The Adjustable-Bands Z-Test

by Jacinta Chan, PhD

Markets generally trend or move in a range. If you apply a trending algorithm to a ranging market, you will end up with whipsaws that yield losses. This indicator can help you avoid some of those false entry whipsaws and capture a new trend early.

Some traders depend entirely on technical analysis and mechanical technical trading systems, mainly because algorithmic technical trading systems can be backtested and examined to see if they have a statistical edge. Here’s a look at quantitative technical analysis on the historical prices of Malaysian futures markets, namely the Kuala Lumpur Composite Index Futures (Fkli) and crude palm oil futures (Fcpo), using popular technical indicators like moving averages, adaptive moving averages, and z-test statistics.

This article follows my March 2006 Stocks & Commodities article titled “Trading Trends With The Bollinger Bands Z-Test.” The idea of the z-test is derived, in turn, from a 2002 Working-Money.com article by Veronique Valcu. The Bollinger Bands z-test (Bbz) uses the concept of z-test statistics to determine where the current price is in relation to the moving average and standard deviation. The formula is:

Z-test statistic =


Current price - Moving average
     Standard deviation

If the z-test statistic is above 1, the current price is above the upper one standard deviation band. Bbz issues a buy long signal. If the z-test is below -1, then the current price is below the lower standard deviation band, at which point Bbz issues a sell short signal. The area enclosed by the bands is deemed to be range trading, which is a no-trade zone for Bbz. This is to avoid some of the range-trading whipsaws. Bbz uses the conventional 21-day moving average and standard deviation.

Adjustable bands
Now let us look at how you can automatically adjust the moving average and standard deviation bands according to the prevailing market condition, either a ranging market or a trending market. Algorithms that function well in either market but not both is a classical limitation in technical analysis.

Contract	Mean	Standard Deviation	Skewness	Kurtosis
FKLI	-0.03	13.97	-0.0024	14.97

Figure 1: DAILY kULALA LUMPUR COMPOSITE INDEX FUTURES (FKLI) RETURNS DISTRIBUTION (DECEMBER 15, 1995 TO DECEMBER 31, 2008)

…Continued in the December issue of Technical Analysis of Stocks & Commodities

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