In time series analysis, stationarity is an essential concept. A time series that exhibits constant statistical attributes over a given period of time is referred to as stationary. The modelling process is made simpler by the lack of seasonality or trends. Two varieties of stationarity exist:
Strict Stationarity: The entire probability distribution of the data is time-invariant.
Weak Stationarity: The mean, variance, and autocorrelation structure remain constant over time.
Transformations like differencing or logarithmic transformations are frequently needed to achieve stationarity in order to stabilise statistical properties.
Let’s check the stationarity of the ‘logan_intl_flights’ time series. Is the average number of international flights constant over time?
A visual inspection of the plot will tell you it’s not. But let’s try performing an ADF test.
The Augmented Dickey-Fuller (ADF) test is a prominent solution to this problem. Using a rigorous examination, this statistical tool determines whether a unit root is present, indicating non-stationarity. The null hypothesis of a unit root is rejected if it is less than the traditional 0.05 threshold, confirming stationarity. The integration of domain expertise and statistical rigour in this comprehensive approach improves our comprehension of the dataset’s temporal dynamics.
