By Walter Dnes – Edited by Just The Facts
Investopedia defines “Leading Indicator” thusly…
A measurable economic factor that changes before the economy starts to follow a particular pattern or trend. Leading indicators are used to predict changes in the economy, but are not always accurate.
Economics is not the only area where a leading indicator is nice to have. A leading indicator that could predict in February, whether this calendar year’s temperature anomaly will be warmer or colder than the previous calendar year’s anomaly would also be nice to have. I believe that I’ve stumbled across exactly that. Using data from 1979 onwards, the rule goes like so…
- If this year’s January anomaly is warmer than last year’s January anomaly, then this year’s annual anomaly will likely be warmer than last year’s annual anomaly.
- If this year’s January anomaly is colder than last year’s January anomaly, then this year’s annual anomaly will likely be colder than last year’s annual anomaly.
This is a “qualitative” forecast. It doesn’t forecast a number, but rather a boundary, i.e. greater than or less than a specific number. I don’t have an explanation for why it works. Think of it as the climatological equivalent of “technical analysis”; i.e. event X is usually followed by event Y, leaving to others to figure out the underlying “fundamentals”, i.e. physical theory. I’ve named it the “January Leading Indicator”, abbreviated as “JLI” (which some people will probably pronounce as “July”). The JLI has been tested on the following 6 data sets, GISS, HadCRUT3, HadCRUT4, UAH5.6, RSS and NOAA
In this post I will reference this zipped GISS monthly anomaly text file and this spreadsheet. Note that one of the tabs in the spreadsheet is labelled “documentation”. Please read that tab first if you download the spreadsheet and have any questions about it.
The claim of the JLI would arouse skepticism anywhere, and doubly so in a forum full of skeptics. So let’s first look at one data set, and count the hits and misses manually, to verify the algorithm. The GISS text file has to be reformatted before importing into a spreadsheet, but it is optimal for direct viewing by humans. The data contained within the GISS text file is abstracted below.
Note: GISS numbers are the temperature anomaly, multiplied by 100, and shown as integers. Divide by 100 to get the actual anomaly. E.g. “43” represents an anomaly of 43/100=0.43 Celsius degrees. “7” represents an anomaly of 7/100=0.07 Celsius degrees.
- The first 2 columns on the left of the GISS text file are year and January anomaly * 100.
- The column after “Dec” (labelled “J-D”) is the January-December anomaly * 100
The verification process is as follows:
- Count all the years where the current year’s January anomaly is warmer than the previous year’s January anomaly. Add a 1 in the Counter column for each such year.
- For each such year, we count all where the year’s annual anomaly is warmer than the previous year’s annual anomaly and add a 1 in the Hit column for each such year.
| Jan(current) > Jan(previous) | J-D(current) > J-D(previous) | ||||
| Year | Counter | Compare | Hit | Compare | Comment |
| 1980 | 1 | 25 > 10 | 1 | 23 > 12 | |
| 1981 | 1 | 52 > 25 | 1 | 28 > 23 | |
| 1983 | 1 | 49 > 4 | 1 | 27 > 9 | |
| 1986 | 1 | 25 > 19 | 1 | 15 > 8 | |
| 1987 | 1 | 30 > 25 | 1 | 29 > 15 | |
| 1988 | 1 | 53 > 30 | 1 | 35 > 29 | |
| 1990 | 1 | 35 > 11 | 1 | 39 > 24 | |
| 1991 | 1 | 38 > 35 | 0 | 38 < 39 | Fail |
| 1992 | 1 | 42 > 38 | 0 | 19 < 38 | Fail |
| 1995 | 1 | 49 > 27 | 1 | 43 > 29 | |
| 1997 | 1 | 31 > 25 | 1 | 46 > 33 | |
| 1998 | 1 | 60 > 31 | 1 | 62 > 46 | |
| 2001 | 1 | 42 > 23 | 1 | 53 > 41 | |
| 2002 | 1 | 72 > 42 | 1 | 62 > 53 | |
| 2003 | 1 | 73 > 72 | 0 | 61 < 62 | Fail |
| 2005 | 1 | 69 > 57 | 1 | 66 > 52 | |
| 2007 | 1 | 94 > 53 | 1 | 63 > 60 | |
| 2009 | 1 | 57 > 23 | 1 | 60 > 49 | |
| 2010 | 1 | 66 > 57 | 1 | 67 > 60 | |
| 2013 | 1 | 63 > 39 | 1 | 61 > 58 | |
| Predicted 20 > previous year | Actual 17 > previous year | ||||
Of 20 candidates flagged (Jan(current) > Jan(previous)), 17 are correct (i.e. J-D(current) > J-D(previous)). That’s 85% accuracy for the qualitative annual anomaly forecast on the GISS data set where the current January is warmer than the previous January.
