Looking at moving averages from the perspectives of stochastic processes and signal processing: An N-day moving average is essentially taking the average of a discrete random sequence of N points. From a signal processing standpoint, it can be viewed as a moving average filter with N taps, where all filter coefficients are 1. A larger N means more taps and better filtering performance. This filter is the simplest low-pass filter, primarily used to filter out high-frequency noise.

A stock signal is actually the superposition of a low-frequency signal and high-frequency noise. The low-frequency signal reflects the trend, i.e., the intrinsic value, while the high-frequency noise reflects volatility. The new sequence obtained by calculating the moving average of the stock signal is equivalent to the stock signal passing through a low-pass filter, resulting in a sequence containing only the low-frequency signal, which reflects only the stock's value. The stock price and the moving average price are essentially the sequences of the price before filtering and the value after filtering. The idea of "adding to a position when the price falls below the N-day moving average" means that at this point, the stock price is lower than its intrinsic value, providing a margin of safety for adding to the position. It all boils down to the phrase "price fluctuates around value."

I'm wondering, what would happen if we replaced the moving average filter with a filter of another shape? 🤔