# Stationarity

## What is Stationary Data in Time Series?

The properties of stationary time series data don’t depend on the time at which the series is observed. If we take consecutive sets of data with the same size, they should have identical covariance regardless of the starting point. This is also called a weak form of stationarity or covariance stationarity.

## Features of Stationary Data

1. Constant Mean
2. Constant Standard Deviation
3. Consistent Covariance

The time series data which follows the above three assumptions is also called covariance stationarity or a weak form of stationarity.

## Points to Note

1. Time Series data with Trend or Seasonality are not stationary.
The trend and seasonality will affect the value of the time series at different times.
2. White Noise is a good example of a weak form of stationarity.
Variance is always stationary
Autocorrelation is always 0
since correlation is = cov*std ⇒ 0, hence covariance =0

## Strict stationarity

Samples of the same size should have the same distribution. For any strictly stationary random variable x. But since these cases are very restrictive, we rarely observe them in the natural world.

Hence stationarity is used to define covariance stationarity.

## How to Detect Stationarity in Time Series Data?

To analyse time series data, it is vital to find if the data is stationary or non-stationary. Below are two tests that can be used to detect stationary in a time series data:

1. Augmented Dickey-Fuller Test (ADF Test)
2. Kwiatkowski-Phillips-Schmidt-Shin Test (KPSS Test)