And now for the years where January is colder than the previous January. The procedure is virtually identical, except that we count all where the year’s annual anomaly is colder than the previous year’s annual anomaly and add a 1 in the Hit column for each such year.
| Jan(current) < Jan(previous) | J-D(current) < J-D(previous) | ||||
| Year | Counter | Compare | Hit | Compare | Comment |
| 1982 | 1 | 4 < 52 | 1 | 9 < 28 | |
| 1984 | 1 | 26 < 49 | 1 | 12 < 27 | |
| 1985 | 1 | 19 < 26 | 1 | 8 < 12 | |
| 1989 | 1 | 11 < 53 | 1 | 24 < 35 | |
| 1993 | 1 | 34 < 42 | 0 | 21 > 19 | Fail |
| 1994 | 1 | 27 < 34 | 0 | 29 > 21 | Fail |
| 1996 | 1 | 25 < 49 | 1 | 33 < 43 | |
| 1999 | 1 | 48 < 60 | 1 | 41 < 62 | |
| 2000 | 1 | 23 < 48 | 1 | 41 < 41 | 0.406 < 0.407 |
| 2004 | 1 | 57 < 73 | 1 | 52 < 61 | |
| 2006 | 1 | 53 < 69 | 1 | 60 < 66 | |
| 2008 | 1 | 23 < 94 | 1 | 49 < 63 | |
| 2011 | 1 | 46 < 66 | 1 | 55 < 67 | |
| 2012 | 1 | 39 < 46 | 0 | 58 > 55 | Fail |
| Predicted 14 < previous year | Actual 11 < previous year | ||||
Of 14 candidates flagged (Jan(current) < Jan(previous)), 11 are correct (i.e. J-D(current) < J-D(previous)). That’s 79% accuracy for the qualitative annual anomaly forecast on the GISS data set where the current January is colder than the previous January. Note that the 1999 annual anomaly is 0.407, and the 2000 annual anomaly is 0.406, when calculated to 3 decimal places. The GISS text file only shows 2 (implied) decimal places.
The scatter graph at this head of this article compares the January and annual GISS anomalies for visual reference.
