[pup55]

As part of a continuing series, here is another attempt to try to predict the peak of a scarce resource by trying to predict the peak in organisms dependent on it.

Today's example is the sales of Walmart corp, a frequent topic in other parts of the forum, and thought by many to be completely dependent on the high-energy-consumption consumer culture so often noted by the posters and other commentators.

The data is easy to come by. Annual reports going back to the 70s are available from http://www.walmartstores.com

I have chosen not to adjust the data for inflation. Also, maybe it would have been good to include the total sales for others in this category (Target and Kmart) to understand the whole market, so if anyone wants to provide the data I will curve fit it. Old Kmart sales data kind of hard to come by.

Again, the methodology is to use the “logistic curveâ€

[Jack]

Intriguing. I'll want to study this more later...

[pup55]

I take back what I said in (f) above, by the way. The recent sales figures, year-over-year, are up about 2% from the same period a year ago. A couple of years ago, they were up about 11-12% year over year, so their sales growth is, indeed, slowing. Their FY ends in January.

[Colorado-Valley]

In a peak-energy scenario, I wonder if Wal-Mart strategists would have the foresight and ability to morph the company into a local-economy distributor if the global model goes away.

I have my doubts, since the company really is built on foreign labor and cheap energy for global transport of goods. Efficiency and scale might no longer work without mass markets.

Maybe they could franchise their old buildings into community flea markets.

[Soft_Landing]

For visual consumption

[pea-jay]

I dont think the sales numbers are the way to go. There are too many variables that affect the final figure.

I think a better way to go would be by number stores. That is a tangible number and ma be more useful

[JohnDenver]

[quote="pup55"]b. Just as an exercise, I tried to predict the peak as if it were 1995, that is, using the same methodology but without the last 10 years of data, to see what happens to the prediction for an organism that is still on the upslope of this model. In this case, the peak prediction was 2004, so not all that far off, but the “peak heightâ€

[ohanian]

[quote]b. Just as an exercise, I tried to predict the peak as if it were 1995, that is, using the same methodology but without the last 10 years of data, to see what happens to the prediction for an organism that is still on the upslope of this model. In this case, the peak prediction was 2004, so not all that far off, but the “peak heightâ€

[Carmiac]

There is a big problem with applying Hubbert modeling to this kind of thing. Hubbert modeling applies to recovery of a finite, non-renewable resource. Consumers and money are both renewable resources.

[Soft_Landing]

$this->bbcode_second_pass_quote('JohnDenver', 'J')ust curious, but why did you throw out the prediction from the <1995 data? It sounds like the model blew up and gave you a bum prediction.

[Aaron]

1. Gates, William H. III, United States, 46, $52.8, Microsoft

2. Buffett, Warren E., United States, 71, $35.0, Berkshire Hathaway

3. Albrecht, Karl and Theo, Germany, $26.8, retail

4. Allen, Paul G., United States, 49, $25.2, Microsoft

5. Ellison, Lawrence J., United States, 57, $23.5, Oracle

6. Walton, Jim C., United States, 54, $20.8, Wal-Mart

7. Walton, John T., United States, 56, $20.7, Wal-Mart

8. Walton, Alice L., United States, 53, $20.5, Wal-Mart

8. Walton, S. Robson, United States, 58, $20.5, Wal-Mart

10. Walton, Helen R., United States, 82, $20.4, Wal-Mart

[pup55]

patrickjford:

The reason I used sales rather than the number of stores is that nowadays, their sales includes places like Sam's and the Supercenters, which are a lot bigger than the little old walmarts used to be.

Johndenver:

I think you are catching on. I didn't really "throw out" the last 10 years of data, but used various subsets of the data to test how partial data sets affect the estimate of the peak. We are working with a partial set of data for oil and hydrocarbons, aren't we? The root question is: how useful is this form of modeling, based on partial data sets, in predicting a peak event? You can make the argument that if it blows up for some subset of the data, is might not be necessarily valid for the "complete" data set either, since it is not really "complete" but just "complete as far as we know today".

Most importantly, since the Hubbert model as practiced by Lahererre and others (including APSO) is based on more or less the same methodology, could it blow up when trying to predict the "oil peak"? Maybe a lot of the forum readers are really worried about predictions based on a mathematical model concept that could be questionably useful.

So this is my guinea pig. Judge it if you will, but judge fairly.

Ohanian:

Okay.

