Identifying Stationarity

pbenavides

What is Stationarity?

• A time series is said to be stationary if its statistical properties (mean and variance) are constant over time.

• Stationarity is important because many time series forecasting methods assume that the underlying data is stationary.
• Non-stationary data can lead to inaccurate forecasts and misleading interpretations.

• There are two main types of stationarity:
  • Strict Stationarity: The joint distribution of any set of observations is the same regardless of the time at which they are observed.
  • Weak Stationarity: The mean, variance, and autocovariance of the series are constant over time.
• In practice, we often focus on weak stationarity because it is easier to test and work with.

A time series with an upward trend.

A time series with a downward trend.

A time series with yearly seasonality.

A time series with yearly seasonality and a shifting trend.