Now for a verification comparison amongst the various data sets, from the spreadsheet referenced above. First, all years during the satellite era, which were forecast to be warmer than the previous year
| Data set | Had3 | Had4 | GISS | UAH5.6 | RSS | NOAA |
| Ann > previous | 16 | 15 | 17 | 18 | 18 | 15 |
| Jan > previous | 19 | 18 | 20 | 21 | 20 | 18 |
| Accuracy | 0.84 | 0.83 | 0.85 | 0.86 | 0.90 | 0.83 |
Next, all years during the satellite era, which were forecast to be colder than the previous year
| Data set | Had3 | Had4 | GISS | UAH5.6 | RSS | NOAA |
| Ann < previous | 11 | 11 | 11 | 11 | 11 | 11 |
| Jan < previous | 15 | 16 | 14 | 13 | 14 | 16 |
| Accuracy | 0.73 | 0.69 | 0.79 | 0.85 | 0.79 | 0.69 |
The following are scatter graph comparing the January and annual anomalies for the other 5 data sets:
HadCRUT3
HadCRUT4
UAH 5.6
RSS
NOAA
The forecast methodology had problems during the Pinatubo years, 1991 and 1992. And 1993 also had problems, because the algorithm compares with the previous year, in this case Pinatubo-influenced 1992. The breakdowns were…
- For 1991 all 6 data sets were forecast to be above their 1990 values. The 2 satellite data sets (UAH and RSS) were above their 1990 values, but the 4 surface-based data sets were below their 1990 values
- For 1992 the 4 surface-based data sets (HadCRUT3, HadCRUT4, GISS, and NCDC/NOAA) were forecast to be above their 1991 values, but were below
- The 1993 forecast was a total bust. All 6 data sets were forecast to be below their 1992 values, but all finished the year above
In summary, during the 3 years 1991/1992/1993, there were 6*3=18 over/under forecasts, of which 14 were wrong. In plain English, if a Pinatubo-like volcano dumps a lot of sulfur dioxide (SO2) into the stratosphere, the JLI will not be usable for the next 2 or 3 years, i.e.:
“The most significant climate impacts from volcanic injections into the stratosphere come from the conversion of sulfur dioxide to sulfuric acid, which condenses rapidly in the stratosphere to form fine sulfate aerosols. The aerosols increase the reflection of radiation from the Sun back into space, cooling the Earth’s lower atmosphere or troposphere. Several eruptions during the past century have caused a decline in the average temperature at the Earth’s surface of up to half a degree (Fahrenheit scale) for periods of one to three years. The climactic eruption of Mount Pinatubo on June 15, 1991, was one of the largest eruptions of the twentieth century and injected a 20-million ton (metric scale) sulfur dioxide cloud into the stratosphere at an altitude of more than 20 miles. The Pinatubo cloud was the largest sulfur dioxide cloud ever observed in the stratosphere since the beginning of such observations by satellites in 1978. It caused what is believed to be the largest aerosol disturbance of the stratosphere in the twentieth century, though probably smaller than the disturbances from eruptions of Krakatau in 1883 and Tambora in 1815. Consequently, it was a standout in its climate impact and cooled the Earth’s surface for three years following the eruption, by as much as 1.3 degrees at the height of the impact.” USGS
For comparison, here are the scores with the Pinatubo-affected years (1991/1992/1993) removed. First, where the years were forecast to be warmer than the previous year
| Data set | Had3 | Had4 | GISS | UAH5.6 | RSS | NOAA |
| Ann > previous | 16 | 15 | 17 | 17 | 17 | 15 |
| Jan > previous | 17 | 16 | 18 | 20 | 19 | 16 |
| Accuracy | 0.94 | 0.94 | 0.94 | 0.85 | 0.89 | 0.94 |
And for years where the anomaly was forecast to be below the previous year
| Data set | Had3 | Had4 | GISS | UAH5.6 | RSS | NOAA |
| Ann < previous | 11 | 11 | 11 | 10 | 10 | 11 |
| Jan < previous | 14 | 15 | 13 | 11 | 12 | 15 |
| Accuracy | 0.79 | 0.73 | 0.85 | 0.91 | 0.83 | 0.73 |
Given the existence of January and annual data values, it’s possible to do linear regressions and even quantitative forecasts for the current calendar year’s annual anomaly. With the slope and y-intercept available, one merely has to wait for the January data to arrive in February and run the basic “y = mx + b” equation. The correlation is approximately 0.79 for the surface data sets, and 0.87 for the satellite data sets, after excluding the Pinatubo-affected years (1991 and 1992).
There will probably be a follow-up article a month from now, when all the January data is in, and forecasts can be made using the JLI. Note that data downloaded in February will be used. NOAA and GISS use a missing-data algorithm which results in minor changes for most monthly anomalies, every month, all the way back to day 1, i.e. January 1880. The monthly changes are generally small, but in borderline cases, the changes may affect rankings and over/under comparisons.
The discovery of the JLI was a fluke based on a hunch. One can only wonder what other connections could be discovered with serious “data-mining” efforts.
