Friday, May 24, 2013

Regularized Indicators

In the volume 21:7 of the TASC Chris Satchwell presented the concept of regularization in place of the conventional smoothing. The full article is available on the net for those who are interested. In the article Satchwell presents a regularized EMA. In conventional smoothing we have to deal with two things wiggle, which is the high frequency oscillations especially in short term smoothing and then the lag. We can reduce wiggle by increasing the smoothing period but we will much larger lag.  So it would be whipsaws or lag and often it is a compromise between the two.  Regularization has a factor “Lamda” by adjusting which we can control the wiggle. A Regularized EMA would be exactly the same when the lamda is set to zero. The calculation of Regularized EMA is as follows

             Rp + alpha*(close - Rp) + lambda*(Rp + (Rp-Rpp))
     REMA = ---------------------------------------------
                      1             +      lambda
alpha = N-day smoothing per EMA 
Rp = yesterday's REMA
Rpp = day before yesterday's REMA
Lambda is a factor controlling the amount of “regularization”.

However Satchwell makes it very clear that the regularized indicators may not be suitable for trading strategies with crossover. These are more useful for strategies based on gradient or slope.  Satchwell Says “Regularization has an advantage in that it enables the gradients of regularized quantities to form part of the trading logic. However, the position of a regularized indicator is dependent on prior curvature; unlike conventional and exponential moving averages, there is no guarantee it will never trespass beyond the maximum or minimum function values on which it is based. This implies that conventional averages may be better for standard trading logic involving crossovers or threshold penetrations Regularization removes wiggle and associated gradient oscillations, so to exploit it fully, the consequences of having less-oscillatory gradients must be appreciated. This may not be as easy as it sounds, since conventional averaging usually fails to provide sufficiently consistent gradients, leaving a legacy of common trading logic (crossovers, threshold penetrations, and so on) that for the most part ignore gradients. Our expectations on how to use indicators tend to get in the way of appreciating that many trading decisions can be reduced to whether a price gradient is positive or negative. That is what regularization can do quite well.”

The regularization opens vast oppurtunities for fine tuning the conventional indicators. So the first indicator we will look at a Regularized MACD. So we will use two regularized moving averages instead of conventional EMA. The Regularized MACD is quite similar to the KMACD introduced recently. It is less prone to whipsaws and catches the big trends very well. However there is always a lag in catching the turning points. The little delay in entry does ensure more probable profitable trades. Drawdown can be reduced by proper trail stops.

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