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.


22 November 2015
The generation of the 1000 series relies on the generation of random numbers. That presents a difficulty, because current computers do not generate truly random numbers. There is a widely-used method of addressing the difficulty: use a computer routine that generates numbers that seem to be to random (i.e. fake it). Numbers generated by that method are called “pseudorandom”.

A computer routine that generates pseudorandom numbers is called a “pseudorandom number generator” (PRNG). PRNGs have been studied by computer scientists for decades. All PRNGs have weaknesses, but some have more serious weaknesses than others.

The Contest was announced on 18 November 2015. Shortly afterward, a few people pointed out to me that the PRNG I had used might not be good enough. In particular, it might be possible for researchers to win the Contest by exploiting weaknesses in the PRNG. I have been persuaded that the risk might be greater than I had previously realized.

The purpose of the Contest is to test researchers' claimed capability to statistically analyze climatic data. If someone were to win the Contest by exploiting a PRNG weakness, that would not conform with the purpose of the Contest. Ergo, I regenerated the 1000 series using a stronger PRNG, together with some related changes. Note that this implies that the files Answers1000.txt and Series1000.txt were both revised.

The 1000 regenerated series were posted online four days after the Contest was announced—on 22 November 2015. (Each person who submitted an entry before then was invited to submit a new entry, with no fee.) When the Contest closes, the computer program for the original 1000 series and the encryption key for the original Answers1000 file will be posted here—together with the program and encryption key for the regenerated series.

18 August 2016
A paper by Lovejoy et al. was published in Geophysical Research Letters. The paper is about the Contest.

The paper is based on the assertion that the Contest “used a stochastic model with some realism”; the paper then argues that the Contest model has inadequate realism. The paper provides no evidence that I have claimed that the Contest model has adequate realism; indeed, I do not make such a claim. Moreover, my critique of the IPCC statistical analyses (discussed above) argues that no one can choose a model with adequate realism. Thus, the basis for the paper is invalid. I pointed that out to lead author of the paper, Shaun Lovejoy, but Lovejoy published the paper anyway.

When doing statistical analysis, the first step is to choose a model of the process that generated the data. The IPCC did indeed choose a model. I have only claimed that the model used in the Contest is more realistic than the model chosen by the IPCC. Thus, if the Contest model is unrealistic (as it is), then the IPCC model is even more unrealistic. Hence, the IPCC model should not be used. Ergo, the statistical analyses in the IPCC Assessment Report are untenable, as the critique argues.

For an illustration, consider the following. Lovejoy et al. assert that the Contest model implies a typical temperature change of 4 °C every 6400 years—which is too large to be realistic. Yet the IPCC model implies a temperature change of about 41 °C every 6400 years. (To confirm this, see Section 8 of the critique and note that 0.85×6400/133 = 41.) Thus, the IPCC model is far more unrealistic than the Contest model, according to the test advocated by Lovejoy et al. Hence, if the test advocated by Lovejoy et al. were adopted, then the IPCC statistical analyses are untenable.

I expect to have more to say about this in the future.

01 December 2016
Regarding the 1000 series that were generated with the weak PRNG (prior to 22 November 2015), the ANSWER, the PROGRAM (Maple worksheet), and the function to produce the file Answers1000.txt (with the random seed being the seventh perfect number minus one) are now 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