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Willis Eschenbach says:
> February 3, 2014 at 2:56 am
> Now, is there value in saying that in a red-noise dataset
> of this type, January change and annual change are
> correlated? Yes, there is … but not what you think. It is
> valuable because it gives you a baseline that you have to
> beat in order to for your actual forecast to have skill.
> Otherwise, it’s no more than we’d expect.
Are we possibly talking past each other? I don’t care if hitting 80%+ correct is considered “zero skill”, due to “cheating” by using January data and taking advantage of auto correlation. I’ll gladly settle for it. Or are you saying that this was a fluke, and could be 80% wrong the next 20 or 30 years.
> That’s why I implored you a while back to learn to do
> Monte Carlo analysis … so you could see for yourself
> that you get the same results on red noise. Let me
> suggest again that you invest the time and effort to
> learn to do that, so you can determine the odds for yourself.
Do you have pointers to tutorials on general monte carlo simulation? My Google-searching returns either PDF’s full of complex equations+integrals, or some very problem-specific apps.
Willis: “Now, is there value in saying that in a red-noise dataset of this type, January change and annual change are correlated? Yes, there is … but not what you think. It is valuable because it gives you a baseline that you have to beat in order to for your actual forecast to have skill. Otherwise, it’s no more than we’d expect.”
This is an interesting point. ENSO index is a fairly crude and clunky three month running mean, so Jan ENSO is NDJ mean.
Now if we apply the same logic, the “ENSO-meter” has no more predicitive ability than OP’s effort. It is simply a restatement of the basic monthly AR1 structure of the data.
ENSO has the added interest that this relatively small region of SST seems to lag-correlate with many other basins. Though to what extent this represents common cause rather than the assumed causation has never been assessed to my knowledge.
So does ENSO have any predictive ability?
Doing the same exercise on the Met Office Hadley Centre Central England Temperature record from 1659-2013 gives the following results :-
January higher than previous and year higher than previous – 106; year lower 66 (success 62%)
January lower than previous and year lower than previous – 106; year higher 63 (success 63%)
There were 13 Januaries, and 2 years, that were the same as previous years.
The January Leading Indicator is not supported by the longest temperature record.
Whether or not the JLI has skill, it appears to provide us with an essential ingredient for policy making. This ingredient is information about the outcomes from policy decisions. None of the climate models referenced by AR4 provide us with information.
Richard Mallett says:February 3, 2014 at 8:18 am
Do you know what the post 1979 data shows?
January high and year high 9 year low 8 success 53%
January low and year low 10 year high 7 success 59%
That coin toss theory is looking better and better.
Terry Oldberg says:
February 3, 2014 at 8:30 am
Walter says:
OK, let me see if an example makes it any clearer. In the spirit of “January Leading Indicator” (JLI), let me propose a Monthly Leading Indicator (MLI). The Monthly Leading Indicator says that if a given month is warmer than last year, the average of that given month and the following month has an astounding 84% chance of being warmer than the average of those same two months in the previous year.
That is a much more impressive performance than the January Leading Indicator. Eighty-four percent correct, not just on some specially selected subset of the data (e.g. the subset of non-volcano years after 1978 where the dataset shows cooling, as in Walter’s example above), but on the entire GISS LOTI dataset, every year, N = 1595, a very solid result.
So, Walter and Terry … does my MLI (Monthly Leading Indicator) “provide us with an essential ingredient for policy making”?
Or to put it another way, “do you not see any value” in the impressive MLI results?
Me, I say a very positive no to both questions … I say the MLI is neither meaningful nor valuable. I say it’s in the category of such “successful” predictions as saying tomorrow will be like today. Yes, that is true in general … and no, it’s not particularly valuable information.
So I ask you both … does the 84% success rate of the MLI make it a valuable leading indicator providing us with essential information for policy-making? And if not, why not?
Bear in mind that the MLI and the JLI are identical in form, suffer from the same flaw (predictand includes the predictor variable), and differ only in the length of the average …
w.
Willis Eshenbach:
Thank you for taking the time to respond.
