William M. Briggs

Statistician to the Stars!

Can We Predict The Unpredictable?

Figure 1 (b) from the paper.

Figure 1 (b) from the paper.

The most intriguing thing about the new peer-reviewed paper of the same name as today’s post in Nature: Scientific Reports by Abbas Golestani and Robin Gras is that it is longer than the one word it takes to authoritatively answer the question.

No. We cannot predict the unpredictable.

Nor do we do that good a job at predicting the predictable, as anybody who has ever spent time with models of complex systems like the stock market and global climate system realize (or should realize).

Those who have long been at this game have seen every form of hype and promise come down the pike, each new method touted to fix the shortcomings of the previous wonder. Yet the glory always fades.

Anyway, our authors have devised a “novel” algorithm which they christen GenericPred, which fixes the shortcomings of models such as ARMIA, GARCH, and MLP. Before describing it, at the top of this post is a picture of one of the predictions of the Dow Jones Industrial Average.

We don’t need to understand how forecast “goodness” was defined to be able to see that GenericPred handily beats three other standard methods. Two other pictures show similar performance for other periods of the DJIA. The GenericPred also seems to do well predicting (one version of) the global average temperature anomaly (it predicts an increase of a whopping ~2.5C over the next century).

Looking only at these pictures, it appears GenericPred is hot stuff. Obviously, the old-fashioned methods bit into the seeming increase of the DJIA (pictured above) and were burnt. But not GenericPred. No, sir. It—somehow—sensed that changes were coming and, more or less, nailed the decrease.

I don’t buy it. I may be wrong—yes, dear reader, it is possible that I am mistaken—but I don’t think so. My misgivings flow from the nature of their algorithm and its relation to chaotic signals. But, hey, if I’m wrong and these guys really can predict the stock market two years in advance, they’ll be billionaires in short order and I’ll still be running this penny-ante blog.

GenericPred is based on a good idea, which I’ll roughly summarize. Take a series y1, y2, …, yT and compute some measure of chaos, like a Lyapunov exponent. Now posit new values of the series, yT+1, yT+2, …, yT+m, and then compute the (say) Lyapunov exponent for the augmented series y1, …, yT+m. Pick those values of yT+1, …, yT+m that minimize the distance between the (say) Lyapunov exponent of the original and the augmented series.

This makes some sense because, if the series is indeed chaotic, and no external changes in the causes of this series are expected, then the nature of that series, as measured by various indexes, should remain constant. That there are or can be external changes in causes is obvious, and is why the authors look before and after the last financial “crisis.”

Still with me?

Now if you have had any experience with chaotic time series, you know that, like the DJIA, they are apt to fly off hither and yon. Chaotic signals are those that are caused (as is every time series) but which are sensitive to initial conditions. The weest perturbation at the beginning (or really anywhere) could and does result in wildly different values now. This is why they are so difficult to predict.

Take another look at the prediction picture above. The data before (on or about 1 July 2007) were used to fit the various models, and the predictions came afterward. What would this plot look like if the authors had used date up to, say, 29 June 2007? The old-school models would probably still stink. But it’s not at all clear GenericPred would do as well—because the series is chaotic. Chaotic signals are just as likely to rise as fall. Very curious they got it so startlingly right.

And could something as humble as the Lyapunov exponent (or some other univariate measure) really hold the secret to all possible future values of the stock market?

Every scientist wants to think the best of his creation. Could these researchers have played (in honest earnestness) with the dates to show us the most dramatic discrepancies between their model and the old-school methods? Since these series are chaotic it would be truly remarkable if the method weren’t sensitive to the dates chosen to model and forecast.

The pictures look a little too neat, the points of departure of the old-school models and GenericPred a little too sharp. I do not suggest any nefariousness. But if this new method is to follow the history of all other methods, and prove to be not as exciting as initially promised, it will be because the authors fooled themselves by tinkering one step too many to present their best case.

Anyway, I predict at least a brief GenericPred boom among prediction clients. If the model works as well as promised by these figures, then the authors ought to get rich off the stock market.

Incidentally, all predictions methods should be accompanied by measures of uncertainty. The old-school methods automatically give these, but GenericPred does not. That should be the authors’ next step.

Update One of the authors (Gras) responded in comments below.

—————————————————————————-

Thanks to reader Rich Kyllo for bringing this paper to our attention.

