Forecasting With The Theta Method E-Book

Konstantinos (Kostas) Nikolopoulos

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Sprache: Englisch

Seitenzahl: 257

Veröffentlichungsjahr: 2018

Beschreibung

The first book to be published on the Theta method, outlining under what conditions the method outperforms other forecasting methods This book is the first to detail the Theta method of forecasting - one of the most difficult-to-beat forecasting benchmarks, which topped the biggest forecasting competition in the world in 2000: the M3 competition. Written by two of the leading experts in the forecasting field, it illuminates the exact replication of the method and under what conditions the method outperforms other forecasting methods. Recent developments such as multivariate models are also included, as are a series of practical applications in finance, economics, and healthcare. The book also offers practical tools in MS Excel and guidance, as well as provisional access, for the use of R source code and respective packages. Forecasting with the Theta Method: Theory and Applications includes three main parts. The first part, titled Theory, Methods, Models & Applications details the new theory about the method. The second part, Applications & Performance in Forecasting Competitions, describes empirical results and simulations on the method. The last part roadmaps future research and also include contributions from another leading scholar of the method - Dr. Fotios Petropoulos. * First ever book to be published on the Theta Method * Explores new theory and exact conditions under which methods would outperform most forecasting benchmarks * Clearly written with practical applications * Employs R - open source code with all included implementations Forecasting with the Theta Method: Theory and Applications is a valuable tool for both academics and practitioners involved in forecasting and respective software development.

Leseprobe

Table of Contents

Cover

Author Biography

Preface

Part I: Theory, Methods and Models

1 The

‐legacy

1.1 The Origins…

1.2 The Original Concept: THETA as in THErmosTAt

Appendix

2 From the

‐method to a

‐model

2.1 Stochastic and Deterministic Trends and their DGPs

2.2 The

‐method Applied to the Unit Root with Drift DGP

2.3 The

‐method Applied to the Trend‐stationary DGP

3 The Multivariate

‐method

3.1 The Bivariate

‐method for the Unit Root DGP

3.2 Selection of Trend Function and Extensions

Part II: Applications and Performance in Forecasting Competitions

4 Empirical Applications with the

‐method

4.1 Setting up the Analysis

4.2 Series CREDIT

4.3 Series UNRATE

4.4 Series EXPIMP

4.5 Series TRADE

4.6 Series JOBS

4.7 Series FINANCE

4.8 Summary of Empirical Findings

5 Applications in Health Care

5.1 Forecasting the Number of Dispensed Units of Branded and Generic Pharmaceuticals

5.2 The Data

5.3 Results for Branded

5.4 Results for Generic

Appendix

Part III: The Future of the θ-method

6

‐Reflections from the Next Generation of Forecasters

6.1 Design

6.2 Seasonal Adjustment

6.3 Optimizing the Theta Lines

6.4 Adding a Third Theta Line

6.5 Adding a Short‐term Linear Trend Line

6.6 Extrapolating Theta Lines

6.7 Combination Weights

6.8 A Robust Theta Method

6.9 Applying Theta Method in R Statistical Software

7 Conclusions and the Way Forward

References

Index

End User License Agreement

List of Tables

Chapter 1

Table 1.1 Theta lines and extrapolation methods employed for the Theta method in...

Chapter 4

Table 4.1 Model nomenclature used in empirical applications,

‐ and

‐based.

Table 4.2 Model nomenclature used in empirical applications, benchmarks.

Table 4.3 Full sample statistics, 1997–2017, series CREDIT.

Table 4.5 Subsample statistics, 2014–2017, series CREDIT.

Table 4.6 CREDIT‐1‐60‐3.

Table 4.7 CREDIT‐1‐60‐36.

Table 4.8 CREDIT‐2‐30‐24.

Table 4.9 CREDIT‐2‐60‐36.

Table 4.10 CREDIT‐3‐30‐24.

Table 4.11 CREDIT‐3‐60‐36.