Whether the MLI provides information about the outcomes of events is unclear pending further work on your part. The JLI has the same shortcoming. Not withstanding the alleged “flaw,” with further work either indicator might be found to provide information to a policy maker. It is doubtful that this information, if present, would be of interest to a policy maker on global warming. Currently, policy makers on global warming make policy without having information. The IPCC seems to have duped policy makers into thinking they have information when they have none.
My interest in Mr. Dnes’s work flows from my belief that nearly all climatologists need tutoring in elementary ideas of probability theory, statistics, information theory and logic. Mr. Dnes’s work is of didactic value because recognizable in his methodology are the ideas of event, observed event, unobserved but observable event, outcome, condition, population, sample, frequency, relative frequency, probability and inference. All of these ideas are crucial to the creation of a model that: a) supplies information to a policy about the outcomes from his policy decisions and b) makes falsifiable claims. None of these ideas are evident in the report of Working Group I, AR4 on the allegedly scientific (but actually pseudo-scientific) basis for the IPCC’s claims, thus the need for tutoring climatologists.
Willis Eschenbach says: February 3, 2014 at 10:58 am
The answer is No, it can only be used as a Global Indicator, which is of no practical use.
If JLI worked at local levels it would be of some practical use in terms of at least ensuring that you had enough Salt & Grit to last the cold period, so that you don’t run out as we did in the UK a few years ago.
However as Richard Mallett has shown it certainly doesn’t work for the locale of Central England.
This illustrates a more general problem – that one can debate about how much the globe is warming or cooling per century; but this tells us little or nothing about whether individual governments at national / state / county level have a climate problem, and, what (if anything) they should be doing about it.
For completeness, I’d like to point out that use of the term “noise” is inappropriate in reference to the problem of prediction. This is true though the use of this term is appropriate in reference to the problem of retrodiction.
A communications system is an example of a retrodictor, for the outcomes of events lie in the past. A predictive system is an example of a predictor, for the outcomes lie in the future. Under Einsteinian relativity, a physical signal may travel from the present toward the future
as it can do so without its speed exceeding the speed of light. However, a physical signal may not travel from the future, toward the present as to do so its speed would have to exceed the speed of light. It follows that “noise” does not exist for a predictive system. Thus, the IPCC’s argument that that fluctuating temperatures prior to the recent run up in CO2 concentrations constitute “noise” with respect to a postulated “anthropogenic signal” fails from its violation of relativity.
Einsteinian relativity presents no barrier to the flow of information from the future to the present as information is non-physical. While relativity does not bar the flow of information, professional climatologists have barred this flow. They have done so by their choices in designing their studies of global warming. The net result is that we have gained nothing of any value in regulating the climate from the $200 billion thus far spent in pursuit of this goal.
Terry Oldberg
Re: “petitio principii, or the circular argument”
See petitio princippi fallacy search. This is also known as “begging the question”.
“””””…..Willis Eschenbach says:
February 2, 2014 at 6:53 pm
george e. smith says:
February 2, 2014 at 2:18 pm
Now I have seen everything, there is to know about the climate. A graph with absolutely no time scale at all.
George, you might google “scatterplot”. They don’t have time scales. Instead, they have pairs of values……”””””
Willis, I truly do appreciate your effort to explain Walters plots of annual anomalies versus monthly anomalies; but I must admit, I just don’t get it.
Now I do know what scatter plots are; I use them ALL the time. It is one of the few graphing means in Micro$oft Excel, that is of any use for engineering or scientific graphing. I use M$ excel exclusively to do all my math analysis; even though it is the most brain dead piece of trash, I have ever encountered, and I plot my results using the scatter plot, as pie charts, or bar graphs are simply not a good way to plot the surface profile of a precision optical element.
But when I saw both year and month, in the same graph, I fully expected to see no more than 12 plotted points, that being how many months on average, there are in an average year.
So if I look at any one dot on Walter’s first graph, I see an X-axis value on the monthly anomaly axis, with a yearly anomaly value on the y-axis, but no way to know what month or what year, these two numbers are extracted from, or even if they are from the same year or the same month.
