Article/Paper - "Filtering in Finance"

[horribilicus]

Electronic filters made of resistors and capacitors have simple mathematical input-output functions that can be programmed in very few lines of software. There's a web page "Resistor Capacitor Circuits for Fun and Profit" which does exactly that. One of the circuits contains two resistors and two capacitors. When used to filter commodity prices, the results are:

results bp trades= 81 net_profit= 43112.50 profit/tr= 532.25
results cd trades= 63 net_profit= 30980.00 profit/tr= 491.75
results cl trades= 54 net_profit= 49300.00 profit/tr= 912.96
results ct trades= 56 net_profit= 79315.00 profit/tr= 1416.34
results cu trades= 75 net_profit= 157925.00 profit/tr= 2105.67
results dx trades= 53 net_profit= 59420.00 profit/tr= 1121.13
results fv trades= 34 net_profit= 41384.38 profit/tr= 1217.19
results hg trades= 68 net_profit= 33262.50 profit/tr= 489.15
results ho trades= 79 net_profit= 27571.20 profit/tr= 349.00
results hu trades= 63 net_profit= 22545.60 profit/tr= 357.87
results jy trades= 61 net_profit= 123575.00 profit/tr= 2025.82
results kc trades= 81 net_profit= 108318.75 profit/tr= 1337.27
results lb trades= 70 net_profit= 93494.00 profit/tr= 1335.63
results mb trades= 47 net_profit= 49168.75 profit/tr= 1046.14
results ng trades= 38 net_profit= 76530.00 profit/tr= 2013.95
results oj trades= 83 net_profit= -5280.00 profit/tr= -63.61
results sf trades= 69 net_profit= 102325.00 profit/tr= 1482.97
results ty trades= 53 net_profit= 68471.88 profit/tr= 1291.92
results tu trades= 21 net_profit= 52115.63 profit/tr= 2481.70
results us trades= 75 net_profit= 72218.75 profit/tr= 962.92
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total 1224 total 1285753.94 avg 1050.45

I downloaded these from mjohnson dot com .

 

[stephencrowley]

Filtering might not be so stupid after all.. this paper describes a method of minimizing the "fat tails" of the error and doesn't rely on gaussian assumptions... hmmm

http://arxiv.org/abs/cond-mat/0004369

The Kalman filter combines forecasts and new observations to obtain an estimation which is optimal in the sense of a minimum average quadratic error. The Kalman filter has two main restrictions: (i) the dynamical system is assumed linear and (ii) forecasting errors and observational noises are taken Gaussian. Here, we offer an important generalization to the case where errors and noises have heavy tail distributions such as power laws and L\'evy laws. The main tool needed to solve this ``Kalman-L\'evy'' filter is the ``tail-covariance'' matrix which generalizes the covariance matrix in the case where it is mathematically ill-defined (i.e. for power law tail exponents $\mu \leq 2$). We present the general solution and discuss its properties on pedagogical examples. The standard Kalman-Gaussian filter is recovered for the case $\mu = 2$. The optimal Kalman-L\'evy filter is found to deviate substantially fro the standard Kalman-Gaussian filter as $\mu$ deviates from 2. As $\mu$ decreases, novel observations are assimilated with less and less weight as a small exponent $\mu$ implies large errors with significant probabilities. In terms of implementation, the price-to-pay associated with the presence of heavy tail noise distributions is that the standard linear formalism valid for the Gaussian case is transformed into a nonlinear matrice equation for the Kalman-L\'evy filter. Direct numerical experiments in the univariate case confirms our theoretical predictions.

 

[kut2k2]

Quote from stephencrowley:

Filtering might not be so stupid after all.. this paper describes a method of minimizing the "fat tails" of the error and doesn't rely on gaussian assumptions... hmmm

Filtering isn't stupid at all. My TA totally depends on it.

The question is, is a given filter based on reasonable or unreasonable assumptions? You corrected me when I said the Kalman filter used in the first article was linear. That's cool (and thanks ), but the ukf still depends on a price model. So the question is, can price reasonably be modelled? How do you model 9-11, or any other unforeseen event that rocks the markets? Best to stick with robust filters that don't depend on guesswork about what the market "should" be doing. They may not be as fancy but they're less likely to lead you astray. My 2 cents ...