Table 4.12 CREDIT‐4‐30‐12.

Table 4.13 CREDIT‐4‐60‐36.

Table 4.14 Full sample statistics, 2000–2017, series UNRATE.

Table 4.16 Subsample statistics, 2006–2017, series UNRATE.

Table 4.17 UNRATE‐1‐60‐24.

Table 4.18 UNRATE‐1‐90‐24.

Table 4.19 UNRATE‐3‐60‐6.

Table 4.20 UNRATE‐3‐90‐6.

Table 4.21 UNRATE‐3‐120‐6.

Table 4.22 UNRATE‐4‐120‐4.

Table 4.23 Full sample statistics, 2000–2017, series EXPIMP.

Table 4.25 Subsample statistics, 2006–2017, series EXPIMP.

Table 4.26 EXPIMP‐1‐60‐3.

Table 4.27 EXPIMP‐1‐90‐3.

Table 4.28 EXPIMP‐3‐60‐24.

Table 4.29 EXPIMP‐3‐90‐24.

Table 4.30 EXPIMP‐4‐60‐4.

Table 4.31 EXPIMP‐4‐90‐3.

Table 4.32 Full sample statistics, 1985–2014, series TRADE.

Table 4.34 Subsample statistics, 2001–2014, series TRADE.

Table 4.35 TRADE‐2‐30‐3.

Table 4.36 TRADE‐2‐60‐3.

Table 4.37 TRADE‐2‐60‐12.

Table 4.38 TRADE‐3‐30‐6.

Table 4.39 TRADE‐3‐30‐24.

Table 4.40 TRADE‐4‐30‐12.

Table 4.41 TRADE‐4‐60‐12.

Table 4.42 Full sample statistics, 2000–2017, series JOBS.

Table 4.44 Subsample statistics, 2007–2017, series JOBS.

Table 4.45 JOBS‐1‐60‐3.

Table 4.46 JOBS‐1‐90‐3.

Table 4.47 JOBS‐2‐60‐3.

Table 4.48 JOBS‐3‐60‐4.

Table 4.49 JOBS‐3‐60‐12.

Table 4.50 JOBS‐3‐60‐24.

Table 4.51 JOBS‐3‐120‐36.

Table 4.52 JOBS‐4‐60‐6.

Table 4.53 JOBS‐4‐90‐24.

Table 4.54 JOBS‐4‐120‐24.

Table 4.55 Full sample statistics, 1999–2017, series FINANCE‐1.

Table 4.58 Full sample statistics, 1999–2017, series FINANCE‐2.

Table 4.59 Subsample statistics, 2000–2005, series FINANCE‐2.

Table 4.62 FINANCE‐3‐60‐3.

Table 4.63 FINANCE‐3‐60‐36.

Table 4.61 FINANCE‐1‐60‐3.

Table 4.64 FINANCE‐3‐90‐3.

Table 4.65 FINANCE‐3‐90‐36.

Table 4.66 FINANCE‐3‐120‐3.

Table 4.67 FINANCE‐3‐120‐36.

Table 4.68 FINANCE‐4‐60‐3.

Table 4.69 FINANCE‐4‐60‐36.

Chapter 5

Table 5.1 Basic information on the seven most‐prescribed substances in the datab...

Table 5.2 Tenormin..B.‐1‐119‐3.

Table 5.6 Tenormin..B.‐1‐119‐24.

Table 5.7 Tritace..B.‐1‐119‐3.

Table 5.8 Tritace..B.‐1‐119‐4.

Table 5.9 Tritace..B.‐1‐119‐6.

Table 5.11 Tritace..B.‐1‐119‐24.

Table 5.12 Zantac..B.‐1‐119‐3.

Table 5.13 Zantac..B.‐1‐119‐4.

Table 5.14 Zantac..B.‐1‐119‐6.

Table 5.15 Zantac..B.‐1‐119‐12.

