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.
Of course, the cognoscenti will fully recognize that the Plasticine era was at the very height of the “modeling” tradition of theoretical science.
I thought this post was a quirky fun piece of weekend trivia until I read all the comments. I, for one, will keep the JLI in mind in future to see how it fares. Thank you for intriguing me, Walter. Since I suppose that Mother Nature doesn’t know her Gregorian calendar from her elbow, I would say that any observed correlation would be a fluke, but time will tell. That’s science. Observation leading to hypothesis and so on.
Leading on from your research here, I’d be fascinated to find out that a particular individual date had a colossally high correlation in terms of the annual anomaly, either plus or minus. Kind of a Groundhog Day that we should all eagerly anticipate.
Indeed, George, during the Plastocene optimum global mean temperature was notably higher than it is today. That’s why nowadays temperature data needs to be massaged for some considerable time to make it maleable enough to be suitable for modelling purposes.
😉
Willis: “Greg, while in other cases you might be right, in this case he’s arbitrarily removed about three-quarters of the GISS LOTI data.
Are you seriously arguing that there is a “good, accepted, physical reason” why three quarters of the data should have a different behavior??? Or the same for the data around the time of Pinatubo?”
I read that he removed 1991-93. How do you get from there to “three quarters of the GISS LOTI data “?
William T Reeves:
It is the events of Mr. Dnes’s model that need to be statistically independent. He ensures that his events are statistically independent by defining each of them on a different calendar year.
By the way, in his write-up Mr. Dnes references event X and event Y. As his is a multivariate model, it would have been appropriate to refererence event (X, Y) where the elements of X are the possible conditions and the elements of Y are the possible outcomes. A pairing of a condition with an outcome is a description of an event for a multivariate model.
Werner Brozek says:
> February 2, 2014 at 2:01 pm
>
> walterdnes says:
> February 1, 2014 at 6:55 pm
> HadCRUT4 0.488
>
> This is the number obtained from WFT or where you
> add all anomalies and divide by 12. However the
> HadCRUT4 site itself gives 0.486, presumably by taking
> into account such things as February having fewer days.
Interesting. I double-checked, and it is 0.488 from the downloaded data. I even edited out the leading “0.” from the text file, to make it all integers, and re-imported the year. This ensures a lot fewer possible round-off errors. It came out as 488. One more thing to watch for down the road.
A C Osborn says:
February 2, 2014 at 10:46 am
So … you ragged all over me, and you accused me not being able to read, but the reading error was yours.
And that is your apology?
All too typical of your style, A. C.
w.
Hoser says:
February 2, 2014 at 10:41 am
In other words, you don’t like my results, but you’re not saying why.
In other words, you don’t like my results, but you’re not saying why.
In other words, you like Walter’s results, but you’re not saying why.
OK, I saw it. You’ve calculated the results of Walter’s claims in a slightly different manner … which has nothing to do with what I said. In other words, you don’t like what I said, but you’re not saying why.
In other words, you can’t find one single flaw in my analysis … but you don’t like it. Oh, and you think Walter’s got no balls.
OK, Hoser, let me summarize your contribution to this thread. To date, you have seriously and firmly established that:
1. You don’t like my analysis, but you haven’t put forward one single solitary reason why you don’t like it. You have not pointed out any scientific flaws in my analysis, heck, you haven’t even tried … but by heaven, you don’t like it. OK, got it.
2. You think Walter has no balls.
Regarding the second one of these, I disagree entirely. Walter had the necessary nerve to put his scientific ideas out here, and to defend them. It takes real nerve to put a radical idea out in a head post on WUWT, hand around the hammers, and invite people to see if they can demolish the idea. As someone who does that regularly, I salute him.
And meanwhile, all you’ve had the blanquillos to do is complain about my analysis without providing even the slightest scientific objection to what I’ve done.
I’ll take Walter’s approach over yours any day,
w.
Greg says:
February 2, 2014 at 3:08 pm
Sorry for the lack of clarity. The GISS LOTI data is 133 years long. He’s arbitrarily decided to look at only a bit more than thirty years of the data, starting in 1979. Since the dataset starts in 1880, that’s one hundred years of data he’s removed from the GISS LOTI dataset.
How do you get from there to him not removing heaps of data?
Now, if later on he wants to do the analysis on the satellite data, fine. But that’s not a reason to ignore a hundred years of perfectly valid data.
w.
William T Reeves says:
February 2, 2014 at 12:21 pm
Couldn’t agree more. As I said above,
Terry Oldberg says:
February 2, 2014 at 3:44 pm
I agree that the events need to statistically independent of each other, as you say.
