TRADING SYSTEMS
Use Past And Present Prices To Determine Tomorrow's Price
Trading IBM Intraday
by Dennis Meyers, PhD
Here's how to develop a trading system that measures the real price dynamics of the market.
The fading memory polynomial was first introduced in one of my previous articles, titled "The Yen Recursed." In that article, I discussed how to use a first-order fading memory polynomial to trade the yen futures on a daily basis. Here, I will use a fourth-order fading polynomial to trade IBM one-minute bars on an intraday basis.
The fading memory polynomial is a mathematical technique that fits an nth-order polynomial to the last T price bars, but calculates the n coefficients of the polynomial such that the error between the polynomial and the current bar is weighted much higher than the error between the price and value of the polynomial n bars ago. As an example, if the latest price is at time t and the price made a turn at time bar t-10, then you do not want prices prior to t-10 affecting the polynomial fit as much. As is shown in the sidebar "Fading memory polynomial mathematics," the most familiar case of the fading memory technique is the zeroth-order fading memory polynomial better known as the exponential moving average. The fading memory technique is in contrast to the least-squares polynomial fit, which equally weights all past errors between the polynomial and the price bar.
FADING MEMORY FOURTH-ORDER POLYNOMIAL
The fading memory fourth-order polynomial best estimate of the next bar's value, pest(t+1), is constructed at each bar by solving equation 3 from the sidebar with n=4. The pest(t+1) value is then plotted on the price chart. When the plotted curve increases by a percentage amount pctup from the previous prior low of the curve, you want to go long. When the curve falls by the percentage amount pctdn from the previous prior high of the curve, you want to go short. For this article, the price series will use one-minute bars of IBM.
...Continued in the June 2002 issue of Technical Analysis of STOCKS & COMMODITIES
Excerpted from an article originally published in the June 2002 issue of Technical Analysis of STOCKS & COMMODITIES magazine. All rights reserved. © Copyright 2002, Technical Analysis, Inc.