Analysis of Non-Displayed Liquidity transactions based on one-day time series data set (Nasdaq ITCH feed)

The aim of this project is to find and test potential variables that explain the hidden order flows, i.e. order flows executed against non-displayed liquidity, that happen in a one-day time series through different variables. The data set includes Cisco ITCH trades occurring throughout one day, from 9:30am to 4:00pm.

The GAUSS code which determines the discussed results is provided below:

• code
• data

Hidden order flows (h) are computed as the proportion of order flows of non-displayed liquidity to the total volume of transactions. Transactions can be of four different kinds:

1.     executed order flows (E);

2.     order flows executed at a price different than the one originally present in the order book (C);

3.     cross trades, coming from Nasdaq matching sessions, generally at the beginning and end of the day (Q);

4.     trades against non-displayed liquidity (P).

The proportional hidden volume of transactions is given by

h =         P        

        E + C + P

Hence, cross trades are disregarded in order to find covariants of hidden liquidity order flows.

After selecting the relevant data divided in 5-minute intervals, and computing the proportional hidden volume, it is possible to notice how h varies across time. In particular, two peaks can be observed at the beginning at and at the end of the end, signaling relevant order flows of hidden liquidity occurring when trades open and close. Yet, a high volatility of h is present throughout the day, as the following figure displays.

Then, in order to explain and predict the value of h, it is possible to regress the proportional hidden order flows on some relevant variables, such as one-period lagged hidden order flows, signed order flow, total volume and squared realized volatility of trade price, i.e.

h_t = β₀ + β₁ h_t-1 + β₂ sof_t + β₃ tv_t + β₄ r_t² + ε_t

The following table reports the ols estimates for the coefficients (confidence intervals in brackets), and the t-Student test statistics.

	β (95% CI)	t
constant	1.4919E-01 (1.2190E-03)	2.0195E+00
ht-1	1.4394E-01 (2.2210E-02)	4.5647E-01
soft	-1.8165E-05 (2.9011E-09)	-1.5939E-01
tvt	-9.1790E-08 (9.3422E-15)	-4.4883E-01
rt2	-4.2962E-06 (7.1418E-12)	-7.5977E-01

 All coefficients are hence not significantly different from zero at a 5% significance level, except for the constant term, which is significant at a 5% significance level but not at a 1% significance level. In order to assess the degree of explanatory power of the considered variables as determinants of the proportional hidden volume, it is possible to observe the value of the coefficient of determination:

R₁² = 1.4191E-01

This result implies that a very low fraction of the variability observed in the dependent variable (proportional hidden order flows) is explained by the estimated variability in the right hand side variables.

Now, let us introduce an additional variable among the regressors. In particular, the mean price (mp) in each 5-minute interval is considered as a potentially good indicator of order flows with non-displayed liquidity. The ols estimates of the new model, given by

h_t = β₀ + β₁ h_t-1 + β₂ sof_t + β₃ tv_t + β₄ r_t² + β₅ mp_t  + ε_t

are reported in the following table.

	β (95% CI)	t
constant	3.1046E-02 (1.9108E+01)	3.3567E-03
ht-1	1.4399E-01 (2.2214E-02)	4.5660E-01
soft	-1.7875E-05 (3.0159E-09)	-1.5383E-01
tvt	-9.1295E-08 (9.6787E-15)	-4.3857E-01
rt2	-4.3317E-06 (8.8718E-12)	-6.8732E-01
mpt	6.9148E-07 (6.5454E-10)	1.2774E-02

Unfortunately, all coefficients, including the constant and the newly added regressor, are now not significantly different from zero. This decrease in the explanatory power is not reflected by the coefficient of determination for the second model which is slightly higher than R₁²:

R₂² = 1.4192E-01

Yet, correcting for the difference in the number of regressors in the two models, obtaining and comparing the two adjusted coefficients of determination,

adjR₁² = 9.4237E-02

adjR₂² = 8.1496E-02

it is apparent how such a loss in the significance of the estimated coefficients occurred in the second model is reflected in the loss of explanatory power if we include the mean price as a covariant of the proportional hidden order flows.