Table 5.16 Zantac..B.‐1‐119‐24.

Table 5.17 Tagament..B.‐1‐104‐3.

Table 5.18 Tagament..B.‐1‐104‐4.

Table 5.19 Tagament..B.‐1‐104‐6.

Table 5.20 Tagament..B.‐1‐104‐12.

Table 5.21 Tagament..B.‐1‐104‐24.

Table 5.22 Naprosyn..B.‐1‐119‐3.

Table 5.23 Naprosyn..B.‐1‐119‐4.

Table 5.24 Naprosyn..B.‐1‐119‐6.

Table 5.25 Naprosyn..B.‐1‐119‐12.

Table 5.26 Naprosyn..B.‐1‐119‐24.

Table 5.27 Mobic..B.‐1‐111‐3.

Table 5.31 Mobic..B.‐1‐111‐24.

Table 5.32 Lustral..B.‐1‐105‐3.

Table 5.33 Lustral..B.‐1‐105‐4.

Table 5.34 Lustral..B.‐1‐105‐6.

Table 5.35 Lustral..B.‐1‐105‐12.

Table 5.36 Lustral..B.‐1‐105‐24.

Table 5.37 Atenolol..G.‐1‐51‐3.

Table 5.38 Atenolol..G.‐1‐51‐4.

Table 5.39 Atenolol..G.‐1‐51‐6.

Table 5.40 Atenolol..G.‐1‐51‐12.

Table 5.41 Atenolol..G.‐1‐51‐24.

Table 5.42 Cimetidine..G.‐1‐119‐3.

Table 5.46 Cimetidine..G.‐1‐119‐24.

Table 5.47 Naproxen..G.‐1‐119‐3.

Table 5.48 Naproxen..G.‐1‐119‐4.

Table 5.49 Naproxen..G.‐1‐119‐6.

Table 5.50 Naproxen..G.‐1‐119‐12.

Table 5.51 Naproxen..G.‐1‐119‐24.

Table 5.52 Ranitidine..G.‐1‐119‐3.

Table 5.53 Ranitidine..G.‐1‐119‐4.

Table 5.1 Monthly data for (i) atenolol and Tenormin and (ii) ramipril and trita...

Chapter 6

Table 6.1 Forecasting performance of the Theta method for various seasonal adjus...

Table 6.2 Forecasting performance of the Theta method when the

value of the sho...

Table 6.3 Forecasting performance of the Theta method when a third theta line is...

Table 6.4 Forecasting performance of the Theta method when a short‐term linear t...

Table 6.5 Forecasting performance of the Theta method using automatic forecastin...

Table 6.6 Forecasting performance of the Theta method with optimized combination...

Table 6.7 Forecasting performance of the Theta method with combination weights s...

Table 6.8 Forecasting performance of the standard and robust Theta methods.

List of Illustrations

Chapter 1

Figure 1.1 A randomly selected series from M3: Theta‐model deflation.

Figure 1.2 A randomly selected series from M3: Theta‐model dilation.

Figure 1.3 An example of a Theta‐model extrapolation in an M3 series.

Figure 1.4 Microsoft Excel template for the basic model of the Theta method.

Figure 1.5Figure 1.5 Theta‐line calculations.

Figure 1.6 Theta‐line graph.

Figure 1.7 Theta‐line extrapolations.

Figure 1.8 Template in MS Excel: main graph.

Chapter 4

Figure 4.1 Time series plots of series CREDIT.

Figure 4.2 Time series plots of series UNRATE.

Figure 4.3 Time series plots of series EXPIMP.

Figure 4.4 Time series plots of series TRADE.

Figure 4.5 Time series plots of series JOBS‐1.

Figure 4.6 Time series plots of series JOBS‐2.

Figure 4.7 Time series plots of series FINANCE‐1.

Figure 4.8 Time series plots of series FINANCE‐2.