89 Comments

  1. There is an unspoken beast about these kinds of miracle algorithms, namely that, even if it was true that this “algorithm” somehow nailed a much better predictor of the future, then the very presence of this algorithm would radically change the landscape of the stock market, because obviously all the smart money would start to use it in order to better predict the outcomes of their actions. The very usage of this predictor by all important parties in the stock markets would nullify all predictions by the algorithm itself (not only because everyone would be using it, but everyone knew everyone would be using it, and so on and so on).

    So I am even willing to buy the notion that we have improved our capability to understand the stock market by a thousand fold in the last century, the problem is, obviously, that so have all of any one’s competitors, and therefore you are back to square zero.

  2. JustAnotherPoster

    December 2, 2014 at 10:01 am

    Very east test to do.

    Ask the authors of this paper if they are willing to bet $10,000 of their own money on their predictions.

    If they don’t they paper is obvious rubbish.

  3. Luis,

    “So I am even willing to buy the notion that we have improved our capability to understand the stock market by a thousand fold in the last century, the problem is, obviously, that so have all of any one’s competitors, and therefore you are back to square zero.”

    You are mistaken. The problem you describe happens so fast that no one ever gets off square zero in the first place.

  4. The seizure prediction part of the paper looked to have very good results, which was quite surprising. Whatever is actually physically occurring seems to be well approximated by their method. I’m with you, though, I would love to see some shifting of the prediction starting point backwards in time.

    The thing I don’t know enough about are the measures of chaos that they are using. They say they use Poincaré section and fractal dimension, and I haven’t bothered to learn what that is yet. However, if there are measures out there that act on data in a certain way, then all they’ve done (in my view) is create a method that gives you back mostly the same data that you have already.

    For example, if the measure can indicate that the data move up and down like a wave, then data produced by their algorithm that follows that behavior would come back to you. If a straight line had the same measure, then it might not be a very good measure!

    This is probably why the ends points were chosen where they were. Any sooner in the DIJA, and there wouldn’t be the right kind of information buried in the measure. Any later and the reviewers would call them out on it. The climate modeling section is next to useless. A line and some sine waves can make the same approximation to that noisy data. There’s not enough interesting behavior in the temp data that they used to wow me.

    Also, they generate their next prediction points (before selecting the ‘best’ one) from normal distributions. I wonder why they can’t just run an optimizer to pick the ‘best’ next point without needing to randomly draw 10 points and pick one of those. Computers are fast these days! It seems arbitrary to me, and also makes me wonder if doing so produced bad predictions. If it did make bad predictions, the 10 ‘random’ options for the next predicted point would act to reduce the possible spread of future predictions. This is just another way of returning the data you already have back to you.

  5. In horse racing, you can tell right away the SuperDuperEasyMoney method doesn’t work. If it’s for sale, it’s no good. A thoroughbred handicapper has to stay ahead of the crowd to win. It doesn’t do any good to have the crowd bet with you. The stock market is just the opposite. If the method is any good it’s likely because it is self-fulfilling by itself generating the increases it predicts.

    Now here’s something I’ve always wondered. How can anyone claim the stock indices and the weather are chaotic? Sure chaotic functions produce something similar looking but that’s not proof.

  6. You are mistaken. The problem you describe happens so fast that no one ever gets off square zero in the first place.

    This is what is usually called “Furiously agreeing with someone” (rolleyes). Rigorously speaking, there’s always a window of opportunity for an individual (or more) to make some bucks, but that window will close as fast as the size of the advantage.

  7. This post follows the pattern of earlier posts and comments here — no need to dig deeply into the science, because we can always wave our hands and throw in a few technical terms to dismiss a result we don’t like. Presto; what’s next?

    The first point, with respect to predicting global climate, is that unpredictability, if true, doesn’t change our current situation at all. It would be no justification for inaction. Not being able to predict the future time series of our cholesterol levels doesn’t mean we need not eat healthily. Not know when — of even if — you will have a heart attack from high cholesterol doesn’t mean you don’t have to consider your cholesterol. Instead, we seek to minimize our chances by eating better and exercising more.

