General Modeling

The results from the R fitting procedure are summarized in table format below. Note all datasets were not able to be run, and only select few were able to be modeled for parameter values because an unforeseen constraint was the time required for modeling. The Hawkes Parameterization we used has an algorithmic complexity of O(n^2) and thus requires a lot of time (for a dataset of 30k points it would take about 2 hours).

Hawkes Fit Parameters Large, Day Trades (Week of 1/15/18)

Date Mu
Alpha Beta Branching Ratio E[Arrival Intensity] Futures % Move
1/15/18 0.0687 1.3683 3.1048 0.4407 0.1229 +.0448
1/16/18 0.3366 2.3447 3.1704 0.7396 1.2924 -0.6071
1/17/18 0.2754 2.5020 3.3820 0.7398 1.0584 +0.4419
1/18/18 0.3207 2.3911 3.2248 0.7415 1.2405 -0.2497
1/19/18 0.2274 2.4708 3.3348 0.7409 0.8777 +0.2586

Hawkes Fit Parameters Large, Day Trades (Week of 1/22/18)

Date Mu
Alpha Beta Branching Ratio E[Arrival Intensity] Futures % Move
1/22/18 0.2100 2.6330 3.5820 0.7351 0.7926 +0.8896
1/23/18 0.2264 2.3973 3.3010 0.7262 0.8270 +0.2029
1/24/18 0.3624 2.4414 3.2802 0.7443 1.4172 -0.1230
1/25/18 0.3627 2.3263 3.2087 0.7250 1.3189 -0.2458
1/26/18 0.2655 2.4696 3.3140 0.7452 1.0420 +0.8333

Hawkes Fit Parameters Small, Day Trades (Day of 1/22/18)

Date Mu
Alpha Beta Branching Ratio E[Arrival Intensity] Futures % Move
1/22/18 0.5753 2.9869 3.9238 0.7612 2.4094 -0.2522

Hawkes Fit Parameters Small, Night Trades (Week of 1/29/18)

Date Mu
Alpha Beta Branching Ratio E[Arrival Intensity] Futures % Move
1/29/18 0.1755 2.3182 3.6454 0.6369 0.4820 -0.2522
1/30/18 0.2374 2.4521 3.4908 0.7024 0.7978 -0.4819
1/31/18 0.2179 1.8832 3.2801 0.5870 0.6961 +0.5490
2/1/18 0.1764 2.2264 3.4912 0.6377 0.4869 0.000
2/2/18 0.2557 2.4761 3.6126 0.6854 0.8128 -0.7253

Visually, when compared they look like the following:

 

 

Parameter Prediction

Because the fitting process took so long, an approach used was trying to see if we could predict parameter values for a day based on historical values. In this study, we tried to see if we could predict parameter values for a given Friday for small/large and day/night, by using the parameter values from Monday – Thursday. We used two methods: a simple average of the parameters for Mon-Thurs parameters as Fridays, and a weighted average method which is summarized below.

Simple Average Parameter Prediction

 

Date

Average Predicted

(Actual)

Average Predicted

(Actual)

Average Predicted

(Actual)

1/19/18 (Day, Large)

0.2504
(0.2774)

2.1515

(2.4708)

3.2205

(3.3348)

1/26/18 (Day, Large)

0.2904

(0.2655)

2.4496

(2.4495)

3.3430

(3.3140)

2/2/18 (Night, Small)

0.2018

(0.2557)

2.2200

(2.4761)

3.4589

(3.6126)

 

Weighted Average Parameter Prediction

Friday Param = (1/2)*Thurs + (1/4)*Wed + (1/8)*Tues + (1/8)*Mon

 

Date

Weighted Predicted

(Actual)

Weighted Predicted

(Actual)

Weighted Predicted

(Actual)

1/19/18 (Day, Large)

0.2799

(0.2774)

2.2852

(2.4708)

3.2423

(3.3348)

1/26/18 (Day, Large)

0.3265

(0.2655)

2.4023

(2.4495)

3.2848

(3.3140)

2/2/18 (Night, Small)

0.1943

(0.2557)

2.1803

(2.4761)

3.4397

(3.6126)

When compared visually to the actual fitted intensities, the two methods yielded the following results: