Hands-On Machine Learning for Algorithmic Trading

How to build moving average models

An MA model of order q uses q past disturbances rather than lagged values of the time series in a regression-like model, as follows:

Since we do not observe the white-noise disturbance values, ε_t, MA(q) is not a regression model like the ones we have seen so far. Rather than using least squares, MA(q) models are estimated using maximum likelihood (MLE), alternatively initializing or estimating the disturbances at the beginning of the series and then recursively and iteratively computing the remainder.

The MA(q) model gets its name from representing each value of ${\mathrm{yt}}^{}$ as a weighted moving average of the past ...