    Or, as Dick Cheney put it, “If there’s a 1% chance that Pakistani scientists are helping al-Qaeda build or develop a nuclear weapon, we have to treat it as a certainty in terms of our response. It’s not about our analysis … It’s about our response.”
    http://en.wikipedia.org/wiki/The_One_Percent_Doctrine

    Same with climate. There are very good reasons why it should now be changing, and, indeed it is observed to be changing, with no other cause in sight except anthropogenic GHGs. Studying past climates, we know what this probably means — our CO2 emissions can cause significant climate change. Not being to say exactly how much — impossible even in principle, because that requires knowing future economic and sociological factors that no one can foresee — is no cause for inaction on climate change. Whether temperatures in 2100 are 1.8 C above baseline or 3.2 C, both situations are serious.

    Some researchers are trying to stretch climate models to make decadal scale predictions, but what climate models project best is the ECS — equilibrium climate sensitivity, the change in surface temperature from a doubling of CO2 levels after climate change is finished and it comes back to stability (equilibrium). Depending on the feedbacks you consider — fast and/or slow — you can get different values for different points in time, but all are (depending on the emissions trajectory) for a century or 10 in the future. (For the IPCC ARs, modelers attempt to project what’s in store for 2100.) They’re not predicting the evolution of the time series, they’re projecting the probable end state, which depends on conservation of energy. (Is there any such constraint for the DJIA?) Because on millennial scales climate change does seem to have a pattern:
    http://en.wikipedia.org/wiki/Ice_age#mediaviewer/File:Vostok_Petit_data.svg

    Nonetheless, in the last 20 years climate scientists have realized that abrupt climate change has happened in the past (such as the Younger Dryas), and could happen again, due to nonlinearities inherent to the system. 1976 may be an example of that, where some think the climate entered a new “regime.” No one claims to have a handle on predicting those, and no one rules them out. See, for example, “Abrupt Impacts of Climate Change,” National Academy of Sciences (2013) http://www.nap.edu/catalog/18373/abrupt-impacts-of-climate-change-anticipating-surprises

    All the scientists I know and read admit there is a great deal of uncertainty in climate projections (i.e., the IPCC’s range for ECS is 1.5-4.5 C, and these aren’t error bars around an average of 3.0 C, they’re a range that can’t be pinned down further so far). They (and others) also don’t think that’s a reason for inaction — because what if climate change happens to be on the high end of the range? We’re putting more and more energy into a nonlinear system — no one knows for sure the consequences of that.

    Uncertainty is always going to be part of the picture, and we will have to make decisions about climate change in the face of those uncertainties. But we make such decisions all the time (see Cheney, Dick, above).

  8. Sander van der Wal

    December 2, 2014 at 12:35 pm

    @David Appell

    Because science says something might happen, it doesn’t mean that you need to take those action that will prevent it from happening. You might like the results better, or you don’t like the costs preventing it.

    Science is to help you formulate the best policy for what is the most likely thing to happen. It doesn’t determine policy.

    Let’s take some non-climate example. NEO’s, asteroids that are capable of being in the same place as Earth. If a reasonable sized one hits, nobody is going to worry about Climate Change at all. And what measures are being taken to prevent one from hitting us? None whatshowever.

    While the science clearly shows the effects of one hitting us. People just don’t care that much, given that most of the people alive now will be dead by that time of old age.

  9. Thanks Matt. My thoughts were that the seizure prediction looked like a potentially useful application. Short term pattern kind of thing where you have enough of a window to take some action before divergence really takes hold and messes up the prediction. The stock market and climate predictions get progressively more fanciful as they push their prediction window out to a couple of years and then to the end of the century. That’s a whole lot of time for chaos to send everything sideways.

  10. Quoting Dick Cheney is always a nightmare in the making. It’s as if current day politicians can’t make any politics except this kind of selling Nightmares and telling us that they will “Protect us!” from these nightmares. Vote on me, I will defend you from the Atom Islamic Nightmare! No, you vote on me, I will protect you from Climate Change Thermageddon! I mean, if there’s 1% chance of these things happening we MUST DO ANYTHING AT ALL COSTS, right?

    And we see in the middle east the price we all paid for that kind of reasoning.

  11. David Appell:

    Temperatures have been rising for over 350 years, and were falling for about 8000 years before that.

    Sea level has been rising for about 20,000 years.

    Yes – humans are changing the climate – I have no doubt of that.

    What I doubt is that we know how much humans are changing the climate.

    I personally doubt we (humans) are even 50% of the change we have seen over the last century.

    All I know is that the climate sensitivity number seems to have been falling for quite a while – from around 3.0 C to a little under 1.8 C presently. Obviously some quibble with these numbers, but it seems pretty clear to me that humans role in climate change has been exaggerated.