Carmiac:

If you read Savinar's book, he makes the statement that "money" per say, is government issued scrip that represents, in essence, some incremental amount of "energy". It's an interesting section, in there somewhere if you can find it. Based on that, why does this not make sense? Energy is finite, therefore Walmart is finite. If energy availability peaks, Walmart, or to be more accurate, walmart plus other similar operations in the same market should peak at about the same time. If you believe Jay Hanson, so should population.

Seems to me like money, itself, is either a scarce resource that has limits, or represents a scarce resource that has limits. Some may argue otherwise.

If you think of Walmart as an organism that takes in money (energy) and spews out merchandise, growing in the process, and is dependent on the energy and cultural infrastructure of the environment (money) for its survival, maybe it is subject to the "logistic peak" concept.

Soft Landing:

Thanks for your help in graphing this. I think it looks pretty good. I will play with the partial data sets above, and would be happy to run other data sets through the model for the entertainment and education of the forum. I'm getting better at fitting these curves, if I do say so myself.

[pup55]

The peak shifts leftward (sooner) the smaller the data set, The height of the peak shifts quite a bit, though. Reason: It's dependent on the "ultimate reserves" Q-inf which has to be adjusted to improve the prediction of the cumulative sales for each of the estimates vs. actual sales for that period.

In fact, once you get it loaded into your spreadsheet, you can check and see how well the predictions are. Sum the "actual" sales figures from the start until, say, 1985, and then the "Predicted" sales figures from the start until 1985, and compare.

The interesting paper by Lahererre below has some guidelines about when to apply the Hubbert model, and when not.

http://dieoff.org/page191.htm

$this->bbcode_second_pass_code('', '

