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I am working on a problem that I think ARIMA modeling could be useful for, and am researching the theory behind ARIMA. I came across this website that says:

ARIMA(p,d,q) forecasting equation: ARIMA models are, in theory, the most general class of models for forecasting a time series which can be made to be “stationary” by differencing (if necessary).

My question is, what does this mean? When and why is it needed to make a time series ¨"stationary", and what is differencing?

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This question explains what stationarity is and why we want it. Intuitively, a time series is stationary if its distribution does not change over time. Anything with trends or seasonality is not stationary.

Differencing means taking differences between observations one period apart, i.e. working with $y_2-y_1, y_3-y_2, ...$ instead of $y_1, y_2, y_3, ...$. This addresses some kinds of non-stationarity. See here for other ways to address non-stationarity.

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