recent developments in high frequency financial ... - Index of

Asymmetries in bid and ask responses to innovations in the trading process 61
data. Quote changes and trade indicators are computed analogously to the NYSE
case. Since price improvements are impossible in the SSE, there are no transaction
prices inside the bid–ask spread. Therefore, we do not require trade-direction
algorithms to classify the trades as either buys or sells.
We rely on the theoretical and empirical research in market microstructure to
determine the exogenous variables to be included in the vector MCt. Easley and
O’Hara (1987) formally show that large-sized trades are more informative.
Empirically, Hasbrouck (1991) and Barclay and Warner (1993), among others,
show that this relationship is increasing but concave. In Easley and O’Hara’s
(1992) model, higher trading intensity signals new information. Consistently,
Easley et al. (1997) and Dufour and Engle (2000) find that shorter trade durations
are associated with larger price impacts. Subrahmanyam (1997) finds that trades in
the regional markets are less informative than NYSE trades, arguably because they
attract liquidity-motivated traders (see Bessembinder and Kaufman 1997). Price
instability means uncertainty about the true value of the stock (e.g., Bollerslev and
Melvin 1994). Finally, a positive (negative) order imbalance between limit orders
to sell and limit orders to buy may signal an overvalued (undervalued) stock (e.g.,
Huang and Stoll 1994).
The following variables are defined so as to capture the relationships detailed
above. The trade size (Vt) is measured in shares. Trade durations (Tt) are computed
as the time in seconds between two consecutive trades. A dummy variable (Mt) identifies regional trades. Order imbalance (OIt) is computed as the difference
between ask depth and bid depth. Finally, short-term volatility (Rt) is computed as
the sum of the square changes of the quote midpoint Pz k¼1 ð qkÞ
2 in a 5-min
interval before each trade. 13
Finally, we construct eight trading-time dummies for the NYSE session: one for
trades during the first half-hour of trading, five for each trading hour between 10:00
A.M. and 3:00 P.M. and, finally, two for the last trading hour, divided in two halfhour
intervals. Similarly, for the SSE session (9:00 A.M. to 5:30 P.M.), we construct
nine dummy variables: one for the first half-hour of trading, another one for the
second half-hour, six for each trading hour between 10:00 and 5:00 P.M. and, finally,
one for the last half-hour.
5 Estimation of the baseline model for IBM in 1996
In this section, we present the details of estimating a restricted version of model Eq.
j
(3.7) described in Section 3 where fi (MCt,Dt)=1 for all i and j. We use data on a
representative NYSE stock, IBM, in 1996. In the next section, we check whether
the dynamic patterns about to be reported for IBM can be generalized to other
stocks, other markets, other time periods, and other model specifications, including
the unrestricted model Eq. (3.7).
We consider two alternative specifications of the model. The first one uses
the trade-sign indicators xt B S
and xt to represent the trading process. The second
one uses the trade-size indicators ex B t ¼ xBt log ðVtÞ and ex S t ¼ xSt log ðVtÞ. The
polynomials in the autoregressive matrix A(L) are all truncated at lag five, as in
13 This variable is not defined for trades performed during the first 5 min of trading. In these cases,
we treat volatility as missing.