Forex Trading System- Moving Trend Analysis

OVERVIEW

Trend analysis is a somewhat nebulous term when applied to the science of forecastingprice movements. Some traders will probably think of J. Welles Wilder’s RelativeStrength Index or George Lane’s stochastic oscillators. In this chapter we define a trendin terms of its most basic mathematical properties.

LINEAR REGRESSION

A linear regression is a statistical tool that traders can use to determine how closely adata set (say, a stream of sequential closing prices) fits a straight-line model. From ele-mentary geometry, we recall the diagram and formula shown in Figure 10.1.

The general formula for the straight-line model is:
y = Ax + B
wherex=independent variable (time units)
y=dependent variable (prices)
A=slope
B=intercept
The straight-line model has only two regression coefficients: intercept and slope.
The intercept is the point where the y-axis and the straight line intersect. In this ex-ample, the intercept equals +2.
The slope is the ratio of the y-axis value less the intercept to the x-axis value forevery point along the straight line:
One observed point on the straight line is x = 15 and y = 7. Therefore:
In other words, for every unit of price that the model advances along the y-axis,
three time units are advanced along the x-axis.
An alternate (and more accurate) definition of slope is the quotient of the change inthe y-axis divided by the change in the x-axis for any two points along the straight line:
Note that the slope can be positive, negative, or zero.

ORDINARY LEAST SQUARES METHOD

The slope and intercept for any set of continuous data can be calculated by using the ordi-nary least square (OLS) regression model for a straight line seen in Figures 10.2 and 10.3.

COEFFICENT OF CORRELATION

Calculating the regression coefficients for the estimated slope and intercept for a dataset is only half the battle. We also need to know how well our estimated values matchthe raw data. For this purpose, we use another statistical tool called the coefficient ofcorrelation or simply r. (See Figure 10.4.)

Any introductory text on descriptive statistics will supply traders with additional in-
formation on these and other regression techniques, their purpose and usage.

TREND OSCILLATORS

The whole purpose behind burdening traders with this refresher course in elementarystatistics is to provide a method for scrutinizing trending properties in actual forex data.In Figure 10.5, we present two new oscillators: the moving slope oscillator and the mov-ing correlation oscillator.

MOVING SLOPE OSCILLATOR

In a sufficiently large set of closing prices, the moving slope oscillator will fluctuate arounda mean of zero. Positive values represent uptrends and negative values represent down-trends. The magnitude indicates how sharply the prices are trending. The vertical scale tothe right of the oscillator is expressed in terms of pips in the quote currency per time units.

MOVING CORRELATION OSCILLATOR

The quality or reliability of a trend is represented by the oscillator at the bottom of thechart, the moving correlation oscillator, which has been adjusted to fluctuate between 0and +100 as seen in the vertical scale to the right. When the correlation value drops be-low 85, a change in trend is normally indicated.

MOVING TREND INDEX

The moving trend index is analogous to a moving average index. It defines the numberof elements to include in each sample moving across the x-axis. The same moving trendindex must be used for both oscillators. In Figures 10.6 through 10.8, gradually increas-ing moving trend indexes are employed.

OBSERVATIONS

The obvious effect of increasing the size of the moving trend index is a correspondingdecrease in the number of peaks and valleys in the moving slope oscillator and in themoving correlation oscillator. Another rather logical result is the fact that the values forthe moving slope oscillator tend to decrease as the moving trend index increases. Coin-cidentally, moving trend analysis may also be employed to extract information on thewavelengths of dominant cycles indigenous to the time series.