Makridakis Competitions

The Makridakis Competitions are a series of open competitions to evaluate and compare the accuracy of different time series forecasting methods. They are organized by teams led by forecasting researcher Spyros Makridakis and were first held in 1982.

Competitions

Summary

First competition in 1982

The first Makridakis Competition, held in 1982, and known in the forecasting literature as the M-Competition, used 1001 time series and 15 forecasting methods. According to a later paper by the authors, the following were the main conclusions of the M-Competition:

Statistically sophisticated or complex methods do not necessarily provide more accurate forecasts than simpler ones.
The relative ranking of the performance of the various methods varies according to the accuracy measure being used.
The accuracy when various methods are combined outperforms, on average, the individual methods being combined and does very well in comparison to other methods.
The accuracy of the various methods depends on the length of the forecasting horizon involved.

The findings of the study have been verified and replicated through the use of new methods by other researchers.
According Rob J. Hyndman "... anyone could submit forecasts, making this the first true forecasting competition as far as I am aware.
Newbold was critical of the M-competition, and argued against the general idea of using a single competition to attempt to settle the complex issue.
Before the first M-Competition, Makridakis and Hibon published in the Journal of the Royal Statistical Society an article showing that simple methods perform well in comparison to the more complex and statistically sophisticated ones. Statisticians at that time criticized the results claiming that they were not possible. Their criticism motivated the subsequent M, M2 and M3 Competitions that proved the thesis of the Makridakis and Hibon Study.

Second competition, published in 1993

The second competition, called the M-2 Competition or M2-Competition, was conducted on a larger scale. A call to participate was published in the International Journal of Forecasting, announcements were made in the International Symposium of Forecasting, and a written invitation was sent to all known experts on the various time series methods. The M2-Competition was organized in collaboration with four companies and included six macroeconomic series, and was conducted on a real-time basis. Data was from the United States. The results of the competition were published in a 1993 paper. The results were claimed to be statistically identical to those of the M-Competition.
The M2-Competition used much fewer time series than the original M-competition. Whereas the original M-competition had used 1001 time series, the M2-Competition used only 29, including 23 from the four collaborating companies and 6 macroeconomic series. Data from the companies was obfuscated through the use of a constant multiplier in order to preserve proprietary privacy. The purpose of the M2-Competition was to simulate real-world forecasting better in the following respects:

Allow forecasters to combine their trend-based forecasting method with personal judgment.
Allow forecasters to ask additional questions requesting data from the companies involved in order to make better forecasts.
Allow forecasters to learn from one forecasting exercise and revise their forecasts for the next forecasting exercise based on the feedback.

The competition was organized as follows:

The first batch of data was sent to participating forecasters in summer 1987.
Forecasters had the option of contacting the companies involved via an intermediary in order to gather additional information they considered relevant to making forecasts.
In October 1987, forecasters were sent updated data.
Forecasters were required to send in their forecasts by the end of November 1987.
A year later, forecasters were sent an analysis of their forecasts and asked to submit their next forecast in November 1988.
The final analysis and evaluation of the forecasts was done starting April 1991 when the actual, final values of the data including December 1990 were known to the collaborating companies.

In addition to the published results, many of the participants wrote short articles describing their experience participating in the competition and their reflections on what the competition demonstrated. Chris Chatfield praised the design of the competition, but said that despite the organizers' best efforts, he felt that forecasters still did not have enough access to the companies from the inside as he felt people would have in real-world forecasting.
Fildes and Makridakis argue that despite the evidence produced by these competitions, the implications continued to be ignored by theoretical statisticians.

Third competition, published in 2000

The third competition, called the M-3 Competition or M3-Competition, was intended to both replicate and extend the features of the M-competition and M2-Competition, through the inclusion of more methods and researchers and more time series. A total of 3003 time series was used. The paper documenting the results of the competition was published in the International Journal of Forecasting in 2000 and the raw data was also made available on the International Institute of Forecasters website. According to the authors, the conclusions from the M3-Competition were similar to those from the earlier competitions.
The time series included yearly, quarterly, monthly, daily, and other time series. In order to ensure that enough data was available to develop an accurate forecasting model, minimum thresholds were set for the number of observations: 14 for yearly series, 16 for quarterly series, 48 for monthly series, and 60 for other series.
Time series were in the following domains: micro, industry, macro, finance, demographic, and other. Below is the number of time series based on the time interval and the domain:

