Price Discovery and Volatility Spillovers in Futures and Spot ...

the ‘size effect’ and the ‘sign effect’ of the shocks on volatility. The first is a typicalARCH effect while the second is an asymmetrical effect, for example, the leverage effect.In equation (8), the EGARCH model allows for leverage effects. Ift1the effect of shock on the log of conditional variance is1 1. Ift1effect of shock on the log of conditional variance is 1 1.0.5t10.5t1is positive,is negative, theNow, we can represent the bivariate EGARCH (1, 1) model as follows: 2 ln ln ln ln 9 2 t 1 t2 2 1f , t ff f f 2, t1 f s, t1 t1 t12 t2 2 2 1 tln 1st ,ss sln sln 2, t1 sln st, 1(10) t1 t1The unrelated residuals f ,tand s,tare obtained from the equations (3) and (4). This twostepapproach (the first step for the VECM and the second step for the bivariateEGARCH model is asymptotically equivalent to a joint estimation for the VECM andEGARCH models (Greene, 1997). Estimating these two models simultaneously in onestep is not practical because of the large number of parameters involved. Moreover,although the paper focuses more on volatility spillovers (second moment) thancoinetgration (first moment), the error correction term must be included in the conditionalmean equation. Otherwise, the model will be misspecified and the residuals obtained inthe first step (and, consequently, the volatility spillovers results) will be biased.4. Empirical results and discussionsThe empirical analysis reported here is based on two-stage estimation. In the first stage,cointegration analysis is used to identify the cointegrating relationship among thevariables. If cointegrating relationship is identified, the model should include residualsfrom the vectors (lagged one period) in the dynamic Vector Error Model (VECM)system.14