In addition, however, it’s considered bad form at a minimum to include your predictor variables in what you are trying to predict. Suppose I said “WOW! The average of the year up to September and the average for the whole year have the same sign almost every year!” Would you consider that impressive?
Of course not, because the data you know is included in what you are trying to predict.
Now, that’s by no means everything that’s wrong with Walter’s analysis. However, it is one of the things wrong with it, as William Reeves correctly surmised.
w.
Let me take another shot at explaining my objection, since some folks don’t get it.
In a dataset that contains multi-year, decadal, and multidecadal trends, we EXPECT that if this January is warmer than last January, that this year will be warmer than last year. It is not a peculiarity of the Earth’s climate system. It is not a “leading indicator”. It is the EXPECTED AND INEVITABLE result of the “persistence” in the dataset. It is just another example of the well-known fact that the best estimate for tomorrow’s temperature is today’s temperature … and the same is true for next week’s temperature, next month’s temperature, and (as Walter points out in the head post) next year’s temperature.
That is why we find Walter’s indicator operating in “red noise”, which is autocorrelated random noise. It’s not a secret window into the climate, it is a consequence of the nature of the dataset. We’ll find it in a host of natural datasets—the best estimate of tomorrow is today.
Now, weather forecasters of any sagacity know this. As a result, they are not surprised or impressed by it, as many people here seem to be.
The sagacious forecasters know about and use things like Walter’s indicator, but not as a forecasting method.
Instead, they use things like Walter’s indicator as a yardstick to measure their forecasts. Remember, Walter’s indicator is present in red noise data … so if you can’t do at least as well as Walter did, then your forecast sucks.
Well, except for the fact that Walter’s predictand contains the predictor variable … but you take my meaning, and Walter could correct that.
In that regard, wasn’t there a post here on WUWT a while back regarding how well the climate models did, year over year, compared with just assuming that next year would be the same as this year?
Now that would be a good analysis. Use a lag-1 based forecast like Walter’s (without the predictor/predictand overlap) to see if the climate models can beat a Walter-style analysis …
My regards to everyone,
w.
george e. smith says:
February 2, 2014 at 2:18 pm
George, you might google “scatterplot”. They don’t have time scales. Instead, they have pairs of values.
Huh? Walter is plotting what happened in a given year against what happened the year before. This kind of time-lagged plot is quite common, and for a good reason. It is often quite informative. And there is total regard given to the “time correspondence between them”. It is the basis upon which they are paired—any given year versus the previous year.
While I do love the idea of the “Plasticine Age”, I fear that your scorn and sarcasm merely reveal that you don’t understand what’s going on.
Nor is your example of plotting “plant species anomalies in the pre-Cambrian, against the animal species anomalies in the Plasticine” valid. Why? Because a scatterplot is used, as Walter did, for paired data, where each “x” is logically paired with a corresponding “y”.
Now as you point out, no such correspondence exists between the plant and animal species … but that just means you shouldn’t use a scatterplot for that particular pile of data. However, it means nothing about the utility of the scatterplot … there’s a good reason why it’s used so much, and Walter is using it properly.
w.
Willis Eschenbach says:
February 2, 2014 at 6:41 pm
The sagacious forecasters know about and use things like Walter’s indicator, but not as a forecasting method.
I believe the MET office would do better if they did use some version of what Walter used.
walterdnes says:
February 2, 2014 at 2:13 pm
Thanks, Walter. Yes, you are right.
It is also an equally good “leading” indicator of red noise random data … and in neither case is that a significant, unexpected, or unusual finding. It is an EXPECTED RESULT in any autocorrelated, persistent dataset.
As a result, your “leading” indicator is useful, but only as a yardstick against which to compare a real forecast system.
Best regards,
w.
PS—Calling it a “leading indicator” is totally misleading, since you are using data that does NOT lead the result you are trying to predict. You need to either change the name or change the method … my suggestion would be to compare January to the following Feb to Jan year.
A leading indicator is called a “leading indicator” because, well, it leads …
Walter, one more thing. I just ran the numbers. When you actually turn your method into a true leading indicator, by having January predicting the 12 months following January (and NOT including that January), your January correlation in the satellite era drops from 83% down to 74%. In addition, if we look at the entire GISS LOTI record, the January indicator drops from 70% to 61%.
So by what are usually considered to be improper methods in the world of forecasting (including your prediction variable January in the yearly average to be predicted), you’ve inflated your results by no less than 9% … which is why it’s generally considered to be a forecasting no-no.
My spreadsheet is available here, showing these results.
w.
Werner Brozek says:
February 2, 2014 at 7:27 pm
Thanks, Werner. Actually, the MET office uses a variety of metrics to assess the skill of their forecasts, which is an entire field of study in itself. See e.g. here, here, and here.
