Forex Trading System - Swing properties

OVERVIEW

We mentioned earlier that swing data is bivariate data; that is, it is represented in pairs: a price member and a time member. It is true that univariate data like daily closing prices also has a time element, but since the time elements are all equally spaced, the data is normally presented as an ordered set of prices only.

WAVE ANATOMY

The height of a wave is the number of pips it spans along the y-axis (the current price minus the previous price). The width of a wave is the number of time units along the x- axis that it spans. (See Figure 30.1.) The distance of each wave is calculated using the Pythagorean theorem:

SWING AVERAGES

Table 30.1 displays averages for heights, widths, and distances for both bull waves and bear waves using EURUSD tick data (7,000,000+ closing quotes). A box size of one pip is used, while reversal amounts range from 3 to 25 boxes.

The column definitions for the table are:

Rev Amt is the reversal amount of the swing algorithm using a box size of one pip.
Swings is the number of peaks and valleys in the swing data. The number of waves
equals swings minus 1.

+X is the average number of time units (ticks) in each bull wave.
–X is the average number of time units (ticks) in each bear wave.
+Yis the average number of pips in each bull wave.
–Yis the average number of pips in each bear wave.
+Z is the average diagonal distance in each bull wave.
– Zis the average diagonal distance in each bear wave.

One obvious feature about the table is that the averages for the bull values are
slightly higher than the averages for the bear values. This implies some sort of statistical bias. However, this is not the case. The opening price of the EURUSD currency pair on 1/1/2002 was 0.8896 while the closing price on 12/31/2002 was 1.0489. This discrepancy of 1,593 pips accounts for the slight (and negligible) skew in the averages. (Coincidently, January 1, 2002, was the day that the euro currency became the legal tender of the member countries in the European Monetary Union.)

It is, however, a good guideline to estimate the average price movement (Y) and its
corresponding averagetime duration (X). For example, assume for some external rea-
son that a reversal amount of 12 boxes was selected where each box equals one pip.
Also assume that we know that we have just hit a vertex (either a peak or a valley) and price direction will reverse. On average the following wave will reach 18 pips.

SWING DATA PRELIMINARIES

Prior to delving deeper, we must explain some of the tools we use when analyzing swing data. In Figure 30.2 , we use the following data to illustrate swing concepts using a simple three-wave cycle. The letters A–D define discrete prices:
A
1.0000
B
1.0020
C
1.0010
D
1.0030


BIVARIATE DATA

We now need to devise some new statistical tools that pertain specifically to swing data. The first characteristic of swing data that we must emphasize is that it is bivariate in nature. That is, for each peak or valley price there is a corresponding time value. This is the sequence number of that price in the raw data time series.
Thus, the peaks and valley in Figure 30.2 are more accurately displayed as shown in
Table 30.3. To capitalize on the bivariate nature of swing data, we must infuse a little more complexity into the diagram in Figure 30.2, although it consists entirely of simple algebraic operations. (See Figure 30.3.)

SWING VOLATILITY

It is common practice for traders to use the standard deviation of a data set to describe the volatility of an underlying security. However, the conventional standard deviation from descriptive statistics normally applies to a univriate set of data, in which the closing price is almost always chosen as the dependent variable. We have devised an alternative method to describe deviations when bivariate swing data is involved.

First, we must sum the total diagonal distance traveled using only the absolute val-
ues (waves with downward slopes are treated as positive):

Sum = Abs(z1) + Abs(z2) + Abs(z3)

Thus, by using the diagram in Figure 30.3, we can calculate just how much the three
waves z1, z2, and z3 deviate from the single wave Z. First, we note that the mathematical lower limit of swing volatility approaches zero. The upper limit approaches +100, which can be attained only if both cycles have only one identical wave.

One interesting feature of swing volatility is its ability to confirm how closely a
given data set follows a linear trend. In this respect, swing volatility is similar to the coefficient of correlation from an ordinary least squares (OLS) linear regression.

More importantly, swing volatility provides us with a tool by which we can compare
a single set of raw data that has been converted to multiple sets of swing data using different reversal amounts.

SWING VELOCITY

Swing velocity is another tool we developed in order to measure the magnitude or cer-
tainty of a trend. For this purpose, it was necessary to borrow an inverse function from trigonometry, the arc sine.

Most computer languages express the values returned from trigonometric functions
in terms of radians, a convention to which we have also adhered. The return value
above, however, has been rescaled to range from +100 to –100, where +100 represents
abnormally high upward trending, –100 represents violent downward trending, and a
value of 0 indicates that prices are moving horizontally. Essentially, it is the magnitude of the angle q that determines how quickly a single wave or a composite wave approaches its destination in relation to the distance traveled diagonally.