Fundamentals

Stationarity

A series is stationary when its mean and variance sit still over time. Many classical models assume that. Real business series usually do not — they trend, they season, they jump when you change the website.

ARIMA-style work often differences the series (today minus yesterday) until the leftover looks still. That leftover is not the thing finance wants to read. You difference to fit, then you undo it to report.

You do not need stationarity to forecast. You need to know whether your method assumes it. Tree models and foundation models are less fussy. They still suffer if the future is a different regime than the training window.

A quick visual check beats a p-value you will misread. If the series walks away from its mean, it is not stationary. If the swings get bigger as the level rises, variance is not sitting still either.