Google “forecast skill” for various discussions of the issues in the field.
w.
Willis Eschenbach (Feb. 2 at 8:17 pm):
You seem to base your conclusions regarding Mr. Dnes’s work upon the claim of David B. Stockwell that “if a methodology generates the same results with random data as with real data it is highly likely the methodology simply embodies a logical fallacy know [sic] as petitio principii, or the circular argument, where the conclusions are assumed in the premises.” Stockwell does
not provide a citation to a proof of his generalization that it is “highly likely the methdology simply embodies a logical fallacy…” Can you supply a citation?
Terry Oldberg says:
February 2, 2014 at 9:14 pm
Thanks, Terry. Interesting question, but I’m absolutely not basing anything on that. First, I’ve never read the Stockwell quote.
Second, only a part of Walter’s results are due to petitio principii. Both the premises and the conclusion contain January … but that’s only one month in twelve.
The other part of Walter’s positive results are due to the autocorrelation structure of the data.
I do not agree with his generalization, and I have no idea what he bases it on. In any case, I’m allergic to providing citations for another man’s claims. More to the point, I say something quite different.
I say the “Monte Carlo Method” which I used above is a valid way to estimate the effect of a methodology. So my citation would be to e.g. Wolfram Mathworld, which says:
I’ve used it for exactly that purpose, for “obtaining numerical solutions to problems which are too complicated to solve analytically”, in this case the expected success of Walter’s non-leading indicator.
At the Wolfram site, there are ten references to the history, development, and details of the method, along with four interactive examples (right column).
In addition, Wikipedia has a good description of the Monte Carlo method here.
Regards,
w.
Willis, you seem to be hung up on the term “leading indicator”. Would you be happier if I simply called it a “Rule of Thumb” or “Heuristic” or “Algorithm”? I’m using a term from economics, to refer to a climate event. Is there a technical “Statistics 101” definition of “Leading Indicator”? The January anomaly leads the annual (calendar-year) anomaly by 11 months, by definition. A more detailed definition is at http://www.investorwords.com/2741/leading_indicator.html
> An economic indicator that changes before the economy
> has changed. Examples of leading indicators include
> production workweek, building permits, unemployment
> insurance claims, money supply, inventory changes, and
> stock prices. The Fed watches many of these indicators
> as it decides what to do about interest rates. There are
> also coincident indicators, which change about the same
> time as the overall economy, and lagging indicators,
> which change after the overall economy, but these are
> of minimal use as predictive tools.
As far as I’m concerned, a growing workweek, rising building permit numbers, and falling unemployment means the economy has improved already. Some aspects of the economy react before others.
Another question; Given that last year’s January…
UAH5.6 anomaly was 0.497 and RSS anomaly was 0.439
assume that this year the anomalies are lower, 0.183 and 0.175 respectively (You don’t want to know how I got these numbers)
Do you not see any value in saying that 17 out of the last 19 times a similar event happened for RSS, and 17 out of 20 for UAH, during a non-volcanic year, the current year’s annual anomaly was lower than the previous year’s anomaly?
Just the facts, Willis
I’m impressed with the results of JLI. Offhand I see it’s not trivial. Do the math to prove the results are non-trivial.
Case A – this year’s January anomaly is greater (warmer) than last year’s January anomaly. Two possible outcomes: 1) This year’s annual anomaly is greater than last year’s annual anomaly; 2) This year’s annual anomaly is less than last year’s annual anomaly. Apply probability theory and null hypothesis. Assume each outcome is random and equally probable. P = 0.5 for outcomes 1 and 2.
From 1980-2013 data, actual results: Outcome 1 = 17/20 = P = 0.85; Outcome 2 = 3/20 = P = 0.15
Case B – this year’s January anomaly is less (colder) than last year’s January anomaly. Two possible outcomes: 1) This year’s annual anomaly is less than last year’s annual anomaly; 2) This year’s annual anomaly is greater than last year’s annual anomaly. P = 0.5 for outcomes 1 and 2.
From 1982-2012 data, actual results: Outcome 1 = 11/14 = P = 0.78; Outcome 2 = 3/14 = P = 0.22
Are these results due to chance? Apply Monte Carlo simulation to answer this. For Case A, run the simulation 20,000 times divided into 1,000 sets of 20 runs per set. Assign P = 0.5 for outcome 1 and 2. Plot outcome 1 in a histogram, each set represented by a frequency bar. Since this is a random event, the histogram will resemble a normal curve. Calculate the mean and the standard deviation.
