Theoretical Waveforms

MESA Indicators are as easy to use as any of the standard indicators. As opposed to fixed rule indicators, all MESA indicators dynamically adjust to current market conditions.

It is essential for any cycle-measuring program to prove that complex cycles are actually being accurately measured. In addition, you should become aware of the theoretical capabilities and limitations of your market analysis tools. This section addresses these two goals.

The Sinewave example of Figure 1 is a trivial measurement. The 24-bar cycle length can be determined simply by measuring the distance between successive lows or successive highs. The factors that make cycle analysis difficult are noise mixed with the cycle, shifts in the cycle over a period, combinations of several simultaneous cycles and combinations of these effects. We prove that MESA Indicators handle these cases using deterministic theoretical waveforms. We also challenge any other trading program to make comparable analyses.

Figure 1 has four major segments. These are the price bars, the Sinewave Indicator, the phase of the measured dominant cycle and the dominant cycle segment. The Mode is not displayed because the market is obviously only in the Cycle Mode for this theoretical example.

1. Price Bar Segment
   The blue price bars extend from the high of the day to the low of the day. The opening price is indicated as a tick on the left side of the bar and the closing price is indicated as a tick on the right side of the bar. The scale for the prices is at the right of the display. The Instantaneous Trendline (the straight red line) and the Kalman filter (the cyan line closely following the price midpoints) are used to indicate a Trend Mode. When in the Cycle Mode, the Kalman filter line crosses the Instantaneous Trendline every half cycle. Failure to make this crossing denotes the onset of a trend. The trend is over when these two lines again cross.
   
   
2. Sinewave Indicator Segment
   The Sinewave Indicator is formed as the sine of the measured phase of the dominant cycle. The leading curve uses the phase advanced by 45 degrees (1/8th of a cycle) while the lagging curve uses the unaltered phase. As a result, the curves cross prior to every cycle turn, and provide an advance indication.
   
   The indicator curves should look similar to sinewaves at the time of the signal, one indication the market is in a cycle mode. When the market is in a trend mode, the curves will wander around erratically and will tend to run parallel. Trades entered on the basis of the indicator crossings should be exited immediately when a trend mode is identified if the trend is in the opposite direction of your cycle mode trade.
   
   
3. Measured Phase Segment
   The third display segment displays phase of the measured dominant cycle. One definition of a cycle is a phenomenon that has a constant rate change of phase. For example, a cycle completes 360 degrees, or one full rotation, every cycle. Therefore, a perfect 10-day cycle would have a rate change of 36 degrees per day. If the cycle is not perfect, then the rate change of phase will not be constant. This is a particularly sensitive way to detect whether the market is in a cycle mode or a trend mode. Failure of the phase to increase linearly is a sensitive indication that a cycle mode can be failing.
   
   
4. Dominant Cycle Segment
   The bottom display segment shows the ebb and flow of the cycles in the market by displaying the measured dominant cycle length synchronized with the price bars. In this segment, the length of the cycle is indicated by the vertical scale of the segment. The fact that the indicated dominant cycle length is 24 bars shows the theoretical cycle has been accurately measured.

Variations of the cycle frequency pose real problems for spectral estimators. The difficulty arises from the data not being stationary over the observation period. In statistical communication theory, stationary data means that the probability distribution of the data is independent of the selection of the time origin. In our case, this means the cycle is not stable and consistent over the observation period. The shorter MESA Indicators observation period achieves a nearly stable cycle condition with a higher probability than with other spectral estimators, such as Fast Fourier Transforms.

We next examine the effect of nonstationarity on the MESA Indicators displays. Figure 2 shows a theoretical sinewave whose period is continuously increasing at a slow rate. The very important point is that the continuously varying period of the cycle is accurately measured by MESA Indicators on a bar-by-bar basis. There is no course appraisal similar to estimating the period by counting the bars between successive lowest lows. The MESA Indicators measurement is continuous.

Figure 2 shows that MESA Indicators accurately measure the cycle periods over the range from 8-bar cycles to 40-bar cycles. In addition, Figure 2 demonstrates that the Sine and LeadSine signals have a constant amplitude and consistent phase relationship over the entire range of the Chirp cycle periods. This means their crossings give accurate Cycle Mode turning point signals over the full range of cycles that are likely to be encountered.

We have vigorously exercised the measurement capabilities of MESA Indicators. As a result, you have gained some insights into the strengths and limitations of the program. Recognizing these, you will know best how to apply the displays to your trading. You can also compare the analysis capabilities of MESA Indicators to any other cycles program on a deterministic basis. The theoretical waveforms free you from relying on anecdotal evidence. You should never forget that if analysis becomes too complex or confusing it is perfectly acceptable to stand aside until the confusing issues are resolved.

Now that we understand what MESA Indicators can and cannot do theoretically, we will look at some real-world examples for insight in how to use it in our trading.