الثبات والفروق

Most forecasting models assume the series behaves consistently over time. That property has a name: stationarity. 🎯

A stationary series has a stable mean and spread that do not drift over time. Its statistical mood stays the same.

A rising trend means the mean keeps climbing, so the series is non-stationary. Many models will struggle until you fix that.

Repeating seasonal swings make the average rise and fall on a cycle. That changing pattern also counts as non-stationary.

You do not have to guess. The ADF test checks stationarity and returns a p-value you can read.

If the ADF p-value is below 0.05, the series is likely stationary. Above it, you probably still have a trend to remove.

Differencing replaces each value with how much it changed from the last step. This simple move often erases a trend.

By looking at changes instead of levels, a steady climb becomes a flat line wobbling around zero, which is stationary.

The very first row has nothing to subtract, so diff leaves it NaN. Drop it before testing or modeling.

If one round is not enough, difference the result a second time. The number of rounds becomes the d term in ARIMA.

To kill a yearly cycle, subtract the value 12 steps back. That seasonal diff targets the repeating pattern directly.

An ADF test on your raw series returns a p-value of 0.40. What does that suggest?

You learned to test stationarity with ADF and to remove trends and cycles using differencing before modeling.