    I think CS will settle out somewhere between 1.2C and 1.8C (probably around 1.5C). That is 1.5C from baseline (.8C have already been experienced). So maybe another .7C between now and when CO2 hits 560 ppm (whenever that happens).

    By that time we will have burned up most (if not all) of the hydrocarbons and will have moved onto either nuclear, renewables or some other non-carbon energy source.

    The market will get us to move off oil, coal and natural gas as these energy sources get more expensive (as we use all these resources up). Someday, solar and wind will be cheaper than oil, coal and natural gas (by some combination of hydrocarbons getting more expensive, alternatives getting cheaper or both) – but that day is far off.

    Right now, oil, coal and natural gas are just plain cheaper than all other forms of energy – that is a fact.

    And yes – I am ignoring all of the theoretical externalities that some wish were priced into energy costs – because the people buying the energy ignore these externalities and make their economic decisions without paying any mind to them.

    It seems inevitable to me that the share of energy produced using Nuclear will only rise as coal, oil and natural gas get more expensive.

    So bottom line – I am not worried about the temperature rise we will experience between now and 2100 (or 560 ppm).

    I think it will be small – I think it has happened before – and I think humans will handle it with very little if any trouble.

    I think it will be slow – slow enough that people won’t even notice it (like the 8 inches of sea level rise that happened over the last 100 years). How many people are running around complaining about the 8 inches of shoreline they have lost over the last 100 years? Not many.

    So given my frame of mind – perhaps you can see why someone with my outlook is harder to convince to take action which will make everything (food, fuel and energy) more expensive – for little, if any benefit and to the great detriment of third world people (and 1st world people for that matter).

    You might wonder – what is someone with my frame of mind willing to do to help future generations?

    I am willing to invest in research to find sources of energy which are actually cheaper than oil, coal and natural gas which do not produce as much or no carbon. We are doing that now – but I wouldn’t be adverse to increasing basic research in these areas.

    I am willing to invest to make nuclear cheaper and safer (and maybe smaller scale).

    I am willing to invest to safely store nuclear waste in many locations and to reprocess it to render it even safer (and get more energy out of it).

    I am willing to invest in cheaper ways to desalinate water and move it around better to where it is needed.

    I am willing to invest in GMO crops to adapt our crops as necessary to a changing world.

    I am willing to invest in space based solar.

    I am willing to invest in moving manufacturing into space.

    I am willing to invest in astroid detection and mining.

    I am willing to invest in fusion research.

    I am willing to invest in a space elevator.

    I am willing to invest in underwater cities and/or adapting people (volunteers of course) to live underwater.

    I am willing to invest in better data gathering over the long term over the entire planet to monitor the climate.

    Hell – I am even willing to invest in more research to make climate models better (although better data over the long term will cause them to fix themselves organically in my opinion).

    So it is not that I am not willing to do anything – it is just that I only want to do what is prudent.

    A lot of the proposals made by your side of the debate do not seem very prudent to me.

    But I enjoyed reading your post and wanted to respond in kind.

  12. ” I mean, if there’s 1% chance of these things happening we MUST DO ANYTHING AT ALL COSTS, right?”

    I think that comes from a weird kind of misunderstanding of probability. These people view a 1% chance as meaning inevitable. It’s like this month there is a 1% chance and next month there is still a 1% chance and the same the month after that, so it’s like guaranteed to happen within 10 yrs, RIGHT!? So we’d better do something about it now!

  13. RickA commented:
    “Temperatures have been rising for over 350 years, and were falling for about 8000 years before that.”

    Yes, they were falling since about 8000 BP:
    http://davidappell.blogspot.com/2013/03/the-hockey-stick-gets-much-longer-shaft.html

    but they haven’t been rising for the last 350 years; see the first graph here:
    http://thinkprogress.org/climate/2013/07/08/2261531/most-comprehensive-paleoclimate-reconstruction-confirms-hockey-stick/

  14. RickA commented:
    “Sea level has been rising for about 20,000 years.”

    Not at its current rate. Sea level rise since 5000 years ago to the Industrial Revolution was only a meter, or an average of 0.2 mm/yr. Its now 15 times larger, about 3 mm/yr:

    http://en.wikipedia.org/wiki/Current_sea_level_rise#mediaviewer/File:Post-Glacial_Sea_Level.png

  15. Rich Kyllo wrote:
    “I think that comes from a weird kind of misunderstanding of probability. These people view a 1% chance as meaning inevitable.”

