Saturday, February 19, 2011

Putting it together

Here I plot four versions of the same trading day.  The Y axis is variance per trade (Noise) , measured in nats.  The plots come from the encoder which recodes trades that already have been partially coded by traders.  The jagged line is the actual trading noise, and the dark dots are the new codings put out by the Huffman encoder.  The smooth line contains two plots, one a scaled F ibonacci series, and the other, the optimum bandwidth noise if trades could be quantized to the nearest penny by infiitely many traders.

Items of interest.  The Fibonacci and the optimum smooth line correlate, as they should, a result of the maximum entropy result from the Huffman encoder.  Traders generate less noise, overall, but do much less quantization and lose much information.  The quants determined by the Huffman encoder are higher noise where quantization takes place, but there are fewer quantization points then either smooth line ot the real trading line.  The perfect Fibonacci trading scheme would scal up trading sizes along the curve because the F series contains only eight trading trading stations.

In short, the dark dots are fewer traders doing more efficient work.
I should add a big warning.  These are events happening on one day, obviously the economy extends trading cycles out to 30 years.  Time scales need reconciliation via serious thought, but the method is still effective over long and short time horizons.

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