Chapter 5

Figure 5.1 The figure presents the differences between the number of prescriptio...

Guide

Cover

Table of Contents

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Forecasting with the Theta Method

Theory and Applications

Kostas I. Nikolopoulos

Prifysgol Bangor University Gwynedd, UK

Dimitrios D. Thomakos

University of Peloponnese Tripolis, GR

Copyright

This edition first published 2019

© 2019 John Wiley & Sons Ltd

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The right of Kostas I. Nikolopoulos and Dimitrios D. Thomakos to be identified as the authors of this work has been asserted in accordance with law.

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Dedication

Kostas

I extend my deep and sincere gratitude to all those who have contributed to my post‐DEng journey in academia from late 2002 onwards:

First, my “father” Vasillis, and my big “brother” Dimitrios with his unbelievable capacity.

Then, my younger “brother” Fotios who fortunately avoids the mistakes I made, and my oldest mate in the field Aris for the really great things we have done together.

Also, my good old friends and frequent collaborators Kostas and Vicky.

Always in debt to my wise mentors Shanti and Brian.

Last but not least, unbelievably proud of my academic “children” to date: Nicolas, Vassilios, Sam, Vivian, Greg, Sama, Christina, Tolu, Azzam, Waleed, Ilias, Chris, and Axilleas.

Dimitrios

This volume is just a quick stop in a journey that began many years ago.

A heartfelt thank you to Kostas for sharing the road with me, and may we continue to nonlinear paths in the years to come. The intellectual curiosity and research support of my PhD students Lazaros Rizopoulos and Foteini Kyriazi in preparing the manuscript is gratefully acknowledged. This volume is dedicated to my parents, those who first allowed me to prosper freely in my endeavors.

Author Biography

Kostas I. Nikolopoulos is Professor of Business Analytics at Bangor Business School, UK. He is also the Director of forLAB, a forecasting laboratory, and former Director of Research for the College of Business, Law, Education, and Social Sciences. He received both his Engineering Doctorate Diploma in Electrical and his Computer Engineering (MEng) from the National Technical University of Athens, Greece. He is an expert in time series analysis and forecasting, forecasting support systems, and forecasting the impact of special events. Professor Nikolopoulos has published in a number of prestigious journals and is an Associate Editor of Oxford IMA Journal of Management Mathematics and Supply Chain Forum: An International Journal.

Dimitrios D. Thomakos is Professor of Applied Econometrics and Head of the Department of Economics at the University of Peloponnese, Greece, and Senior Fellow and Member of the Scientific Committee at the Rimini Center for Economic Analysis in Italy. Dimitrios holds an MA, MPhil, and PhD from the Department of Economics of Columbia University, USA. His research work has appeared in several prestigious international journals in economics and finance such as the Review of Economics and Statistics, the Canadian Journal of Economics, the Review of International Economics, and many others.

Kostas and Dimitrios have worked together extensively coauthoring in the Journal of Management Mathematics and the Journal of Forecasting among many other journals and recently coedited two volumes for Springer‐Palgrave (A Financial Crisis Manual and Taxation in Crisis).

Preface

The Theta method is the most successful univariate time series forecasting technique of the past two decades, since its origination in the late 1990s. Jointly with the damped trend exponential smoothing, these are the two benchmarks that any newly proposed forecasting method aspires to outperform, so as to pass the test of time. This performance was originally demonstrated in the M3 competition in 2000 that the Theta method was the only method that outperformed Forecast Pro (www.forecastpro.com) and dominated a pool of 18 other academic methods and five more software packages.

The method originated in 1999 from Kostas and his supervisor Professor Vassilis Assimakopoulos, and was first presented in the International DSI 991 while the first full‐fledged academic article and description came in 2000 in the International Journal of Forecasting. In the same journal came the first critique three years later, led by Professor Rob Hyndman and his team in Monash for the similarity of the basic model from the method to simple exponential smoothing (SES) with drift.

