FORECASTING THE FUTURE HORIZONS
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.
IMPLEMENTATION IN R 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