    That’s not what Cheney said.

  16. Note that the authors claim to have performed a sensitivity analysis, but there’s no mention of perturbing the ending points of the time series, only the starting points. I’d love to see how this algorithm performs with an ending point in early 2009 (the bottom of the market).

  17. RickA wrote:
    “I personally doubt we (humans) are even 50% of the change we have seen over the last century.”

    Based on what data and evidence?

    “All I know is that the climate sensitivity number seems to have been falling for quite a while – from around 3.0 C to a little under 1.8 C presently.”

    The 1.8 C number is from a recent paper by Lewis and Curry. I haven’t seen anyone else who really believes that. Their modewl was very simple, the paper has some obvious flaws, not the least of which is that they didn’t use the latest data available, especially for surface temperature and aerosols. Here is a reply from some climate scientists:

    http://www.realclimate.org/index.php/archives/2014/10/climate-response-estimates-from-lewis-curry/

  18. Briggs
    I disagree.
    If they had faith in their model they would not have published until after they had used it to get rich.

  19. “By that time we will have burned up most (if not all) of the hydrocarbons and will have moved onto either nuclear, renewables or some other non-carbon energy source.”

    I don’t think so. The total resource base of fossil fuels is about 125e17 grams of Carbon, 80% of it coal. That’s about 12,000 gigatons of carbon, when we’ve burned about 400 GtC so far. Total surface warming is approximately proportional to cumulative emissions (with the proportionality constant about 1.5 K/TtC (trillion tonnes carbon), with the 2-sigma range 1.0-2.1 K/TtC.

    Data from Swart and Weaver, Nature (2012)
    http://www.nature.com/nclimate/journal/v2/n3/full/nclimate1421.html

  20. Briggs

    December 2, 2014 at 3:38 pm

    Bill Anna,

    You might be right.

    All,

    Wise words from Winston Churchill: “A fanatic is one who can’t change his mind and won’t change the subject.”

  21. “The market will get us to move off oil, coal and natural gas as these energy sources get more expensive (as we use all these resources up). Someday, solar and wind will be cheaper than oil, coal and natural gas (by some combination of hydrocarbons getting more expensive, alternatives getting cheaper or both) – but that day is far off.”

    Renewables are already cheaper, if you cost in the negative externalities of fossil fuels. But many people prefer to believe that what they pay for FFs is only the amount on their monthly bill.

    “Rooftop Solar Cost Competitive with the Grid in Much of the U.S.,” Scientific American, 12/1/14
    http://www.scientificamerican.com/article/rooftop-solar-cost-competitive-with-the-grid-in-much-of-the-u-s/

    “Solar and wind power are now fully cost competitive with fossil fuels – is it time to switch over?” ExtremeTech.com, 12/1/14
    http://www.extremetech.com/extreme/195003-solar-and-wind-power-are-now-fully-competitive-with-fossil-fuels-is-it-time-to-switch-over

  22. “Right now, oil, coal and natural gas are just plain cheaper than all other forms of energy – that is a fact.”

    So your only criteria is “cheaper?” You don’t care what damages FFs are doing now and into the far future?

    There are ethical considerations to consider, not just economics.

    The report:

    “Hidden Costs of Energy: Unpriced Consequences of Energy Production and Use”
    National Research Council, 2010
    http://books.nap.edu/catalog/12794.html

    found the cost from damages due to fossil fuel use to be $120 B for 2005 (in 2007 dollars), a number that excludes much climate change and that the study’s authors considered a “substantial underestimate.”

    I estimate that number for today would be $180-200 B in current dollars, or $600 per American.

    The report found that for electricity generation by coal the external cost was 3.2 cents/kWh, with damages due to climate change adding another 3 cents/kWh (for CO2e priced at $30/tonne). Transportation costs were a minimum of 1.2 cents/vehicle-mile, with at least another 0.5 cents/VM for climate change. Heat produced by natural gas caused damages calculated to be 11 cents/thousand cubic feet, with $2.10/Kcf in damages to the climate. They found essentially no damage costs from renewables. (Yes, some bird deaths – but buildings and vehicles kill far more birds than do wind turbines.)

