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3) The conditional mean equation is concerned.

One arises from the fact that the mean equation is in 'Amari form' (with the weight matrix outside the nonlinearity).

It is well established that when modeling volatility using GARCH family models, the appropriate specification of the mean equation is vitally important.

Combining this equation with Young's equation, the following geometric mean equation is obtained [18] gamma_{L} (1 + cos theta ) = 2left( {sqrt {gamma_{s}^{d} gamma_{L}^{d} } + sqrt {gamma_{s}^{p} gamma_{L}^{p} } } right) (17).

Similar to the VAR model, spillover effects of volatility from one market to another market are measured in the BEKK model over the off-diagonal elements of A and G. Transmission in the conditional mean equation is tested via the off-diagonal elements ϕ ij,l of the parameter matrices Φ l, l = 1 … p.

For an ARCH model, the mean equation is y t  =  x t β +  ϵ t and the variance equation σ t 2 = γ 0 + γ 1 ϵ t − 1 2 + γ 2 ϵ t − 2 2 + …, where ϵ t ~ N 0, σ t 2, ϵ t 2 are the squared residuals (innovations) and γ i are the ARCH parameters; the conditional variance is thus modelled as an AR process.

Further, the lag specification of the mean equation was not properly addressed.

Recently, some results on the existence of solutions for prescribed mean equations were obtained (see [9 12] and references cited therein).

In particular, three different conditional mean equations were estimated: one with the constant only, one with the AR(1) term, and one with AR(2) terms.

The reasons for negative returns and low estimated coefficients in first-stage mean equations were explained in second stage V-IGARCH (1, 1) models.

(3), (4), and (5), estimators in mean equations are used as follows: Estimators ( {widehat{gamma}}_{01} ), ( {widehat{gamma}}_{02} ), and ( {widehat{gamma}}_{03} ) measure the percentage change in total money supply, number of market lots, and impact costs for a given percentage change in other exogenous factors such as non-trading hours.