The journal made a mistake in that they had neither used our review on the paper (as our objections were left unanswered) nor had they offered us a commentary to be published along that article – that is a standard practice in similar situations. This created more confusion as an immediate clear answer from us and Vassilis could not see the light of day; and it took a few more years until we found the means and media to post our response. That 2003 argument is now dead and buried, as every year a new and different successful model is coming out from the Theta method; and none of them is an SES with drift. This was always our counterargument – that the method is much much broader and we cannot see the forest for the trees… But this is history; and actually that 2003 article has probably created even more interest in the method, so welcome it is even if it did not do justice to the method.

A few working papers from 2005 onward and an article of ours in 2011 in Springer LNEE have set the record straight; and from that point on, joint work with Dimitrios in the IMA Journal of Management Mathematics2 proved why the method works well for unit roots – that were the dominant data‐generating processes (DGPs) in the M3 data – while more work in the Journal of Forecasting extended the method in the bivariate space, providing at the same time various successful extensions of it. This trend was picked up by research teams in Brazil, the United States, and, most notably, in the University of Bath and with Dr. Fotios Petropoulos – a scholar of the method – providing further extensions and optimizations. The same stands for the new students of Vassilis in the Forecasting and Strategy Unit (www.fsu.gr) in Greece who continue his legacy. When these lines are written, the original article of 2000 has achieved 209 citations in Google Scholar.

So now we know the method is far, far more than just SES with drift. It was not an easy journey to this point – but the forecasters' journey was never meant to be an easy one anyway from the very first day that the field was founded from Spyros Makridakis, Robert Fildes, and Scott Armstrong. From here onward, now that we have a fair share of the focus of the academic community – in forecasting and beyond – it is going to be a far more exciting one; and to kick start the process we proposed to Wiley – and the publishing house gladly and wisely accepted – to deliver the first book on the method that would capture the work done to date and, more importantly, lay the new theory and foundations for the years to come.

The book also includes a series of practical applications in finance, economics, and health care as well a contribution from Fotios on his honest view of what happened in the past and where things should go from now on. This is topped up by tools in MS Excel and guidance – as well as provisional access – for the use of R source code and respective packages.

When all is said and done, we do believe that this book is a valuable and useful tool for both academics and practitioners and that the potential of the method is unlimited. This is a forecast from forecasters and it comes with the usual caveat: the past success of the method does not guarantee the future one…but only time will tell!

Kostas & Dimitrios

February 2018

Notes

1

Assimakopoulos and Nikolopoulos (

1999

).

2

An article that for two years was reviewed in the

International Journal of Forecasting

(IJF) and never got published there – without a single mistake being found in it. We always took the stance that we should first submit in IJF – for historic reasons – any new work on the method, but that resulted in unnecessary delays in the publication process.

Part ITheory, Methods and Models

1The ‐legacy

By Kostas I. Nikolopoulos and Dimitrios D. Thomakos

The laws of nature are but the mathematical thoughts of God

Euclid 

1.1 The Origins…

(Written in first person by Kostas)

Once upon a time

There was a little boy keen on his (Euclidean) geometry…! It seems like yesterday…but actually it was 22 years ago – winter of 1996 – February of 1996. Me (Kostas), an eighth semester young and promising engineer‐to‐be, having completed a year ago my elective module in “Forecasting Techniques” and keen to start the (compulsory) dissertation in the National Technical University of Athens in Greece.

This is an endeavor students usually engage in during the 10 and last semester of MEng – but given that sufficient progress in my studies had been achieved to that point – I opted for an early start: this without being aware that it would mean moooore work; so a dissertation that usually takes 6 months to complete ended up an 18‐month‐long journey…

The topic “Nonparametric regression smoothing” or, in lay terms, time series smoothing (or filtering) with kernel methods – most notably nearest‐neighbor approaches – would later on prove useful in my academic career as well, for forecasting time series. For a non‐statistician – but math‐bombarded engineer – this was quite a spin‐off, but one that very much paid off intellectually and career‐wise in the years to come.