    This is money we’re all paying in medical costs (and bad health), and US governments now pay about half of all medical costs.

  23. RickA wrote:
    “How many people are running around complaining about the 8 inches of shoreline they have lost over the last 100 years? Not many.”

    Miami, FL. Norfolk VA. Several of the South Pacific island countries.

    Sea level rise isn’t constant across the globe. In the western and south Pacific it’s now up to 12 mm/yr.

    Suppose a beach is inclined at 10 degrees. Then, with 12 mm/yr SLR, the water line comes up the beach by 1.5 feet/yr. At a 5 degree incline, it rises a yard per year. 10 yards per decade. SLR is already starting to ruin freshwater sources on some of these islands.

    What most people don’t yet realize is that you can’t stop sea level rise on a dime. We are committing ourselves to huge increases that are inevitable. In the past sea level has risen (or fallen) up to 20 meters per degree C of warming (or cooling). Unless future inhabitants of the planet find a way to suck CO2 out of the air and store it somewhere, or employ geoengineering (essentially forever), they will not know that sea level was once stable.

  24. swordfishtrombone

    December 2, 2014 at 4:11 pm

    David Appell:

    “the IPCC’s range for ECS is 1.5-4.5 C”

    Yes, pretty much exactly the same range as 30 years ago – millions of dollars (and pounds) spent on useless research. Can we have our money back?

  25. Getting back to the point of the thread even though it’s being hijacked,
    prediction involves a causal law… If you make predictions for a situation in which there is a causal law but the initial and boundary conditions give rise to chaotic behavior, then solutions corresponding to the causal law give regions, multiple paths in phase space for the events which will take place. I refer to the simple example of a real pendulum with damping. See
    http://www.thphys.uni-heidelberg.de/~gasenzer/index.php?n1=teaching&n2=chaos
    In the given graphs for GenericPred I don’t see any multiple paths that are typical of chaos theory solutions. Are any given in the full paper?

  26. RickA wrote:
    “But I enjoyed reading your post and wanted to respond in kind.”

    Thanks — I enjoyed yours too. Clearly you have thought about your positions more then most.

  27. “Winston Churchill: “A fanatic is one who can’t change his mind and won’t change the subject.””

    But what evidence says any minds should be changed about AGW? Just because you say they should?

  28. Appell will always start with a conclusion and then pick and choose his evidence to fit what he already believes. Hence, whatever he does write is usually quite pointless. If climate models correctly capture the primary physical drivers then we evaluate the variability in the models and they within a certain range. The models don’t work as they are already outside their expected variability, and worse, always in one direction. There is no reason to be surprised by this. All different kinds of feedbacks and forcings are likely to operate at different sensitivities at different times, even assuming we have a good grasp of the behaviour of the climate system, which most likely we don’t. This was explained to me once by a rather famous (notorious) climate modeler, very loud in advocacy circles. But climate trolls will believe what they want to believe and it’s got nothing much to do with science, except where they can bend and distort it to fit into their beliefs.

    Back on topic, the opening comment nailed the problem. Even if GenericPred successfully captured all aspects of human behaviour in a neat little mathematical calculation (which of course, unless you believe in magic, it can’t), it would immediately become useless as traders would be using GenericPred in their own software models, completely invalidating it. This has happened before, so it would happen again. A good read on what happened when this was tried a few times in the past:

    http://www.amazon.com/The-Predictors-Maverick-Physicists-Fortune/dp/0805057579

  29. Briggs

    December 2, 2014 at 4:23 pm

    Appell,

    Thus confirming Churchill’s words.

    Bob,

    They do not. Incidentally, the paper is open source; trivial math.

  30. swordfishtrombone

    December 2, 2014 at 4:28 pm

    David Appell:

    “[Sea level rise] Its now 15 times larger, about 3 mm/yr:”

    According to satellite data – tide gauges say about 1.5 mm/yr. Alarmists always choose satellite data for SLR (because it’s higher) but surface data for temperature (because it’s higher).

  31. Back to the question of the applicability of chaos theory to prediction.
    If one has a mathematical differential equation that is modeling some real situation, then conditions can arise when the solutions become extremely sensitive to initial and boundary conditions. Now with respect to the stock market, I’m not sure what those differential equations might be (and thanks Will for the book reference). Are they some modification of William O’Neill’s “CAN SLIM” equations or ???
    I can’t see how chaos theory could be applied if there’s no mathematics for it to develop, but I’m willing to be educated on this point.

