Theta

The Theta model was developed in 2000 by Assimakopoulos & Nikolopoulos is a simple model which works by fitting two theta-lines, forecast both using exponential smoothing and combining the two forecasts to get the final result.

By modifying the local curvature of the time-series Yt​ based on a parameter Theta, θ a new series is created. These maintain the mean and the slope of the original data but not their curvatures. This is what is called a theta-line.

The theta-lines are calculated from the second difference of the time series

The theta-lines are then calculated as

This has the effect of deflating the series towards a linear trend line, a value of θ=0θ=0 results in a straight line.

These two lines are then forecast using simple exponential smoothing and combined, producing a forecast