Interaction between quotations, spread, and volatility in FOREX

In the number of quotations equation (Equation 2.c)
volatility and average spread are highly insigniÞcant. This
implies that there may be some kind of ÔcausationÕ from the
number of quotations to volatility and some kind of feedback
relationship between volatility and average spread.
However, the number of observations is not weakly
exogenous to the system as the variance covariance matrix
of the residuals is not diagonal. In fact, the correlation
matrix of the residuals of the system (Equation 2.a to 2.c) is
presented in Table 4.
Hence, we conclude that, apart from the residual e¤ects,
volatility and average spread are simultaneously determined
and there may be a feedback rule between number of
quotations and volatility. However, the number of quotations
a¤ects the average spread process through volatility
only. This relationship is stronger for the Yen than for the
Deutschemark.
Furthermore, notice that the second lagged volatility in
Equation 2.a is insigniÞcant, and the coe¦cient estimate of
the Þrst lag has a very low value (around 0.2 for both
currencies), which implies a very weak autoregressive conditional
heteroskedasticity e¤ect. However, this is not the case
when average spread and number of observations are excluded
from this equation. In such a case the OLS estimates
of the Þrst and second lag volatility, of the regression of
volatility on Dummies and 2 lagged volatilities, equal 0.322
(6.079), and 0.070 (1.746) for the Mark and 0.319 (7.237), and
0.0717 (2.206) for the Yen (the robust t-statistics are in
parentheses). This implies that these two variables take out
a considerable amount of the conditional heteroskedasticity
e¤ect observed in exchange rate time series. This points out
to the fact that heteroskedasticity type e¤ects, which captured
by ARCH or GARCH type models in a univariate
setups, are mainly due to missing variables in the econometrician
Õs information set.
Moreover, the addition of our dummy variables further
reduces the second order ARCH type e¤ect in the series. If
the SES (Equations 2.a to 2.c) is estimated without the
dummy variables the results exhibited in Table 3 are
obtained.
Now the Þrst lag estimated coe¦cient takes a considerably
higher value than in the case where dummy variables
are included, and the second lag coe¦cient becomes signiÞ-
cant. Notice also that now in the number of quotations
equation volatility has a strong negative e¤ect, something
which is also documented in Bollerslev and Domowitz
(1991), where the dummy variables are excluded from their
model.
To conclude this section we can say that the simultaneity
and the inclusion of dummy variables capture a considerable
part of heteroskedasticity type e¤ect, observed exchange
rate markets. This in e¤ect is due to unobservable
news reßected either in the bid-ask spread or in the dummy
variables which are responsible for changes in tradersÕ desired
inventory positions with the result of changing
spreads, according with the theories of OÕHara and OldÞeld
(1986) and Amihud and Mendelson (1980). These changes in
spread can explain a considerable part of volatility movements,
and consequently decreasing the heteroskedasticity
type e¤ects.