where r, and A, are vectors of returns and trades, respectively; and txf are vectors of residuals; and oL. bo. bk. ck. and dfc are matrices of contemporaneous and lagged coefficients to be estimated for k = 1-20. The trading process is assumed to restart at the beginning of each day. That is, return and trade variables are not lagged across days. Instead, all lagged values are set equal to zero at the start of each day. The coefficients in Eq reflect contemporaneous and serial relationships between returns and trades. Estimates of these coefficients are used to compute the impulse response function of the VAR that ultimate provide the forecast of the permanent price from trade innovations.
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