And, yes, it took 18 months – no discounts there from Vassilis – damping my hopes for a relaxed have‐nothing‐to‐do 10 semester. The reason was my Professor Vassilis Assimakopoulos and the fact that I was lucky enough to join him in the best part of his academic journey, while he was still an Assistant Professor and had this hunger to climb the academic ladder as soon as possible – just like any other academic, although none of them will never admit it, so keen to publish and supervise young promising students like me – and modest (ha ha!). Hope he has not regretted it over the years, but ours is a relationship that is still alive and kicking. I still get the odd phone call wherever I am in the world, and I always find it very hard to say no to any of his academic requests. Vassilis is an extremely bright guy with amazing ideas, all of which you have to pursue until one or none flourishes; but this is a model that I was and still am happy to follow and live by. And, thus began my DEng journey.

The task was simple and bluntly disclosed – in the very words of my supervisor: build a new univariate forecasting method that would win the M3 competition (that was about to be launched). In Greece in the year 1997, in an Engineering school, outperform the entire academic forecasting community and win a blind empirical forecasting competition: probably Mission Impossible! The quest for a new method started with much experimentation – that is out of the scope of this book – and resulted in the “The Theta Model: A Decomposition Approach to Forecasting.”

Earlier participatory attempts in the M3 competition along the lines of Theta‐sm had been far simpler, non‐versatile, and, as such, had never stood the test of time. But the big one had been achieved, and it was a brand new method… A method so versatile that it allowed for many new series to be created from the original data and each one of them could be extrapolated with any forecasting method, and the derived forecasts could be combined in all possible ways: the sky was the limit…

Any action brings on a reaction, inevitably so; in this case, it came from the same International Journal of Forecasting (IJF) with the article “Unmasking the Theta method” from Professor Rob J. Hyndman, who later became Editor‐in‐chief of the journal, and his student Baki Billah in Monash. I have extensively elaborated on this story in the Preface, but I reiterate here that despite that article not doing justice to the method, it did, however, add up to the discussion and kept the interest in the method alive. Looking back, it was an important thing because the next big set of results on the method was not published till 2008 and 2009 (in a series of working papers1 and in the respective presentations in the International Symposium on Forecasting, ISF2 ), where attempts to mix the method with neural networks were made, results in financial time series were presented, as well as a new theory for unit root data‐generating processes (DGPs) in 2009 – the early version of a paper published in the Institute of Mathematics and its Applications (IMA) and the superiority of the method was reconfirmed in the NN3 competition.

1.1.1 The Quest for Causality

Bring in then an econometrician … Then came Dimitrios – switch to the year 2005…spring; I was well situated in North West United Kingdom doing my postdoc in Lancaster. What a guy…I have never seen such capacity in my life. A bright and hardworking academic, educated in Columbia in theoretical econometrics – an ideal scholar to throw light on the why and when the method works; a valuable friend always willing to give sharp and short advice, exactly what at that stage a not‐so‐young‐any‐more academic needed. Somehow he managed to find me in the Daedalian jungle of the School of Electrical and Computer Engineering building in the National Technical University of Athens, where the Forecasting and Strategy unit – that I was still loosely affiliated with and regularly visiting – was based. After that we worked closely, with him leading the research on the model from 2006 to late 2009, coauthoring a series of working papers.

The academic year 2009–2010 was the turning point: 10 years after publishing the method in a descriptive format, Dimitrios finally laid the foundations of the quest why and when it works – starting with how the method works on unit root DGPs. For two years the paper was in review for IJF without a single error being found in the analysis. In the end, we had to employ a third reviewer only to have him say – to still say that despite all the analysis done as requested by the reviewers these results were not interesting enough for the audience of IJF. Academic judgment is academic judgment…and as such we respected it, but this delayed the whole process by two years – the paper was already out as a working paper since 2009.

