# Theta

Ερευνητική Δραστηριότητα - Theta Model

This area presents all the latest advances for the Theta model, a new univariate forecasting method originated in 1999 by Professor V. Assimakopoulos and Dr. K. Nikolopoulos. The method is based on the concept of modifying the local curvature of the time-series through a coefficient "Theta" (the Greek letter Θ). The resulting series, the "Theta-lines" maintain the mean and the slope of the original data but not their curvatures. Their primary qualitative characteristic is the improvement of the approximation of the long-term behavior of the data or the augmentation of the short-term features, depending on the value of the Theta coefficient. The proposed method decomposes the original time series into two or more different Theta-lines. These are extrapolated separately and the subsequent forecasts are combined. The method performed well in the M3 competition, particularly for monthly series and for microeconomic data. To learn more about the model or for any other enquiry please contact: Dr. K. Nikolopoulos

Latest Advances | Research | Discussion | Forthcoming | Citations

Latest advances

"Fathoming the Theta model", K. Nikolopoulos, V. Assimakopoulos, Working paper, May 2005, National Technical University of Athens

"Theta model: decomposition approach or just SES with drift?", K. Nikolopoulos, V. Assimakopoulos, International Symposium on Forecasting ISF 2005, June 12-15, 2005, San Antonio, USA.

"Generalizing the Theta Model", K. Nikolopoulos, V. Assimakopoulos, International Symposium on Forecasting ISF 2004, July 4-7, 2004, Sydney, Australia.

Research

"The Theta Model", V. Assimakopoulos, K. Nikolopoulos, Decision Sciences Institute, 5th International Conference, Proceedings, pp. 584-586, July 4-7, 1999, Athens.

... the beginning of this journey...

"The Theta Model: A Decomposition Approach to Forecasting", V. Assimakopoulos, K. Nikolopoulos, International Journal of Forecasting, Vol 16, Number 4, pp. 521-530, 2000.

... the Theoretical foundation of the model.

Hyndman RJ, Billah B, "Unmasking the Theta method", INT J FORECASTING 19 (2): 287-290 APR-JUN 2003 (View)

... an alternative approach for producing the Theta lines plus the allegation that the model produces forecast equivalent to Simple Exponential Smoothing with Drift!

"A technical analysis approach to tourism demand forecasting", C. Petropoulos, A. Patelis, K. Nikolopoulos, V. Assimakopoulos. Journal of Applied Economis Letters, Forthcoming in Vol 12, Number 1-2, 2005

... extrapolating L(2) with a Rule Based approach.

"Theta Intelligent Forecasting Information System", K. Nikolopoulos, V. Assimakopoulos. Industrial Management and Data Systems, Vol 103, Number 9, pp. 711-726, 2003

... integrating and optimising the model into an Information System: TIFIS!

"eTIFIS: An innovative e-Forecasting Web application", E. Tavanidou, K. Nikolopoulos, K. Metaxiotis, V. Assimakopoulos. Journal of Software Engineering and Knowledge Engineering, Vol 13, Number 2, pp. 215-236, April 2003.

... what about a web application based on TIFIS!

"Forecasting Volatility with the Theta Model", K. Nikolopoulos, K. Maris, G. Pantou, V. Assimakopoulos. Journal of Empirical Economics Letters, Vol 2, Number 6, pp. 216-227, 2003

... an attempt to go deep down and econo-dirty. with major teething problems however!

"Generalizing the Theta Model", K. Nikolopoulos, V. Assimakopoulos, International Symposium on Forecasting ISF 2004, July 4-7, 2004, Sydney, Australia.

... the future is finally here...

Discussion

The essence of the method as competed in the M3 is described in the following statement by Professor Keith Ord (2000):

"In "The Theta Model: A Decomposition approach to Forecasting" Vassilis Assimakopoulos and Kostas Nikolopoulos first remove any seasonal pattern by a classical decomposition method and then decompose the series into two parts. In essence, these two components may be viewed as a trend line to describe longer-term behavior and a second difference for short-term movements. These components are then extrapolated separately and the elements are recombined to produce the final forecasts."

The surprisingly well performance of the model created interest in the Academia, as to what is behind this success:

Robert L. Goodrich (2001) (Dr. Robert Goodrich is one of the co-developers of the Forecast Pro, and president of Business Forecast Systems. Forecast Pro was the top performer among the automated Forecasting Support Systems in M3!):

"Perhaps the success of the Theta method depends upon its use of the global trend rather than the local. In any event, the emergence of this new method may be the single greatest contribution of the M3-competition. It strengthens the conviction that, ceteris paribus, simple methods outperform more complex ones."

Professor Michael Lawrence(2001):

"I was fascinated that a new technique THETA should perform so well but am left wondering what new idea it exploits, that enables its performance to be so good."

Goodrich, R. L. (2001). "Commercial Software in the M3 Competition", International Journal of Forecasting, Vol. 17 No 4, pp.560-565.

Lawrence, M. (2001). "Why another study", International Journal of Forecasting, Vol.17 No 4, pp.574-576.

Ord, K., Hibon, M., Makridakis, S., (2000). "The M3-Competition, International Journal of Forecasting, Vol. 16 No 4, pp. 433-436

Forthcoming

A presentation on the latest advances on the model will be held on

The 25th International Symposium on Forecasting will be held in San Antonio, Texas, USA, June 12-15, 2005.

If that is too far away more seminars, presentations and lectures are coming soon, in Europe this time.

Citations

Miller DM, Williams D

Shrinkage estimators of time series seasonal factors and their effect on forecasting accuracy

INT J FORECASTING 19 (4): 669-684 OCT-DEC 2003

Hyndman RJ, Billah B

Unmasking the Theta method

INT J FORECASTING 19 (2): 287-290 APR-JUN 2003 (View)

Harvey A., Forecasting with Unobserved Components Time Series Models

Faculty of Economics, University of Cambridge, Prepared for Handbook of Economic Forecasting (View)