A lot can be learned about trend-following by using some simple time series processes to describe the behavior of markets. Some key insights on trend-following can be derived using the simple Ornstein-Uhlenbeck (O-U) process. This stationary Gaussian Markov process can help explain trends through variations in a mean reversion parameters, speed of adjustments. Mean reversion will create trends as price return to equilibrium, mean values, after shocks. A short paper, "To Be Or Not To Be a Trend Follower" by Andreas Junge of Methodica Ventures attracted my interest in this topic.
The O-U process states that tomorrow's price is just today's price minus an adjustment of today's price to a mean value plus an error term. The random walk, market efficiency, is just a special case where the mean reversion parameter is zero. This process is not new and has been a workhorse with many derivative pricing models, but it provides a framework on how markets may work.
A framework for how markets operate when they are efficient and a framework for when behavior will differ from efficiency is useful when looking for market opportunities. A framework describing the evolution of price behavior helps to form a prior for trend expectations.
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