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19

Figure 4.4 Price Distribution function (PDF) constructed from 14 days of oex data with m = 20. This chart is produced with the same conditions as in Table 4.2 except m = 20. There is an improvement in resolution over Figure 4.3. The magnitudes of the bars is about 2 times less than that of Figure 4.3 since the intervals are 2 times smaller and the PDF is not normalized by the interval size, the important thing is that the shape is essentially the same as that in figure 4.3.

PDF CHART 06 4/ 6 (N = 14 M= 20)

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longer period. An example of this is shown in Figure 4.6. Here a history of 39 bars was used for the look-back period. To properly resolve the structure of the PDF more intervals were also used (M - 30). The longer time periods are useful for long-term reference; however, it is difficult to construct a responsive, meaningful oscillator when multiple peaks are present. Nonetheless, these plots have value for establishing longer-term congestion and for comparison with support and resistance levels.

reference points

To evaluate market conditions analytically, it is necessary to have points of comparison or reference points. For example, the current price may be compared with the maximum and minimum price values over some look-back period as is done in stochastics. In stochastics, the current price is gauged between these references and the



Figure 4.5 price distribution Function (pdf) constructed from 14 days of OEX data with m = 40. This chart is an example of multiple peaks. The lower peak is a short-term bottom, followed by a sharp rise to

the upper peak. At the upper peak the OEX is pausing and forming a top.

PDF CHART 08/14/96 (N = 14 M = 40)

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proportion between these two positions defines the Stochastics Oscillator. Similarly, trendlines can be used to project the highs and the lows as a reference. When we let the maximum projected high and the minimum projected low over a look-back period define the stochastic range, we have a form of "Projection" oscillator. In general, reference points can be a particular price value on a previous date, an extreme price value within a recent interval, or an average or other statistical measure. The following will relate several common references to the PDF analysis.

Support and resistance levels are common reference points used to describe market behavior. They are local maxima or minima over a period. If a particular high is greater than the prior N bars highs and greater than the following N bars highs, then that high qualifies as a resistance level. Correspondingly, if a particular days low is less than the prior N bars and less than the following N bars, then that low qualifies as a support level. Of course, todays support may become tomorrows resistance and conversely. Generally the greater the period or value of N, the more significant the level. Too short a period gives a large number of levels, some of which may be insignificant, while too long a period may omit important levels. Traders must determine their own time horizon for their particular market and back-test to pick a good



Figure 4.6 The PDF for a longer time period. If a larger time interval is

selected there is more structure in the PDF. in this case, there are two principal peaks corresponding to two steps in the price history. the price spends little time in the central region and at the end points of the range where the distribution values are low.

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value. For example, for a 5-day time horizon for OEX daily data, I find N= 4 days (-4 days to +4 days) to be a good choice.

The PDF, if plotted for long look-back periods, implicitly includes the congestion levels as well as support and resistance. This can be seen in Figure 4.7, where the support and resistance levels clearly match with low spots in the PDF. The support and resistance levels determined with n - 4 are traced to the right on the chart. All the 59 data points that are plotted are used to construct the PDF on the right of the chart. The PDF and the support resistance levels define bands of high and low mobility. Combining this information is useful for forecasting.

Why particular values of support and resistance have significance is not clear, but they do. It could be a reoccurrence of an overvalued or undervalued condition or an exhaustion of one side or the other. My own favorite explanation is that it is an obvious reference point with strong public belief that it is important, therefore it is important. It is a self-fulfilling prophecy, a belief whose consequences are quite real and the consequences reinforce the belief.



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