Stationarity in time series and why ARIMA needs it

WHAT THIS TESTS: Whether you can define stationarity precisely, explain why ARIMA depends on it, and name concrete tools to test and fix it. Interviewers listen for the difference between 'no trend' and the full statistical definition.

A GOOD ANSWER COVERS: Definition: a (weakly) stationary series has a constant mean, constant variance, and an autocovariance that depends only on the lag between points, not on absolute time. Intuitively, the process behaves the same way no matter which window you look at. Why ARIMA needs it: the model estimates a fixed set of AR and MA coefficients; if the mean or variance drifts, those coefficients are no longer valid across the series and forecasts degrade. The 'I' (integrated) term exists precisely to difference the data into stationarity before the AR and MA parts are fit.

TESTING FOR IT: The Augmented Dickey-Fuller (ADF) test checks for a unit root; a low p-value lets you reject non-stationarity. Visual inspection of the ACF plot helps too: a stationary series' autocorrelations decay quickly, while a non-stationary one stays high across many lags.

ACHIEVING IT: Differencing (subtracting the previous value) removes trends and is the standard fix; seasonal differencing handles seasonality. A log or Box-Cox transform stabilizes a variance that grows with the level.

COMMON WRONG ANSWERS: Saying stationarity just means 'no trend' it also requires constant variance and time-invariant autocovariance. Forgetting that over-differencing introduces artificial structure.

ONE CONCRETE EXAMPLE: Monthly sales that trend upward and fan out in variance are non-stationary. A log transform flattens the growing variance, one round of differencing removes the trend, and an ADF test on the result confirms stationarity before you fit ARIMA.