3.2.4 Deep search allowing higher bounds for θVPIN

In the following we have looked to higher bounds for θVPIN from 0.99 to 0.99999. All other parameters of the deep search are the same. Below, one can see the results in Tables 7–10. The results for the naive algorithm are indeed the same.

We remark the following:



Table 7.

bucket of the data set. In Table 6 one can see the results of the naive classifier for the first deep search set of parameters.<sup>6</sup> As it is a naive classifier, results do not depend on direction of prices (bar price classifier) and bar price structure.

Best parameters maximizing precision+recall rate for different futures for the naive classifier.

Advanced Analytics and Artificial Intelligence Applications

Futures Recall Precision Precision+recall θMIR n ω (buckets) ES 1 0.0355 1.0355 0.052 50 2500 EC 1 0.9948 1.9948 0.004 50 2500 CL 1 0.3413 1.3413 0.022 50 2500 NQ 1 0.0076 1.0076 0.084 60 2500 YM 1 0.0174 1.0174 0.055 50 2500

• "Naive classifier" has poor results comparable to those of VPIN for ES, NQ, and YM instruments; although poor, VPIN predictions are better than "naive

• "Naive classifier" has better results than VPIN on EC instrument.

• "Naive classifier" has worse results than VPIN on CL instrument.

is very small to detect a "flash crash" of such a magnitude.

• EC flash crash definition is barely inconsistent, with a MIR threshold of

0.006%; it is obvious that a naive algorithm does better results as the constraint

• On CL and ES cases though, VPIN predictions are better, and these results are obtained when θMIR threshold was on the lower bound of the deep search. It might indicate that VPIN software has a better predictive power than a "naive algorithm" not on a "flash crash" amplitude basis but on a lower amplitude level. Nevertheless, one may wonder whether or not this level of amplitude is

Anyway, previous results may conclude that for "flash crash" prediction, VPIN

That's why in the next paragraph, we benchmark predictive power of "naive"

• Third on higher θVPIN constraints and at the same time lower bounds on θMIR

has overall equivalent poor power prediction with the traditional threshold

• Second on lower bounds of crash amplitude θMIR while θVPIN = 0.99

<sup>6</sup> First tests conducted with EC instrument have been realized with an average to get more robust results. They are really close to the one obtained here with a single realization of randomness.

We remark the following:

Table 6.

algorithm" on ES cases.

We can interpret it as follows:

useful for practitioners.

θVPIN = 0.99, as a "naive" algorithm.

• First on higher θVPIN constraints

and VPIN algorithms:

64

Best parameters maximizing precision+recall rate for different futures and last bar price structure allowing higher bounds for θVPIN.


Table 8.

Best parameters maximizing precision+recall rate for different futures and first bar price structure allowing higher bounds for θVPIN.


#### Table 9.

Best parameters maximizing precision+recall rate for different futures and median bar price structure allowing higher bounds for θVPIN.


To verify whether or not we can get at least better results than a naive algorithm in data sets with a real flash crash, we study in the following first the results allowing lower bounds on θMIR while θVPIN = 0.99 and second the results allowing lower bounds on θMIR and higher constraints on θVPIN. Indeed, the intuition is that on NQ case, the "flash crash" amplitude constraints are far too high to have a good precision rate, because in this case there are too few events detected with MIR algorithm.