I also know what Monte Carlo methods are. They are also used extensively in circuit design fro manufacturing purposes. (they were in the good old days.
You took a circuit design with a list of all of its component values, and their value tolerances. Then the computer ran a simulation of the circuit performance, with random values chosen for each element parameter value, within the stated tolerance range. The result was checked for compliance with the manufacturing spec, and then repeated many times, to find out how many of the circuits, would perform to the manufacturing spec. This information would be used to calculate manufacturing yields of good circuits, and figure the cost of the yield loss.
The designer, could then consider buying cheaper looser spec components to save some manufacturing cost; balancing that cost, against the loss to lower manufactured yields.
I don’t believe I ever designed a circuit that way. We always plugged in the worst case component tolerance value; say perhaps the value that would give the lowest gain for an amplifier, and did that simultaneously for ALL parameters, Then a SPICE or hand analysis, would calculate the result, to see if the gain (or whatever) exceeded the minimum manufacturing spec.
So all my designs were guaranteed by design, and always worked correctly unless some component had a catastrophic failure (from its stated spec).
That probably costs more, than Monte Carlo methodology; but how do you put a cost on a pissed off customer, who got one of your gizmos that was a fringe performer that MC said was a low probability occurrence.
Just like buying a winning lottery ticket; a non functioning gizmo, is not appreciated, no matter how unlikely the MC analysis said it would be. Somebody wins the lottery; and someone always buys your lemon; and then never buys another thing from you.
g
And yes, thanks for trying Willis.
Just the facts, Willis
Do a Monte Carlo simulation. Case A = 20,000 runs and Case B = 14,000 runs at 1,000 runs per set to simulate the results obtained in your exercise using 1,000x the actual data (20 and 14). Compute the probabilities. You will see the results are statistically significant. The null hypothesis will be rejected.
It’s a non-issue that the predictor is included in the prediction. What’s important is the certainty of the prediction. This exercise is equivalent to a statistical sampling where the sample size n = 1 (one month) results to an estimator with confidence level of approximately 80%. In statistical sampling, the sample (predictor) is included in the population (prediction).
Extend the analysis. Try n = 2 (Jan. and Feb.) and see if the confidence level will increase to 90-95%. Try a one-year predictor to predict 5-year and 10-year periods. Try a two consecutive-year predictor and see if the confidence level will increase.
Willis
I see the value of leading indicators. A colder winter in January than last year tells us that there’s 80% chance the rest of the year will be colder than last year. Do the analysis in many countries and it tells us the ‘global warming pause’ will likely extend for another year. At the very least, it debunks the claim that colder winter is also due to global warming. Colder winter indicates colder climate ahead. Perhaps global cooling.
george e. smith says:
February 3, 2014 at 4:47 pm
I must admit, I just don’t get it.
Please allow me to try. I will just use the RSS plot and illustrate a single point. There would be as many points as years, so if Walter plotted 30 years, there are 30 Januaries and 30 years. Each January and each year are represented by a single point for the 2 pieces of information. For 2013, the January anomaly on RSS was 0.439. And the average anomaly for all of 2013 was 0.218. So on the x axis, go to 0.439 which is the January anomaly. Then on the y axis, go to 0.218 which is the average anomaly for 2013. And you see a little diamond where 0.218 on the y axis intersects 0.439 on the x axis. As you noted, there is absolutely nothing to indicate that this point represents 2013.
Early on in the comments
philjourdan says:
> February 1, 2014 at 4:47 pm
>
> Is that pre or post adjustments?
