### Jason Dobry

Husband. Father. Software Engineer. Open Source hacker. Always learning.

TDF

By Jason Dobry

Need Clean Data

Inconsistent intervals,

crazy numbers in off ours, etc.

Clean it

Gathered data every hour on the hour from operational hours

Predicting Returns

Predict next hourly data point?

Or predict opening value?

Closing value?

Um, how?

L2 Regression

Fail

Heavily affected by outliers,

non-linearity,

too many variables, etc.

Kalman Filter

What's that?

The Kalman filter operates recursively on streams of noisy input data to produce a statistically optimal estimate of the underlying system state.

Autopilot

Tracking and Vertex Fitting of charged particles in Particle Detectors

Tracking of objects in computer vision

Economics, in particular macroeconomics, time series, and econometrics

Inertial guidance system

Orbit Determination

Radar tracker

Dynamic positioning &
Navigation systems

Seismology

Simultaneous localization and mapping

Speech enhancement, Weather forecasting, 3D modeling

xt = A * (xt - 1) + w

xt -
hidden variable we're trying to estimate

A - state transition matrix

(xt - 1) -
current state

w -
noise of model

zt = H * xt + v

zt - noisy measurement

H -
observation model

xt -
xt from above

v -
noise of model

xt = A * (xt - 1) + w

xt -
hidden variable we're trying to estimate

A - state transition matrix

(xt - 1) -
current state

w -
noise of model

zt = H * xt + v

zt - noisy measurement

H -
observation model

xt -
xt from above

v -
noise of model

xk | k-1 = 3 (xk-1 - xk-2) + xk-3

assumes that every four consecutive trend values fit a quadratic curve

xk = xk | k-1 + ( Gk * (yk - xk | k-1) )

final estimate combines observation and state change estimate

Risk

Solution

Force Diversification

Restrict Maximum amount of wealth invested per stock

Restrict investment per stock to:

1% of wealth

5% of wealth

20% of wealth

Solve LP for Optimal Portfolio

Trade = Optimal Portfolio - Current Portfolio

Trade:

Every Hour

At Opening

At Closing

Most successful agents had diverse portfolios and traded once a day

By Jason Dobry

Portfolio Optimization with Kalman Filters

- 3,429

Husband. Father. Software Engineer. Open Source hacker. Always learning.