Time interval between successive observations	Micro	Industry	Macro	Finance	Demographic	Other	Total
Yearly	146	102	83	58	245	11	645
Quarterly	204	83	336	76	57	0	756
Monthly	474	334	312	145	111	52	1428
Other	4	0	0	29	0	141	174
Total	828	519	731	308	413	204	3003

The five measures used to evaluate the accuracy of different forecasts were: symmetric mean absolute percentage error, average ranking, median symmetric absolute percentage error, percentage better, and median RAE.
A number of other papers have been published with different analyses of the data set from the M3-Competition. According to Rob J. Hyndman, Editor-in-Chief of the International Journal of Forecasting, "The M3 data have continued to be used since 2000 for testing new time series forecasting methods. In fact, unless a proposed forecasting method is competitive against the original M3 participating methods, it is difficult to get published in the IJF."

Fourth competition (2018)

The fourth competition, M4, was announced in November 2017. The competition started on January 1, 2018 and ended on May 31, 2018. Initial results were published in the International Journal of Forecasting on June 21, 2018.
The M4 extended and replicated the results of the previous three competitions, using an extended and diverse set of time series to identify the most accurate forecasting method for different types of predictions. It aimed to get answers on how to improve forecasting accuracy and identify the most appropriate methods for each case. To get precise and compelling answers, the M4 Competition utilized 100,000 real-life series, and incorporates all major forecasting methods, including those based on Artificial Intelligence, as well as traditional statistical ones.
In his blog, Rob J. Hyndman said about M4: "The "M" competitions organized by Spyros Makridakis have had an enormous influence on the field of forecasting. They focused attention on what models produced good forecasts, rather than on the mathematical properties of those models. For that, Spyros deserves congratulations for changing the landscape of forecasting research through this series of competitions."
Below is the number of time series based on the time interval and the domain:

Time interval between successive observations	Micro	Industry	Macro	Finance	Demographic	Other	Total
Yearly	6538	3716	3903	6519	1088	1236	23000
Quarterly	6020	4637	5315	5305	1858	865	24000
Monthly	10975	10017	10016	10987	5728	277	48000
Weekly	112	6	41	164	24	12	359
Daily	1476	422	127	1559	10	633	4227
Hourly	0	0	0	0	0	414	414
Total	25121	18798	19402	24534	8708	3437	100000

In order to ensure that enough data are available to develop an accurate forecasting model, minimum thresholds were set for the number of observations: 13 for yearly, 16 for quarterly, 42 for monthly, 80 for weekly, 93 for daily and 700 for hourly series.
One of its major objectives was to compare the accuracy of ML methods versus that of statistical ones and empirically verify the claims of the superior performance of ML methods.
Below is a short description of the M4 Competition and its major findings and conclusion:
The M4 Competition ended on May 31, 2018 and in addition to point forecasts, it included specifying Prediction Intervals too. M4 was an Open one, with its most important objective : "to learn to improve forecasting accuracy and advance the field as much as possible".
The five major findings and the conclusion of M4:
There were five major findings of the M4 Competition.

The combination of methods were the best-performing in M4. Out of the 17 most accurate methods, 12 were "combinations" of mostly statistical approaches.
A method submitted by Slawek Smyl, Data Scientist at Uber Technologies, produced the most accurate forecasts as well as the most precise PIs. It used a "hybrid" approach utilizing both Statistical and ML features. According to sMAPE, it was close to 10% more accurate than the Combination benchmark of the Competition. It is noted that in the M3 Competition the best method was 4% more accurate than the same Combination.
The second most accurate method was a combination of seven statistical methods and one ML one, with the weights for the averaging being calculated by a ML algorithm, trained to minimize forecasting error through holdout tests. This method was jointly submitted by Spain's University of A Coruña and Australia's Monash University.
The first and the second most accurate methods also achieved success in specifying correctly the 95% PIs. These are the first methods known to have done so and do not underestimate uncertainty considerably.
The six pure ML methods submitted in the M4 performed poorly, none of them being more accurate than Comb and only one being more accurate than Naïve2. These results are in agreement with those of a recent study published in PLoS One.

The conclusion from the above findings was that the accuracy of individual statistical or ML methods is low and that hybrid approaches and combination of methods is the way forward in order to improve forecasting accuracy and make forecasting more valuable.