Latitude says:
>February 1, 2014 at 4:49 pm
>
> Note: GISS numbers are…….fake
>
> http://stevengoddard.files.wordpress.com/2014/01/hidingthedecline1940-19671.gif
I decided to go back and do the full GISS data set. Then I remembered that I had once pulled the GISS data to the end of 2005 from “the wayback machine”. It was still kicking around on my hard drive. I wrote a script to process the data to the end of 2005. I ran the script on the old GISS data set, and the current data set. Note; both data sets were processed to the end of 2005 to provide an apples-to-apples comparison. The results…
data set issued January 2006, with numbers to December 2005
Warmer forecast
count hit fail
65 45 20
Colder forecast
count hit fail
58 37 21
And 2 Januarys equal to previous January
data set issued January 2014, with numbers to December 2013
Warmer forecast
count hit fail
70 51 19
Colder forecast
count hit fail
54 35 19
And 1 January equal to previous January
The *NET* difference was a handful of years changing. But “it’s worse than I thought”… in the 8 years between the 2 GISS outputs, 17 out of 125 forecast years (i.e. 13.6%) had some change that affected the analysis. This was any of current versus previous January over/under, or current year versus previous year over/under. Willis may be right about me “analysing red noise”, but not the way we thought. There’s an expression in computing “bit rot”, but this is ridiculous.
@walterdnes – Thank you for checking. But I was curious about the numbers you had used originally given the recent revelation of the changes by Goddard.
You are just affirming his work as well as your own
Obviously, it is sometimes possible and useful to indicate the time-ordering (where appropriate) of points on a scatter plot. For example, if there are just a few points, you may be able to put a number near each point. Or, you can mark one point and then connect successive points with unobtrusive straight lines (like a Poincare phase plot). Doesn’t always work. It may be too messy. And oftentimes, there is no inherent ordering of scatter plot points anyway (like students scores in math vs. scores in physics).
Willis, does the “skill level” become significant if you use GISS data 1955 to 2013, especially with 1991-1994 removed? See below for the long explanation.
One of the advantages of being retired is that I can stay up late to work on hunches. Given that the data from 1979 shows high JLI correlation, and analysis of the entire GISS data set shows lower correlation, then it’s obvious that the correlation must’ve been really bad sometime before 1979. I wrote a bash script to parse the data and spit out CSV-formatted running total counts in 3 columns…
Column 1 Year
Column 2 “Greater than” (hits – misses)
Column 3 “Less than” (hits – misses)
Looking at a graph shows
“Greater Than” forecasts verified
* flatline barely positive 1881 to 1918
* good correlation 1919 to late 1930’s
* flatline late 1930’s to 1955 (WWII and aftermath?)
* good correlation from 1955 onwards, except 1991 and 1992
“Less Than” forecasts verified
* flatline barely positive 1881 to 1926
* good correlation 1927 to late 1930’s
* flatline late 1930’s to 1955 (WWII and aftermath?)
* good correlation from 1955 onwards, except 1993 and 1994
Pinatubo hit the analysis badly. 1991-1994 was one of only two “4-consecutive-years-bust” situations in the analysis. The other one was 1897-1900. See http://en.wikipedia.org/wiki/Mayon_Volcano#1897_eruption
> Mayon Volcano’s longest uninterrupted eruption
> occurred on June 23, 1897 (VEI=4), which lasted for
> seven days of raining fire. Lava once again flowed down
> to civilization. Eleven kilometers (7 miles) eastward, the
> village of Bacacay was buried 15 m (49 ft) beneath the
> lava. In Libon 100 people were killed by steam and
> falling debris or hot rocks. Other villages like
> San Roque, Misericordia and Santo Niño became
> deathtraps. Ash was carried in black clouds as far as
> 160 kilometres (99 mi) from the catastrophic event,
> which killed more than 400 people
walterdnes says: February 3, 2014 at 8:59 pm “But “it’s worse than I thought”… in the 8 years between the 2 GISS outputs, 17 out of 125 forecast years (i.e. 13.6%) had some change that affected the analysis”
That is why I said A C Osborn says: February 3, 2014 at 3:39 am “So why would you want to conduct analysis on data that you are fairly sure does not represent what the Climate actually did and for that reason is NOT “valid”?”
David L. Hagen:
Thanks for the citations!
