Integration is the differencing component of ARIMA. It removes nonstationary temporal structure so the remaining series can support forecasting. section 7.3
Apply integration as a validation-driven preprocessing step:
- Partition observations into training and testing sets before preprocessing; fit the ARIMA model and apply subsequent preprocessing to the training subset. section 7.3.7
- Inspect trends, seasonality, ACF, and PACF plots, then use an augmented Dickey–Fuller test to assess nonstationarity. section 7.3.7
Apple closing prices
An ADF test on the training prices produced a p-value of 0.5761. After first-order differencing, the p-value fell to 1.25e-16, while the resulting series was presented as stationary.
