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I’m just finishing up reading the 2017 edition of Trend Following and it occurs to me there may be other mathematical models for trends. Suppose price were not modeled as a statistically random variable but instead as some sort of mechanical vibration. Perhaps the nature of trading is such that price vibration or noise could be modeled by a sine wave with appropriate parameters for different markets. I was thinking a trend would be recognized when the price movement over a given number of time periods exceeded the previous price plus the sign wave value. Perhaps the price could also be required to exceed an expected return plus inflation to meet the definition of a trend. P(t1) >= abs[ P(t0) (1 + x sin(t0) + expected rate of return per time period + rate of inflation per time period)]. Price could be given a speed equal to rate of change per time period and a momentum equal to volume of trading or contracts outstanding times speed. There are also mathematical models from communications theory for signal to noise ratio which might be useful. Modeling price as a mechanical system should enable trends to be analyzed with differential calculus which could be enlightening and rewarding. Perhaps these ideas have been considered already. I have only read the one book. I didn’t see a mechanical modeling approach mentioned. I enjoyed the book. During the 1970’s and 80’s I sat at a desk writing computer programs to do calculations. Applications ranged from management systems to design and analysis of experiments in agriculture. I played with investing formulae on weekends. The experiences of contemporaries described in the book brought back fond memories. Thank you.
Watt
Why do you want to make it more complicated than price alone?
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