The petitio princippi fallacy does not apply. It is a consequence from an argument under the classical logic but this logic applies only to situations in which information for a deductive conclusion is not missing. Here, information is missing. Had Mr. Dnes’s model claimed that the sign of the change in the annual temperature anomaly determines the sign of the change in the annual temperature anomaly information would not have been missing and the model would have been guilty of this fallacy.
Dr. Strangelove says:
February 3, 2014 at 6:16 pm
I did a monte carlo simulation, several of them in fact, and reported on them above. In none of them were the results statistically significant. You’re simply making things up.
w.
Willis
I’m not making things up. Do a Monte Carlo simulation the way I described it. You can probably do it on Excel spreadsheet. You need a random number generator. Assign two possible outcomes: Outcome 1 and Outcome 2 as explained previously. Each with equal probability P = 0.5. Plot the histogram of the 20,000 runs. You will see a normal curve. Then compute the probabilities from the normal curve of the actual results of outcomes 1 and 2 obtained from temperature data. This is not a hoax.
Should we not be looking at the prediction for “the rest of the year”? If January is up and the rest of the year is down less than January was up, the year will still be up.
Willis
My proposed MC simulation is to mathematically prove that the results are statistically significant and reject the null hypothesis. However it is conceptually obvious why the results must be significant. The predictor is actually part of the prediction (population) as you pointed out. The former accounts for 1/12 = 8% of the latter. Clearly the two are causally linked hence disproving the null hypothesis that they completely independent events, that any correlation between the two are purely due to chance. The MC simulation is a simple mathematical proof of what is conceptually obvious.
You also did MC simulation but you correctly demonstrated a different point from the one I made. You demonstrated that the predictor can also predict a random function. It does not actually make the results trivial. It only proves that the method applies to both non-random and random functions. For example, we can do statistical sampling in the population of New York City. These are real data and the results are statistically significant. Then we can invent an imaginary city with random population characteristics and do statistical sampling. These are imaginary random data but the results are also statistically significant. It only proves the rules of statistics apply to both real and imaginary data.
Dr. Strangelove:
Thanks for sharing your view. It looks to me as though you’ve conflated some concepts.
As I’ll use the terms, a “Condition” is a condition on the Cartesian product of the values that are taken on by a model’s independent variables. An “Outcome” is a condition on the Cartesian product of the values that are taken on by a model’s dependent variables. A pairing of a Condition
with an Outcome provides a description of an event.
In establishment of the significance level of the predictions of a model, the appropriate null hypothesis is that the Conditions of the events are independent of the associated Outcomes. In this case, the so-called “mutual information” between the Conditions and the Outcomes is nil. With the mutual information nil, knowing the Condition of an event provides one with no information about the Outcome.
A “population” is a set of events. A “prediction” is an extrapolation from an observed Condition of an event to an unobserved but observable Outcome of the same event. A “predictor” is a condition. Thus, it is untrue that (as you claim) “the predictor is actually part of the prediction (population)” for a population is not a prediction and a predictor is neither a part of a prediction nor a part of a population.
Strangelove,
People here need to see your code. Here the code is necessary (or at least very useful) not because they doubt your results (although they may) but because it may give better clues about what you are talking about. Descriptions in English and even in mathematical formulas may be ambiguous and awkward. Computer code (often, even if in an unfamiliar language) is unambiguous. Computers won’t tolerate ambiguity. The code posted first need not be elegant – in fact the more simple-minded it is, the better at this point.
Terry
Apparently we are talking of different things. You are talking about functions and regression analysis. I’m talking about statistics and probability theory (though statistics is also used in regression analysis). In this context “outcome,” “population” and “prediction” are not how you define them.
Bernie
The concepts are simple enough to understand without computer programming, at least for those familiar with probability theory. If not, a google search on statistics would be more informative.
Dr. Strangelove:
Thank you for taking the time to reply and for sharing your ideas.
In this thread, I have not made reference to regression analysis. I have made reference to probability theory, statistics and information theory, In doing so, I have used the terminology that I have always used in discourse with professional statisticians. They have used the same terminology. If you favor a terminology that differs from this one, what is it?