*3.2. Contagion Tests*

Contagion occurs when there is a significant increase in correlations during the turmoil period compared with those during the tranquil period. However, the estimates of correlation coefficient can be biased by market volatility heteroscedasticity, as pointed out by Forbes and Rigobon (2002). In fact, market volatility tends to increase after a shock or a crisis, which makes the correlation coefficients increase even though the underlying cross-market relationship is the same as during more stable periods. In this paper, the correlation coefficients of stock returns are estimated by the DCC GARCH models, and hence vary with market variances through time. Thus, the conventional contagion effect test that ignores the adjustment for heteroscedasticity can be improved.

To test for the existence of contagion, we use a one-sided *t*-test for the difference between average conditional correlation coefficients of stable and turmoil periods. The test is as follows:

$$\bullet \qquad H\bullet \colon \rho \mathbf{z} = \rho\_{\Pi}$$

• *H*1: *ρ*2 > *ρ*1

where *ρ*1 and *ρ*2 are respectively average conditional correlation coefficients of stable and turmoil periods. Rejecting the null hypothesis supports for the contagion.

This *t*-test of the equality of means is preceded by the preliminary test of the equality of variances.
