Hands-On Machine Learning for Algorithmic Trading

How to build ARIMA models and extensions

Autoregressive integrated moving-average ARIMA(p, d, q) models combine AR(p) and MA(q) processes to leverage the complementarity of these building blocks and simplify model development by using a more compact form and reducing the number of parameters, in turn reducing the risk of overfitting.

The models also take care of eliminating unit-root nonstationarity by using the d^th difference of the time series values. An ARIMA(p, 1, q) model is the same as using an ARMA(p, q) model with the first differences of the series. Using y' to denote the original series after non-seasonal differencing d times, the ARIMA(p, d, q) model is simply:

ARIMA models are also estimated using Maximum Likelihood. Depending ...