  32. Hello,

    You should have a look on the supplementary material of the paper. We have done exactly what you ask for: an analysis of the effect of shifting the prediction windows by some few days.

    Regards

  33. Hey David Appell,

    Just curious – what are your thoughts on climate change? Asking for a friend.

  34. Briggs

    December 2, 2014 at 4:42 pm

    Bob,

    Good question. Chaotic time series models work just like “normal” ones. Just like any statistical model, they are not about causality. They are only correlative.

    Robin Gras,

    Thank you. I did see the supplementary material, but I don’t think you answered the question of how the different forecasts look when the end (not start) point changes. Not just a few days, though that’s a start (as I indicated above), but by a heap of days.

    I wonder if you guys are making bets on the predictions? If you really can nail the DJIA that well, God bless you, you should be able to clear a bundle.

    Say. How about a challenge? We could provide you with some signals of varying natures but withhold from you the prediction period. We’d compare your model with the observations only after the forecasts are made.

    Be a pretty good test, no? Could be fun. Let me know.

  35. Bob,

    What do you mean about multiple paths?

    Briggs,

    When you say that chaotic models are not about causes, I assume you are also saying differential equations are not about causes as well?

  36. Briggs

    December 2, 2014 at 5:08 pm

    Will,

    Well, you know what I mean. I meant chaos time series models like this are not about causes. Some chaotic models are causal models, like Bob’s pendulums, and other diff eqs. This DJIA model is not causal.

  37. Ahhh yes, I do know what you mean.

  38. “Not at its current rate. Sea level rise since 5000 years ago to the Industrial Revolution was only a meter, or an average of 0.2 mm/yr. Its now 15 times larger, about 3 mm/yr:”

    According to Professor Nils-Axel Mörner there is no sea level rise.
    http://scienceandpublicpolicy.org/blog_watch/sea_level_is_not_rising.html

  39. Ray wrote:
    “According to Professor Nils-Axel Mörner there is no sea level rise.”

    Yes. And no one has believed him for a long time.

  40. Bob,

    I can’t see how chaos theory could be applied if there’s no mathematics for it to develop, but I’m willing to be educated on this point.

    My objection is similar. Stock markets are not sensitive to initial conditions in the same way as chaotic physical processes. Physics follows rules. We may not understand how all of them fit together, be able to measure them, etc., but matter does not deviate from the “laws” of physics. The human animal is not so obedient.

  41. Will,
    “What do you mean about multiple paths?”
    Answer: if you go to the given link (here it is again)
    http://www.thphys.uni-heidelberg.de/~gasenzer/index.php?n1=teaching&n2=chaos
    you’ll see some of the figures in phase space that look like balls of yarn–the trajectories vary from one pass to another just slightly, but in a truly chaotic situation manage to cover almost all of phase space.

  42. If I look at some Googled references for chaotic time series I see (and this is very cursory inspection, I admit) difference equations to predict points. Now it is my recollection that difference equations are just another way to model differential equations for discrete mathematics. If that interpretation is correct, it means that such time series are implicitly causal, or is that a naive view?

  43. Hi Bob,

    Yes, but those balls of yarn are just one path in the phase space.

    As far as the causality. In mathematics land, both continuous and discrete differential equations are deterministic. Therefore, they are causal in the sense that we can exactly measure the effect that x has on y. Sometimes these equations are also very much real-life causal in that they are derived from physical laws.

    I think what Briggs is saying is that the method applied in this paper is not causal. It is basically a prediction method that maintains the chaotic behavior of the observed time series.

    For example, if I gave you a prediction of daily temperatures for the next year, but the prediction was a straight line, say 70 degrees everyday, you would say “not only are you wrong, but the prediction doesn’t even behave like a temperature time series!” You might ask that my prediction, however wrong, at least has the same variance as the observed time series. This is a very similar idea, except we are maintaining a measure of chaos.

    Actually, the derivation of differential equations is a place where constraining solutions to some constant measure of the system is a method that works. For example, in a friction less pendulum, we can use the conservation of energy to derive the systems differential equations. An initial condition has a certain level of energy and all future time steps of the path of the pendulum must have the exact same energy (and the system is completed contained, no wind, etc..). This constraint allows us to derive the equation.

  44. btw, regarding the paper.

