oscillator moving average of 40). The calculations for this are:

{Close, - Low,)/{High, - Low,}

n-day oscillator = =-----

N-day moving average ofosdlUuor - MAi, =" - Trendjusted osciliator=Midpoint - {MAo - O)

* Frank Key, Siructured Sottware Systems, Mi Holly. NJ Copynghi 1996 E. MarshaU 1» 1, "RoUing with ihe punches," Futures 1996)

Dynamic Momentum Index

This approach to creating a djuamic, variable-length RSI, which changes the number of dajs based on maitel volatility, can be used to change the calculation period of any technique. In the Dynamic Momentum Index (DMI), the length of the calculation period increases as the volatility declines. You may also select a pivotal period, one around which the calculation period will var for the RSI this will be 14 days. When the volatility increases, the periods will be less than 14 days and when volatility declines it will be greater. Based on this.

DMI = @Int( --1

\ volatility,/

@stdev(close,5)

volatility, = -

@avg(@stdev(close,5),10)

The DMI is 14, the pivotal value, when the volatility is normal; that is, when the current 5-day standard deviation is the same as the lO-day average of the 5-day standard deviation. When the current volatility increases, the ratio is greater than I and the value of the DMI becomes larger than 14. The function fflInt tates the integer value of the calculation to be used as the number of days in the RSI calculation.

h. few changes in the DMI approach may improve results and should be considered when generalizing this technique. First the standard deviation should ahvajs be applied to the changes in price, rather than the prices themselves. This removes the trend component. Alternately, the volatility ratio may be more robust if the sum of the absolute value of the price changes is simply compared against the average of that sum,

volatili - @sum(@absvaluc(closcf - close, i),5)

@avg(@sum(@absvalue(dose, - close, 0,5),10)

AN ADAPTI\E PROCESS

An adaptive method can be a process as well as a formula. Rather than using an index or ratio to change the

smoothing constant, which in turn alters the trend speed to be in tune with the current maitet, you can retest your sjstem regularly using more recent data. The period being retested can alwajs be a fixed number of dajs, or it can be selected visually, beginning when the maitet changed its pattem, became more volatile, underwent a price shock, or moved to new highs or lows. The problem is having enough data to be satisfied that the results are dependable; the fester you react, the less data there is to make a decision. This approach, along with other testing methods, are covered in detail in Chapter 21 ("Testing").

A Development Example

The size of price changes can also be used to varj the period of a moving average. When prices become more volatile, as measured by the standard deviation of the price changes, a shorter period can be used to follow the maitel more closely. When there are smaller price changes, or stable volatility, the preference is to slow the trend by increasing the calculation period. The following steps can be used to build and personalize a variablespeed moving average:

Tu.-Uar . 1 "1. The NewlA*ketTecliiiicianiI"UiiW,ey& Sons, New Y.jk. Amneti, "Bmldine aVariable-Leii; - M.vme Avar" Tecimical Analysis • . ? & CiiinioditieE (June 1991)

1. Select the range over which the period of the moving average may fluctuate For example, a medium to fesi program might range from 5 to 30 dajs.

2. Calculate the mean and standard deviation of price changes over a separate, fixed time period, recommended as the length of the longest trend period (in this case, 30 days), but enough dajs to have a reasonable sample (no less than 10 dajs). Using a smaller period reduces the response time needed to switch from one moving average speed to another, but causes the results to be more erratic.

3- Selea zones, or thredihold levels, at which the maitet is seen to be relatively more aaive or less active. For exanple, within the boundarj of the mean -+- .25 standard deviations, we will define a low-volatility, less active area where the longest period would be used. Outside the boundarj of the mean ± 1.75 standard deviations would be an unusual, highly active maitet requiring a fest frend.

4. Establish the rate at which the moving average period would change as volatility (price change) increases from the inside to outside boundarj This could be the linear relationship

n, = (30 - 5) * ,- ,- iVstdev - .25)/(1.75 - -25) + 5, for 1.75 > {P. - P, - i)/Stdev > .25

when {Pt-P,-i)/stiiev is between 1.75 and .25-Otherwise, it is the max and min values, 30 and 5, respectively. The general form is

todays moWng average period = (max ma period - min ma penod) *

(today s change/stdev of changes - min stdev boundary) / (max stdev boundaiy - min stdev boundaiy) + min moWng average period

CONSIDERING ADAPTIVE METHODS

At first glance, there appears to be a conflict between the sound statistical approach that encourages the choice of a simple set of rules applied to a long period of test data and adtive methods. The classic result is a statistically robust model, but one that might show considerable variation in performance over the test period. To stabilize retums we move away from fixed values in trading sjstems, such as a $500 stop-loss, or a 50oint breakout, and substitute risk and entry criteria that are based on volatility. The simplest of these methods uses a percentage of price; the mosl complex can be very intricate functions of volatility and cycles.

When a variable feature is incorporated into the strategj, the values should smoothly adjust to the maitel pattems, but each case, such as exfreme high or low volatility, has fewer occurrences: therefore, we are not as certain that the sliding scale works at all levels. The best we can expect is that the technique has a sound premise, is well defined, and the profile of performance is improved.

If we follow that logic further, we eventually come to the adaptive, or self-adjusting method, in which the mosl fundamental elements of a calculation can varj based on price level, volatility, or a broad choice of patterns. The methods in this chapter focused on two areas that have not been presented elsewhere in a collected manner. The first is the variation of the trend period itself. The choice of a single trend does not serve us best for prolonged periods in the maitet. Slower trends are reliable, but give bact much of their profits before ending; faster trends wort only during periods when prices move quickly and uniformly. The obvious solution is that the calculation period should change, speeding up when there is a short4ena fastmoving price pattem. At other times, it should focus on the long4erm direction. This concept is perfectly reasonable, although formulating the rules to var the period has not been perfected. The methods shown here may

work better than a static period, but should only be the beginning of a road on which to move forward.

The other adaptive method is the centering of an oscillator to avoid prolonged periods in which the value of the indicator loses significance by pushing against the upper or lower limits. By recording the high and low values of a past time interval, the oscillator values can be continually readjusted to provide a more useful tool. Analysts are encouraged to look fiirther into these methods as an excellent way to improve sjstem robustness.