −0.00011 0.07929 0.7332

Mean test 0.73899 0.76731 – –
Ho:μpre=μpost

Panel B: volatilities

Period σ 1 σ 2 Levene Test
Ho:σ^21 =σ^22

Total 0.01203 0.01399 20.38690∗

Pre-09/11 0.01314 0.014449 2.48221
Post-09/11 0.01381 0.01629 12.03559∗
Levene test 0.01171 3.62934 –
Ho:σpre=σpost

Notes:μ 1 (μ 2 )displays the daily mean return of the S&P500 (IBEX35).σ^21 (σ^22 )displays the daily
standard deviation of the S&P500 (IBEX35). Mean test tests the null hypothesis of equality of daily
mean returns. The Levene’s statistic tests the null hypothesis of equality of daily variances.ρ1,2displays
the correlation between both indexes computed from their daily returns in that period. An asterisk
(*) denotes a test statistic that exceeds 5% critical value.

Table 16.3 Johansen (1988) test for cointegration

Lags Null λtrace(r) Critical Value λmax(r) Critical Value

3r= 0 17.97919 19.96 14.76784 15.67

r= 1 3.211352 9.24 3.211352 9.24

Notes: The lag length is determined using the AIC criterion.λtrace(r) tests the null hypothesis

that there are at most r cointegration relationships against the alternative that the number

of cointegration vectors is greater thanr.λmax(r) tests the null hypothesis that there are r

cointegration relationships against the alternative that the number of cointegration vectors

is greater thanr+1. Critical values are from Osterwald–Lenum (1992).

transmission patterns following the terrorist attack and, therefore, motivates
the analysis that will follow. Finally, correlation between both series has
increased over time. Table 16.3 shows that both series are not cointegrated,
being three the optimal lag length following the AIC criterion.