Yr No 1980 1985 1990 1995 2000 2004 Actual
1967 1 - - - - - 0.013
1968 2 0.05 0.15 0.15 .0.14 0.13 0.13 -
1969 3 0.06 0.18 0.19 0.18 0.17 0.17 -
1970 4 0.08 0.22 0.24 0.23 0.21 0.21 0.038
1971 5 0.10 0.27 0.30 0.30 0.27 0.27 0.044
1972 6 0.12 0.33 0.37 0.38 0.34 0.34 0.078
1973 7 0.16 0.40 0.47 0.48 0.44 0.43 0.124
1974 8 0.20 0.49 0.59 0.61 0.56 0.55 0.167
1975 9 0.26 0.60 0.74 0.77 0.71 0.70 0.236
1976 10 0.34 0.73 0.93 0.98 0.90 0.89 0.34
1977 11 0.43 0.89 1.17 1.24 1.14 1.13 0.478
1978 12 0.55 1.09 1.47 1.58 1.45 1.43 0.678
1979 13 0.71 1.33 1.85 2.01 1.84 1.82 0.9
1980 14 0.90 1.62 2.33 2.55 2.34 2.31 1.248
1981 15 1.16 1.97 2.93 3.23 2.97 2.93 1.642
1982 16 1.48 2.39 3.67 4.10 3.77 3.72 2.444
1983 17 1.88 2.91 4.61 5.19 4.78 4.72 3.376
1984 18 2.40 3.53 5.78 6.57 6.06 5.98 4.666
1985 19 3.04 4.28 7.24 8.31 7.67 7.58 6.4
1986 20 3.85 5.19 9.06 10.50 9.70 9.60 8.451
1987 21 4.85 6.27 11.32 13.24 12.25 12.14 11.909
1988 22 6.08 7.56 14.12 16.67 15.45 15.33 15.959
1989 23 7.57 9.09 17.57 20.92 19.44 19.34 20.649
1990 24 9.36 10.89 21.81 26.16 24.40 24.33 25.81
1991 25 11.45 13.00 26.96 32.58 30.52 30.54 32.601
1992 26 13.85 15.44 33.19 40.37 38.01 38.20 43.886
1993 27 16.50 18.24 40.63 49.69 47.10 47.57 55.483
1994 28 19.33 21.40 49.42 60.68 57.98 58.94 67.344
1995 29 22.20 24.91 59.63 73.38 70.80 72.55 82.494
1996 30 24.90 28.74 71.26 87.70 85.61 88.60 93.627
1997 31 27.23 32.82 84.18 103.35 102.32 107.14 105
1998 32 28.94 37.03 98.10 119.79 120.57 128.04 118
1999 33 29.84 41.21 112.52 136.21 139.75 150.89 137.63
2000 34 29.84 45.19 126.74 151.54 158.91 174.89 165.01
2001 35 28.94 48.75 139.86 164.58 176.80 198.87 191.33
2002 36 27.23 51.67 150.92 174.10 192.01 221.25 217.8
2003 37 24.90 53.74 158.93 179.14 203.12 240.28 229.6
2004 38 22.20 54.82 163.16 179.14 209.00 254.19 256.3
2005 39 19.33 54.82 163.16 174.10 209.00 261.55
2006 40 16.50 53.74 158.93 164.58 203.12 261.55
2007 41 13.85 51.67 150.92 151.54 192.01 254.19
2008 42 11.45 48.75 139.86 136.21 176.80 240.28
2009 43 9.36 45.19 126.74 119.79 158.91 221.25
2010 44 7.57 41.21 112.52 103.35 139.75 198.8
2011 45 6.08 37.03 98.10 87.70 120.57 174.89
2012 46 4.85 32.82 84.18 73.38 102.32 150.89
2013 47 3.85 28.74 71.26 60.68 85.61 128.04
2014 48 3.04 24.91 59.63 49.69 70.80 107.14
2015 49 2.40 21.40 49.42 40.37 57.98 88.60
2016 50 1.88 18.24 40.63 32.58 47.10 72.55
2017 51 1.48 15.44 33.19 26.16 38.01 58.94
2018 52 1.16 13.00 26.96 20.92 30.52 47.57
2019 53 0.90 10.89 21.81 16.67 24.40 38.20
2020 54 0.71 9.09 17.57 13.24 19.44 30.54
2021 55 0.55 7.56 14.12 10.50 15.45 24.33
2022 56 0.43 6.27 11.32 8.31 12.25 19.34
2023 57 0.34 5.19 9.06 6.57 9.70 15.33
2024 58 0.26 4.28 7.24 5.19 7.67 12.14
2025 59 0.20 3.53 5.78 4.10 6.06 9.60
2026 60 0.16 2.91 4.61 3.23 4.78 7.58
2027 61 0.12 2.39 3.67 2.55 3.77 5.98
2028 62 0.10 1.97 2.93 2.01 2.97 4.72
2029 63 0.08 1.62 2.33 1.58 2.34 3.72
2030 64 0.06 1.33 1.85 1.24 1.84 2.93
2031 65 0.05 1.09 1.47 0.98 1.45 2.31
2032 66 0.04 0.89 1.17 0.77 1.14 1.82
2033 67 0.03 0.73 0.93 0.61 0.90 1.43
2034 68 0.02 0.60 0.74 0.48 0.71 1.13
2035 69 0.02 0.49 0.59 0.38 0.56 0.89
2036 70 0.01 0.40 0.47 0.30 0.44 0.70
2037 71 0.01 0.33 0.37 0.23 0.34 0.55
2038 72 0.01 0.27 0.30 0.18 0.27 0.43
2039 73 0.01 0.22 0.24 0.14 0.21 0.34
2040 74 0.00 0.18 0.19 0.11 0.17 0.27
2041 75 0.00 0.15 0.15 0.09 0.13 0.21
2042 76 0.00 0.12 0.12 0.07 0.10 0.17
2043 77 0.00 0.10 0.09 0.06 0.08 0.13
2044 78 0.00 0.08 0.07 0.04 0.06 0.10
2045 79 0.00 0.07 0.06 0.03 0.05 0.08
2046 80 0.00 0.05 0.05 0.03 0.04 0.06
')

[JohnDenver]

$this->bbcode_second_pass_quote('pup55', 'I')f you read Savinar's book, he makes the statement that "money" per say, is government issued scrip that represents, in essence, some incremental amount of "energy". It's an interesting section, in there somewhere if you can find it. Based on that, why does this not make sense?

[pup55]

Excellent! We have gotten someone to think!



$this->bbcode_second_pass_quote('', 'I')t is shocking to realize that this is the much-vaunted "scientific" method by which everyone is predicting the peak. The prediction is entirely dependent on guessing Q-inf (the total amount of recoverable oil), and nobody knows what that value is. There's nothing scientific about it. It's more like a contest of old men trying to tell you how many beans are in a jar that's half-hidden behind a curtain. If you happen to get it right, it's just dumb luck.

[Soft_Landing]

I doubt I'm the only one marvelling at the stability of the peak prediction... That kind of goes against credibility. Suppose you have been influenced to some extent by hindsight, Pup55?

