Forecasting With The Theta Method

6‐Reflections from the Next Generation of Forecasters

By Fotios Petropoulos

The Theta method, as it was applied by Assimakopoulos and Nikolopoulos (2000) to produce forecasts for the M3 competition (Makridakis and Hibon 2000), involved several ad hoc decisions and simplifications, such as the following:

• Adjust the data for seasonality using multiplicative classical decomposition;
• Decompose the seasonally adjusted data into exactly two theta lines, with theta coefficients equal to 0 and 2 corresponding to the simple linear regression line on time and a line with double the curvatures of the seasonally adjusted data respectively;
• Extrapolate the theta line 0 as usual, using the regression model fitted on that line assuming a linear trend;
• Extrapolate the theta line 2 using the simplest form of exponential smoothing models, simple (or single) exponential smoothing (SES);
• Combine the forecasts produced for theta lines 0 and 2 using equal weights.

We further on refer to the Theta method based on the aforementioned settings as the standard Theta method. The standard Theta method can be extended by considering several deviations from the standard setup, such as the following:

• Alternative seasonal adjustments,
• Different values for the theta parameters,
• Multiple theta lines,
• Alternative extrapolation methods,
• Unequal combination weights.

This chapter reports some results in the literature ...