Using the normal curve, you can compute the probability of the actual results in Case A occurring by chance. This is equivalent to the area under the curve. Do this also for Case B. I predict the probability is very small indicating the actual results are non-trivial.
Willis:” When you actually turn your method into a true leading indicator, by having January predicting the 12 months following January (and NOT including that January), your January correlation in the satellite era drops from 83% down to 74%. ”
That step makes sense, excluding correlating someting with itself.
So 74% is pretty much the 75% that someone (Willis?) said ealier would be expected from the autocorrelated nature of the data.
You derived that from “satellite era” which includes the Mt P perturbation, so I wouid presumably there would be a somewhat higher result if 19-93 was excluded. That means that this “predictor” is picking up something about the structure of the data beyond monthly AR1, though it is not a huge difference.
That presumably results from some longer term (inter-annual) structure in the data.
AR1 can easily be removed by taking first difference of the data which is what I do pretty much systematically when analysing any climate time series . Perhaps doing the same process on the first diff would be more enlightening.
Willis: “Sorry for the lack of clarity. The GISS LOTI data is 133 years long. He’s arbitrarily decided to look at only a bit more than thirty years of the data, starting in 1979. Since the dataset starts in 1880, that’s one hundred years of data he’s removed from the GISS LOTI dataset.
How do you get from there to him not removing heaps of data?
Now, if later on he wants to do the analysis on the satellite data, fine. But that’s not a reason to ignore a hundred years of perfectly valid data.”
===
Thanks for the clarification. It would make sense to use all the data unless there is an explicit reason for not doing so.
However, calling GISS LOTI “perfectly valid data” I would question. It’s one of the datasets I have the least faith in due the constant cooling the past “corrections” and the declared activist stance of those in charge of creating, adjusting and maintaining the data.
walterdnes says:
February 2, 2014 at 11:54 pm
Walter, it’s fine whatever you want to call it. I’m trying to emphasize that including your predictor variable in the results you are trying to predict has given you a totally bogus 9% inflation of your results. To try to emphasize that, I pointed out that a leading indication has to occur BEFORE what you are trying to predict … otherwise it’s hardly leading, is it?
First off, in the UAH dataset, out of the 34 January-to-January intervals, only 13 have been negative. Of these, 11 times the year has gone the same way that the January went. So I haven’t a clue where you are getting your data.
The problem is that your results are statistically indistinguishable from the results I get by applying your method to random “red noise”. In other words they are not a characteristic of the climate. They are a characteristic of the type of dataset.
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.
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.
w.
I would like to take a look at what Mr Eschenbach said at February 2, 2014 at 6:07 pm and I quote
“He’s arbitrarily decided to look at only a bit more than thirty years of the data, starting in 1979.
Since the dataset starts in 1880, that’s one hundred years of data he’s removed from the GISS LOTI dataset.”
and
“But that’s not a reason to ignore a hundred years of perfectly VALID data.”
I am sure Mr Eschenbach is aware that GISS data has been the subject of massive adjustments over the past 20+ years.
The least adjusted data is during the Satellite era where their readings have kept it slightly more honest than the data prior to 1979.
The data prior to 1979 has been adjusted to lower the older temperatures and to remove some of the variability of the 1930/40 period and the 1940/1975 period, Steven Goddard and many others have done a great deal of work on this.
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”?
Even the period that he has used has shown marked differences between all the datasets from 1979 onwards.
Although I think he has found something very interesting, I am not sure of it’s value though. It is nice to know that in January you can quite accurately predict the Global Temperature movement for that year, especially compared to other GCM’s output.
But it doesn’t seem to be very useful, it doesn’t help Farmers plan their crops, or Authorities plan for Ice, Snow, Flood or Drought etc.
However if what he has shown also works at the more “Local” level, Continental, Country, State or area that could prove to be much more useful for planners.
Willis Eschenbach says:February 1, 2014 at 9:15 pm
Based on the Mangled GISS data of the last 130 years, it was used to create some “Proxy” random data, the GISS data was Detrended and Random data was generated using the AR and MA coefficients (0.93 and -0.48, typical values for global temperature datasets).
How then do all 7 sets of Random data show almost identical Trends rather than 7 straight lines?
I assume that the random data was therefore placed around the original GISS Trend line.
So what was actually measured when the leading Indicator was used is the effectiveness of it’s use to predict a fixed Trend using random values and as you would expect due to the trend it worked 66 percent of the time.
But as we all know the Global Temperature WAS NOT just a fixed trend prior to NASA/GISS involvement, it was a low level fixed trend with an approximately 60 year cycle overlaid on it, where the temperature in the period of 30/40s was at least as high as it is now.
So was it a fair test, was it really comparing Oranges with Oranges?