Idea Labs Journal

Stuctured time series

Exponential Smoothing (ETS) Framework

Hemanth Sindhanuru


Once we represent the time-series under consideration with a mathematical model, we move on to forecasting the time-series values for future horizons. There are two approaches to forecasting for multiple horizons in general

RECURSIVE APPROACH: We calculate the one-step ahead forecasts recursively for each of the future horizons. This can be better understood as shown below.

If we take a closer look, as the forecasting horizon grows, the no. of estimates on the RHS (please refer the notation in the previous pictorial representations) increases. This leads to an increasing bias component of the error (which we will be discussing in the upcoming topic, Bias-Variance Trade-Off) as the forecasting horizon grows

DIRECT APPROACH:An alternative approach is to extrapolate the modelling equation for the future horizons as shown.


ETS_forecast  forecast( object = ETS_model, h = 20 )
plot( ETS_forecast )
# forecast() is an generic function for forecasting time-series models.
# The function invokes particular parameters which depend on the class of the first arg.
# object ---> an object of class "ets", output of the ets() function
# h          ---> future horizon to be forecasted

Keep watching this space for more

BACK TO THE FUTURE – A Beginner’s Guide to Forecasting
1. A Primer on Time-Series Forecasting
2. Structural Time-Series Models
3. Periodicity of a Seasonal Time-Series
4. Defining Time-Series Attributes
5. Exponential Smoothing Framework
6. ARIMA modelling in a nutshell