A Generic Tool For Technical Analysis

Regularization

by Chris Satchwell, Ph.D.

In the lexicon of technical analysis, terms such as moving averages and least-squares regressions are commonly understood. But what about regularization? Despite their potential, regularization techniques are poorly understood and little used.

Ultimately, indicators exist to aid trading decisions. Most indicators are used in relation to price-related tasks, and there is a crucial and (usually) underresearched step involved in interpreting their values to obtain trading decisions. Such a step might be the crossover of two moving averages, or an indicator penetrating a threshold value.

Often, the smoother the indicator, the easier it is to make good decisions, and regularization helps to smooth indicators. Specifically, regularization aids decision-making logic based on the gradient (that is, the rate of change of a quantity over time) of indicators. It is a generic tool, in that it can be applied whenever an average or regression is needed to find an indicator. Most trading indicators can be reformulated with regularization to help smooth them.

For this article, I have focused on exponential moving averages (EMAS) with regularization, but the principles can be extended to introduce regularization into conventional moving averages and regressions. I will introduce an indicator known as regularized momentum and compare it with moving average convergence/divergence (MACD).

WIGGLE AND LAG

Wiggle describes high-frequency oscillations, typified by those found on short-term moving averages of security prices. Lag describes a tendency of one series to trail another; an example would be a price moving average lagging actual prices.

Often, indicators and similar tools of technical analysis face the dilemma of being either too slow to react to price changes or wiggling too much to make useful conclusions. Where those conclusions depend on the gradient of an indicator, wiggle is a particular problem. Adjusting an indicator to combat wiggle causes other problems. Increasing the length of, say, a moving average results in lag. The answer to lag is to reduce the length of the moving average, but that in turn produces wiggle!

Frequently, developers of technical analysis tools find themselves caught in the position of wanting to see a more rapid response to price changes, but without the associated wiggle or lag. While regularization is not a total solution to the problem, it can help resolve this dilemma.

...Continued in the July 2003 issue of Technical Analysis of STOCKS & COMMODITIES

Excerpted from an article originally published in the July 2003 issue of Technical Analysis of STOCKS & COMMODITIES magazine. All rights reserved. © Copyright 2003, Technical Analysis, Inc.