Forex Trading System- Two Dimensional Momentum

OVERVIEW

The study of momentum is a valuable tool when scrutinizing serial price fluctuations.Historically, standard momentum charts displayed a running series of the differencesbetween one closing price and another closing price that occurred x time units ear-lier, where x is referred to as the momentum or lag index. Selecting the optimumvalue for the number of time units in the momentum index is frequently a difficultand haphazard decision, particularly when visible cycles are present in the time series.

In Figure 9.1, a momentum index of 15 days was arbitrarily selected. The verticalscale in the lower right section of the chart is expressed in terms of quote currency pips(USD). To view the output of a 30-day momentum index, it would be necessary to printan additional momentum chart.

TWO-DIMENSIONAL MOMENTUM \CHART

As a plausible solution in the search for determining the optimum momentum indexvalue, we have created an innovative variation to the classical momentum chartingmethod, which we have named the two-dimensional momentum chart (Figure 9.2).

The most distinctive feature of the two-dimensional momentum chart is the trape-zoidal shape at the bottom of the chart. Each cell in the quadrangle is shaded accordingto one of five unique gradations representing the magnitude of momentum. These grada-tions are described in the legend area directly beneath the chart header. A white cellmeans that the current close is significantly higher than a specific previous close while a black cell means that the current close is significantly lower than a specific previousclose. A medium gray cell indicates that the difference between the two closes, whichare separated by a known lag index, is relatively near the zero mean. The light and darkgray shades are interpolated values explained in the legend.
The bottom row of the trapezoid is equivalent to a one-dimensional one-day mo-mentum chart but the magnitude of momentum is expressed in terms of intensity of thecell shading rather than deviations from the x-axis. The row immediately above the bot-tom row represents a two-day running momentum of closes, and so on. The verticalscale to the right identifies the momentum index (the lag between the current closesand a previous close). The top row of the matrix represents a 15-day momentum chart.Thus, all momentum indexes between one and the maximum number of time units (15days in this example) can be visualized in a single chart.
Additionally, the quadrangular nature of the two-dimensional momentum chart hasanother advantage beyond the horizontal display of multiple momentum indexes in asingle chart. Specifically, this is the vertical interpretation of the matrix. Each columndisplays the differentiating relationship of a single close with all its predecessors in as-cending magnitude of momentum indexes.

ISLANDS

In the two-dimensional momentum charts shown in Figures 9.3, 9.4, and 9.5, the maxi-mum momentum index has been increased gradually to illustrate an interesting chartingphenomenon.
Note that as we increase the size of the momentum index, the top left cell of the mo-mentum matrix scoots to the right. As the momentum index approaches the number ofintervals along the x-axis, the matrix becomes a right triangle.

We have, for want of a better term, called this phenomenon streaking, which de-notes the presence of diagonal island patterns, which are prevalent in all momentummatrices. The length and width of each island can be directly correlated to a trendingpattern in the underlying data, where black patterns indicate a downward trend andwhite patterns indicate upward trending. The number of vertical cells that separatetwo distinct like-colored islands (white versus white and black versus black) indi-cates the size of a wavelength prevalent in an underling cycle in the raw data. The vec-tor direction of each island pattern is always a 45-degree angle (northeast) from thepoint of origin.

SMOOTHING

In an effort to enhance the clarity of the islands in the momentum matrix, a mildprewhitening of the raw data was employed in Figure 9.6, and the daily midrange (highplus low divided by 2) was substituted for the daily close.

The obvious result is that the visibility of the islands is only slightly improved usingthe midrange values. Therefore a more drastic technique is necessary. In Figure 9.7, afive-day arithmetic moving average of the raw daily closes was employed.

Smoothing the daily closes prior to plotting the two-dimensional momentum quad-rangle has a pronounced effect on the visualization of the island patterns. The numberof vertical cells between the center of each island and the center of a vertically adjacentisland of the same shade (white or black) is equal to half the wavelength predominant inthe raw time series. An example of this occurs on days 77 and 78 in Figure 9.7.

OBSERVATION

The interpretation of two-dimensional momentum charts is a topic for extended research,particularly with regard to the identification of dominant cycles in any financial time series.