Or can you explain - What is the feature of the model that ensures the peak date remains so stable in the face of large shifts in the expected sales quantities?

Can anyone suggest a "post peaked" dataset that Pup55 could use (if willing) to prepare a set of psuedo-blind tests, to compare predicted peak and actual peak?

[pup55]

I am CERTAIN to be biased! A lot of the technique on this is "eyeballing" the fit of the curve over the data set, however truncated. I did try to experiment with a few "one off" conditions, but never ended up too far off from the fit of the first part of the curve, because the fit of this model "looked good".

Also, this works better because the "actual" data curve is nice and smooth. If there were a lot of craziness in the data, it would have been subject to even more interperetation and potential bias by the eyeballer.

I will be HAPPY to do a blind test on whatever data set anybody wants.

The ideal would be as follows:

a. Somebody find a data set on a phenomenon that has already peaked.
b. Leave off the post-peak part of the data set, and post it. Truncate anywhere you want.
c. I will predict the peak based on the remaining data, and also predict the magnitude of the peak.
d. the submitter can reveal the actual peak compared to the predicted peak and see how close we got.

Could be cool.

[pup55]

By the way, some more detail on the "technique" on this:

I have a little spreadsheet (well, actually a big spreadsheet) with the logistic curve equation in it. I have another one with the asymmetrical curve in it, and it basically works the same way. Easy to produce an X-Y graph of the actual data and the "predicted" data.

The three "knobs" if you will, are Q-inf, which is the total area under the curve (how big the curve is), k, which is the "fatness" of the curve, and some guesstimate of T-50 or the "peak".

To start with, pretty easy sum the actual data and figure out Q-current, which for the walmart data is "total cumulative production", Then, easy to double it or triple it, along with a SWAG of the "peak" to generate a preliminary curve.

Then, easy to adjust Q-inf so that the predicted production to-date is pretty close to the actual accumulated production to-date. From there, minor adjustments in the three knobs to fine-tune. The goal is to minimize the standard error between predicted and actual as measured by the STEYX function, and still maintain the predicted total cumulative production being equal to the actual.

In fact, if you go through that data, and sum the actual and predicted cumulative production for each of those curves, for the same time period, you will see that I did a pretty good job.

The reason that the peaks are different magnitude but about the same place in the above example is the Q-inf adjustment. k, the fatness, was pretty close to the same the whole time, but in order to get the predicted cumulative production to be about the same as the actual, had to adjust the height by changing Q-inf, and then fine tune by adjusting the guess of the peak slightly.

A really good spreadsheet engineer would probably be able to find a way to minimize STEYX while maintaining P(actual)=P(predicted) in an automated way so as to not have to be subject to graph fudging, but I am not one.

So, plenty of chances for "guessing", "influence", and other non-scientific stuff, especially, like I was saying, if the data is messy. The other day, when trying to predict the peak of Saudi, had to judge the whole left hand side of the curve due to the irregularities in pumping caused by these guys being the swing supplier during the 80's and '90s.

So there you have it. Let the blind test begin!

[pup55]

one more thing, in case it had escaped anybody's notice:

Obviously in the hands of a relatively harmless, well-meaning amateur with a computer and just enough knowlege of mathematical modeling to be dangerous, there is some slop in these estimates.

If, on the other hand, I were some crusty ex-geologist with an axe or two to grind, no telling where this might lead....

I'm just glad I do not have to do all of this by hand, like in the 50's. It must have taken weeks to do even one of these calculations, much less the trial-and-error part.

[EnviroEngr]

Are the function equations you're using to plot those curves at all reminiscent of:

This is going to look a little goofy, but here it goes:

Function
F(x) = 1/(2Ï€)^0.5(e^(-x^2/2))
Read like this: Function of x equals one over the square root of 2 pi times e raised to the negative one half x squared.

First Derivative
F'(x) = -x/(2Ï€)^0.5(e^(-x^2/2))

Second Derivative
F"(x) = (x^2-1)/(2Ï€)^0.5(e^(-x^2/2))

Finding the relative minima and maxima on both the First and Second Derivative curves makes identifying the inflection points of the Function curve really easy, especially if all three 'functions' are graphed together.

Ï€ = pi
^ = exponent follows
e = Inverse Natural Log of 1

I will talk to Admin to see if I can get Math Symbols/Layout functionality (or something approximating it) in here. This is do-able but sufficiently cumbersome to warrant looking for better presentation techniques.