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HOW MESA WORKS The mathematical engine in MESA8 is the Burg algorithm. (Phd. Thesis by John Parker Burg, Stanford University, 1975) This algorithm has been successfully used in the MESA program since 1978. The mathematical procedure is rather complicated and MESA compromises some generality to achieve ease of operation. For example, the order of the mathematical filter is fixed relative to the data length. MESA models the market as a generalized filter. This filter is driven by a white noise generator. (White noise consists of all frequencies with a uniform power amplitude.) The output of the filter is compared with the samples of actual market price data. The result of the comparison is fed back to adjust the filter so that, ultimately, the filter output is a good replica of the true data in the time domain, within the constraints of the filter. The length of data used to tune the filter can be selected independently from the filter characteristics. MESA features an adaptive data length. In general terms, a fraction of yesterday's dominant cycle is today's data length. The adaptive data length avoids measurement latency, or lag, usually produced by a fixed length data window. For example, if a new 10 day cycle appears, we don't have to wait for it to fill a 30 day window before we sense it in the measurement. A secondary measure of the price data has been established within MESA when the filter is tuned. The frequency information described by the filter settings. Since the filter parameters were fixed by the price data, the digital clock can be run into the future so that the filter output is a predictor of future prices where the cycles retain their characteristics. A real-world example of the spectrum as measured by MESA8 is shown in the following figure for the S&P Continuous futures contract for the year prior to November 2005. The spectrum is displayed as a heat map, running from white-hot, through red-hot, to ice cold over a 20 dB range. Colorizing the spectrum this way enables the spectrum to be displayed in time synchronization with the price data.
MESA8 Spectrum for S&P Futures Contract The MESA8 spectrum clearly has high resolution. Further, this and many similar examples shows that there is typically only one tradeable cycle present at a time. This enables the use of the concept of a "dominant" cycle. One can construct a simplified model of the market consisting of only a trend and a cycle component. The dominant cycle is clearly the component of choice, and can be measured using the spectrum computed by MESA8. The dominant cycle is computed as the center of gravity of all the cyclic components between 6 bars and 50 bars. Since we are dealing with sampled data, these bars can be 15 minute bars, daily bars, weekly bars, etc. Your trading style can be accommodated by changing the period at which the data is sampled. There are two major criticisms of the MESA approach. The first is that MESA cannot measure the power in the waveform. This is true. However, once the dominant cycle is established, the cycle power can accurately be measured using the Hilbert Transform. The second critcism is that the spectrum estimate can be unstable. MESA8 avoids this problem by proper preconditioning the data before the MESA algorithm is applied and by proper setting of the MESA computation parameters. The stability of the spectral estimate is self evident. The high resolution spectrum estimate yields the dominant cycle by determining its center of gravity, i.e. the cycle period that contains the majority of signal power. |
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