In the previous session, you gained an in-depth understanding of different smoothing models of forecasting using a time series dataset. In this session and the next session, you will learn about another family of forecasting models called Auto Regressive models. Before we jump into these models, there are two fundamental assumptions to build an Auto Regressive model. They are —

- Stationarity
- Autocorrelation

Let us first hear from Chiranjoy about stationarity.

If a time series is stationary, its statistical properties like mean, variance, and covariance will be the same throughout the series, irrespective of the time at which you observe them.

The following image illustrates a stationary time series in which the properties such as mean, variance and covariance are the same for any two-time windows.

Let’s now listen to Chiranjoy as he delves deeper into the notion of stationarity, with more examples for stationary and non-stationary series.

White noise is an example of a stationary time series with purely random, uncorrelated observations with no identifiable trend, seasonal or cyclical components.

Notice that there are no identifiable trends, seasonal or cyclical components. So a white noise series is basically an example of a stationary series.

In another example, Chiranjoy has explained a non-stationary series called random walk

A random walk is a time series where the current observation is equal to the previous observation plus a random change. Here, variance increases over time resulting in a non-stationary series.

In general, a stationary time series will have no long-term predictable patterns such as trends or seasonality. Time plots will show the series to roughly have a horizontal trend with constant variance.

Stationary processes are easier to analyze and model because their statistical properties remain constant over time. There will be no trend, seasonality and cyclicity in the series. In other words, if the past observations and future observations follow the same statistical properties i.e. there are no change in mean, variance and covariance then the future observation can be easily predicted.

Till this segment of Auto Regressive models, you have learned about the stationarity and its importance in forecasting a time series. In the coming segments, you will learn how to determine if a given series is stationary or not.