Introduction

MESA is a program that gives accurate trading signals based on the measurement of short-term cycles in the market. Cycles exist on every scale from the atomic to the galactic. Therefore, we have every reason to believe cycles exist in the market.

It has been said that the market is characterized by the famous random walk problem. Based on this, proponents that assert the market is basically efficient. This is clearly wrong because there have been a number of consistently successful traders. However, looking deeper, we see that the market is analogous to a constrained random walk. That is because time can only move forward and prices can only move up and down. The constrained random walk is called the “drunkard’s walk” because it describes the staggering as the “drunk” moves from point A to point B.

There are two solutions to the drunkard’s walk problem. In the first case, the “drunk” flips a fair coin to determine whether he steps to the right or left as he steps forward. The random variable is direction. The solution to this formulation of the problem is a rather famous partial differential equation called the Diffusion Equation. It describes natural phenomena, such as heat flowing up the stem of a silver spoon when it is placed in a hot cup of coffee or smoke flowing from a smokestack.

In the second case, the “drunk” asks himself whether he should take the next step in the same direction as the last one or whether he should reverse his direction depending on the outcome of the coinflip. In this case, the random variable is momentum and the solution is another rather famous partial differential equation called the Telegraphers Equation. Among other things, the Telegraphers Equation describes waves on a telegraph wire or the meandering of any river in the world.

Thus, the Drunkards Walk describes the two market modes. The Trend Mode is similar to smoke from a smokestack, having a general direction and a fine grain randomness. The Cycle Mode is analogous to the meandering of a river. As surely as water flows downstream, time moves forward. You can almost imagine being on a raft in the river. Once you enter a given meander, you can accurately project where that meander will take your raft. And, so it is with cycles in the market. Cycles can be accurately measured scientifically. Knowing the cycle content, that content can be subtracted from the composite to produce the trend.

Market cycles can be measured several ways. Perhaps the simplest is to count the number of bars between successive lowest lows or highest highs. The resulting bar count is the cycle period. Cycle periods can also be measured using a frequency discriminator after taking a Hilbert Transform of the data. Fast Fourier Transforms (FFT) are often (and inappropriately) used. FFTs are inappropriate for the measurement of market cycles because the constraints and resulting resolution are overlooked.

The Maximum Entropy Spectral Analysis (MESA) approach was first developed in the 1960s to process seismic information for oil exploration. MESA can make a high resolution measurement of a market cycle using less than one cycle's worth of data. Using a small amount of data is critical because it increases the probability of the data being stationary during the measurement period. Stationary data is crucial for accurate measurements. Put another way, you need to know that you are in a river meander to know where that meander is going to take your raft.

MESA offers five indicators to assist your trading. These are:

1. Measurement of the dominant cycle. This lets you know the distance between successive peaks or valleys. If you have just passed a peak, then it is reasonable to expect the next valley to be about a half cycle into the future. The dominant cycle (or a fraction of it) can be used to dynamically adjust other indicators. For example, Stochastics and RSIs work their best when a half cycle is used to peak their performance.
   
   
2. Measurement of the cycle phase. A constant rate change of phase is a basic definition of a cycle. If the phase is changing at the rate of 36 degrees per day, then you cover 360 degrees in 10 days. Therefore, you have a 10-day cycle. Departure from a constant rate change of phase is a sensitive way to detect the end of a cycle mode.
   
   
3. Sine and LeadSine Oscillator. The Sine Indicator is just plotting the sine of the measured dominant cycle phase. The LeadSine Indicator is a plot where the phase is simply advanced 45 degrees. The crossing of the Sine and LeadSine Indicators are buy and sell points because they anticipate the turning points when the market is in a cycle mode
   
   There are two advantages of the Sine and LeadSine Oscillator. Firstly, the line crossing anticipates the cyclic turning points. This enables timely entry and exits of market positions. Secondly, the phase tends not to advance when the market is in a Trend Mode. This causes the Sine and LeadSine to wander in a somewhat parallel fashion. The lack of line crossings in the Trend Mode is an advantage over the false whipsaw signals generated by most oscillators.
   
   
4. Instantaneous Trendline and Kalman Filter. The Instantaneous Trendline is created by filtering out the dominant cycle, leaving the residual as the trend. This procedure produces a trendline that looks like a moving average, and its advantage is that it has a minimum lag.
   
   The Kalman Filter line is a data smoother that has nearly zero lag. When the market is in a cycle mode, the Kalman Filter line will criss-cross the Instantaneous Trendline every half cycle. Therefore, if the Kalman Filter line fails to cross the Instantaneous Trendline within a half dominant cycle, you can declare the Trend Mode to be in force. The Trend Mode ends when the Kalman Filter line next crosses the Instantaneous Trendline.
   
   
5. Cycle Mode. This is a convenience indicator, displaying the conditions described by the Instantaneous Trendline and the Kalman Filter line. The market is in a Trend Mode when the value of this indicator is 1 (one) and is in a Cycle Mode when the value is 0 (zero).