It has often been claimed that alarm about global warming is supported by observational evidence. I have argued that there is no observational evidence for global-warming alarm: rather, all claims of such evidence rely on invalid statistical analyses.

Some people, though, assert that the statistical analyses are valid. Those people assert, in particular, that they can determine, via statistical analysis, whether global temperatures have been increasing more than would be reasonably expected by random natural variation. Those people do not present any counter to my argument, but they make their assertions anyway.

In response to that, I am sponsoring a contest: the prize is $100 000. Anyone who can demonstrate, via statistical analysis, that the increase in global temperatures is probably not due to random natural variation should be able to win the contest.

A time series is any series of measurements taken at regular time intervals. Examples include the following: prices on the New York Stock Exchange at the close of each business day; the total rainfall in England each month; the total wheat harvest in Canada each year. Another example is the average global temperature each year.

Most data sets used in the study of climate are time series. Yet there are almost no climate scientists that have competence in the statistical analysis of time series.

Statistical incompetence has misled climate scientists into believing that they can distinguish between purely random series and series generated with a trend. The purpose of the Contest is to show that such a belief is false, at least for the series of global temperatures.

Terms of the Contest
The file Series1000.txt contains 1000 simulated time series. Each series has length 135: the same length as that of the most commonly studied series of global temperatures (which span 1880–2014). The 1000 series were generated as follows. First, 1000 random series were obtained (for more details, see below). Then, some of those series were randomly selected and had a trend added to them. Each added trend was either 1°C/century or −1°C/century. For comparison, a trend of 1°C/century is greater than the trend that is claimed for global temperatures.

A prize of $100 000 (one hundred thousand U.S. dollars) will be awarded to the first person who submits an entry that correctly identifies at least 900 series: which series were generated without a trend and which were generated with a trend.

For instructions on how to submit an entry, see the Contest Entry page. Each entry must be accompanied by a payment of $10; this is being done to inhibit non-serious entries. There is a limit of one entry per person.

A person submitting an entry must also specify their real name. Names will be kept confidential, except in very unusual circumstances. If someone wins the Contest, though, then their name will be made public. If the name that they specified at submission was not real, then the prize is forfeited.

Anyone considering submitting an entry should read my critique of the statistical analyses that have been done by the IPCC. The critique illustrates some of the potential pitfalls in analyzing the time series.

(During the generation of the 1000 series, in the first step described above, the initial 1000 random series were obtained via a trendless statistical model, which was fit to a series of global temperatures. The trendless statistical model is preferable to the trending statistical model relied upon by the IPCC, when the models are compared via relative likelihood.)

After someone submits an entry to the Contest, the entry is assessed as to whether it is prize-winning. The person who submitted the entry is then informed about the result of the assessment. No further information is provided to the submitter: in particular, the submitter is not informed about how many of the 1000 series their entry correctly identified.

The Contest closes at the end of 30 November 2016 (UTC), or when someone submits a prize-winning answer, whichever comes first.

When the Contest closes, the computer program (including the random seed) that generated the 1000 series will be posted here. As an additional check, the file Answers1000.txt identifies which series were generated by a trendless process and which by a trending process. The file is encrypted. The encryption key and method will also be posted here when the Contest closes.

UPDATE [2016-12-01]. The Contest has now closed. No winning entry was received. The ANSWER, the PROGRAM (Maple worksheet), and the function to produce the file Answers1000.txt (with the random seed 7654321) are now available. There are also some Remarks on the Contest.


For a detailed discussion of the statistical mistakes that almost all climate scientists have been making, see my critique of the statistical analyses in the IPCC’s 2013 Assessment Report. The critique concluded that the statistical analyses are seriously incompetent, and further, that no one has yet drawn valid inferences, via statistics, from climatic time series.

My critique was submitted to the UK Department of Energy and Climate Change, by Lord Donoughue. Lord Donoughue also arranged for a meeting at the Department: with the Department’s Under Secretary of State and the Department’s Chief Scientific Adviser, among others. The meeting was held on 9 January 2014.

At the meeting, the Chief Scientific Adviser claimed that there was observational evidence for significant global warming. I claimed that there was no such evidence—as per my critique. The Chief Scientific Adviser maintained his claim, but was unable to present any such evidence at the meeting. He said, though, that he would later send details of such evidence to Lord Donoughue.

Details of such evidence, however, were never sent. Thus, the Department seemed to effectively acknowledge that my claim was correct: observational evidence does not exist. Furthermore, twelve days after the meeting, on 21 January 2014, the Under Secretary made a statement in Parliament on behalf of the UK government. The statement was as follows.

Her Majesty’s Government does not rely upon any specific statistical model for the statistical analysis of global temperature time series.

Global temperatures, along with many other aspects of the climate system, are analysed using physically-based mathematical models, rather than purely statistical models.  [HL4497]

In plain English, the UK government stopped using or relying on statistical analysis of observational evidence for global warming; instead, the government started relying solely on computer simulations of the climate system. In short, the government effectively accepted the main conclusions of my critique.

Related analyses in statistical textbooks

Some textbooks on the statistical analysis of time series have indicated that the series of global temperatures seems to be trendless. Two such textbooks are Introductory Time Series with R, by Cowpertwait & Metcalfe, and Time Series Analysis and Its Applications, by Shumway & Stoffer (full references are below).

Cowpertwait & Metcalfe actually present analysis for a series of temperatures for the Southern Hemisphere. The analysis concludes that Southern Hemisphere temperatures are reasonably described as trendless and random. Shumway & Stoffer present analysis for the series of global temperatures (with some of the analysis set as an exercise for the student). The analysis indicates that global temperatures are reasonably described as trendless and random.


Notes that were relevant while the Contest was running are available.

Cowpertwait P.S.P., Metcalfe A.V. (2009), Introductory Time Series with R (Springer). [The analysis of Southern Hemisphere temperatures is in §7.4.6.]

Shumway R.H., Stoffer D.S. (2011), Time Series Analysis and Its Applications (Springer). [Example 2.5 considers the annual changes in global temperatures and argues that the average of those changes is not significantly different from zero; set Problem 5.3 elaborates on that.]

Douglas J. Keenan