The paper took two more years to see the light of day, and in 2014 we finally had why the Theta method works for unit roots (that many of the M3 data series actually are), with the article being published in the Oxford IMA Journal of Management Mathematics. We also had a series of more results from local behaviors of the models, weight optimizations, single theta‐line extrapolations, and many more. It was clear among the academic community that we were looking at a method that allowed for a series of models, to be developed within the same set of principles, more robust and accurate than the ETS or ARIMA family, but still equally or more versatile.

With the statement made and the road paved, the journey that followed was much easier. The year 2015 was another milestone, as the first multivariate extension was proposed: a bivariate Theta method that works very well. The results were presented in the JoF; special thanks go out to Editor Professor Derek Bunn for handling this submission so efficiently and for his personal attention to and handling of the paper.

The year 2016 was another important milestone as it was the first year that saw new results being presented by researchers other than Vassilis (and his team), me, and Dimitrios, or Rob (and his students). Fotios – that had in the past worked on the method with me and Vassilis – engaged in joint work with colleagues in Brazil led by Jose Fiorucci, as well as in the later stages of the project with Anne Koehler, provided further extensions and optimizations of the method and a link to state space models. This was the first time that a team – other than the aforementioned three – was using the method not just as a benchmark for evaluation purposes but was also developing a genuinely new theory.

That was the moment we decided it was about time for this book, and Wiley grabbed the opportunity. A book capturing progress in data but, more importantly, proposing a new and more complete theory on the method and many practical applications of it; with the dual scope of capturing the work done so far and emphatically and more prominently inspiring the next generations of forecasters to evolve the method onwards and upwards …

Reflecting on the journey so far, I believe it is truly an extraordinary story – especially given that it started in the cemented basement of an engineering school in Greece and not in a luxurious Ivy League business school; forecasting is a fragmented field where the ability to improve accuracy per se is very small and differences in performance in between models very very small, at the limits of statistical error. So when out of the blue a new method comes out organically from an academic group and has been evolved and is still evolving after 20 years… it must be something.

1.2 The Original Concept: THETA as in THErmosTAt

Vassilis wanted to see time series behaving like materials under the sun: high temperature would dilate them, while low temperature would make them shrink. This natural process seems quite intuitively appealing for the time series, as through a parameter you could possibly amplify/dilate or constrict/shrink the (curvatures) of a series. In fact, he wanted through this parameter to actually control the …temperature of the material: to control the dilation or shrinkage of the curvatures of the series; enacting exactly like a THErmosTAt. And this is how the name of the parameter came about: THETA or just the Greek letter . The when and how to use, how to extrapolate, and combine those derived dilated/constricted series (the so‐called Theta lines) was not decided in the first few months; and that is exactly what made Theta a method and not just a model. The ability to create as many as you want to (derived series), extrapolate with whatever method you want to, and combine them with whatever approach you want to – this is the true beauty and versatility of the original inception of the method.

In this section, we present more thoroughly the original foundations of the method as discussed for the first time in the proceedings of the International DSI in Athens (1999 proceedings); and more rigorously in the IJF in 2000, from which article most of the following text in this section has been adopted.

1.2.1 Background: A Decomposition Approach to Forecasting

There have been many attempts to develop forecasts based directly on decomposition (Makridakis 1984). The individual components that are usually identified are the trend‐cycle, seasonality, and the irregular components. These are projected separately into the future and recombined to form a forecast of the underlying series. This approach is not frequently used in practice. The main difficulties are in successfully isolating the error component as well as in producing adequate forecasts for the trend‐cycle component. Perhaps the only technique that has been found to work relatively well is to forecast the seasonally adjusted data with a well‐established extrapolation technique like, for example, using Holt's method (Makridakis 1998) or the damped trend method (Gardner 1985) and then adjust the forecasts using the seasonal components from the end of the data.