    Can someone help me with equation (2). I think the function V() in the equation is not meant to be the same V() that is mentioned just sentences before ? I think the V() in the equation is just nay mapping function. Like a dreaded smoothing function.

    Also, it looks like the y_i on the left hand side of the equation is also part of the right hand side, in that it is part of the set S_(i-L+1).

    I could be completely missing something, let me know if any of you can see what I am missing.

    Thank you!

  45. Will, right you are …one path in phase space–no discontinuities. And as you point out differential equations can be derived from mini-max integral principles. And I’m still confused about how chaos actually enters into time series… how is the sensitivity to initial or boundary conditions applied?

  46. Way back forever ago when I was taking some a forecasting course in my MBA program the statistic teacher told the class that forecasting was fairly good for the short range but it would go out the window when and if the world changed. Like it did on 9/11, can this algorithm predict a solar flar that koncks out the nation’s Internet? I do nkt think so.

  47. swordfishtrombone commented:
    “According to satellite data – tide gauges say about 1.5 mm/yr. Alarmists always choose satellite data for SLR (because it’s higher) but surface data for temperature (because it’s higher).”

    Scientists use satellite data for SLR because it’s better, and doesn’t need the degree of adjustments tide gauges to.

    Scientists use surface data for temperature because…we live on the surface. I don’t know what “higher” means — compared to what?

  48. Will Nitschke commented:
    “If climate models correctly capture the primary physical drivers then we evaluate the variability in the models and they within a certain range. The models don’t work as they are already outside their expected variability, and worse, always in one direction.”

    Evidence?

  49. swordfishtrombone commented:
    “the IPCC’s range for ECS is 1.5-4.5 C””
    Yes, pretty much exactly the same range as 30 years ago – millions of dollars (and pounds) spent on useless research. Can we have our money back?”

    What says the ECS as calculated today has to be different from that calculated 30 years ago?

  50. There’s one thing that Cheney and Appell certainly have in common. Both are willing to whittle away at our freedom by using their cause. One uses terrorists to scare us and one uses AGW to scare us. Two peas in a pod. The scary part is they both act with good intentions and the certainty that the actions they prescribe are for the greater good. Be very wary of people that think we need to just “do something”.

  51. Bob,

    How does sensitivity to initial conditions apply to this method in particular? I don’t think it does, except indirectly – by an estimation of the lyapunov exponent.

  52. David Appell wrote:

    “Suppose a beach is inclined at 10 degrees. Then, with 12 mm/yr SLR, the water line comes up the beach by 1.5 feet/yr.”

    By my figuring, the correct math leads to a number less than 3 inches.

  53. Sander van der Wal commented:
    “NEO’s, asteroids that are capable of being in the same place as Earth. If a reasonable sized one hits, nobody is going to worry about Climate Change at all. And what measures are being taken to prevent one from hitting us? None whatshowever.”

    As you know, the probability of a NEO impact that is large enough to do serious damage is very, very low. It’s 100% certain, however, that CO2 absorbs IR and that it plays a significant role in our greenhouse effect. And on Venus. This is basic science that has never been countered, and never will be.

    “People just don’t care that much, given that most of the people alive now will be dead by that time of old age.”

    Big, big difference — nothing happens before the NEO hits, so people don’t need to care very much. But climate change is happening now and will continue to happen, and the science is saying it will likely have significant impacts over the century, in all kinds of ways. You’ll be dead, but what care do you have for how this change might affect anyone other than you? Your children, your grandchildren, the poor of the world, the inhabitants of the world for the next 100,000 years, both human and nonhuman? Nature itself? These are questions of values. You might read “A Perfect Moral Storm: The Ethical Tragedy of Climate Change” by Stephen Gardiner at the Univ of Washington.

  54. Paul W commented:
    “There’s one thing that Cheney and Appell certainly have in common. Both are willing to whittle away at our freedom by using their cause.”

    You’ll still plug your toaster into the same outlet. But with fossil fuels you are already constraining the freedom of many others, now and in the future, all to get out of paying the real cost of the fuel you use.

    The US has had a cap-and-trade program for 20 years. How, specifically, has that constrained or reduced your freedom?

  55. Codfish: Yes, you’re right and I’m wrong. I get 2.7 inches/yr. Thanks for the correction.

  56. On the other hand, I haven’t been able to find out the kinds of beach inclines found in the south Pacific. This page about beaches in general says calls a “steep beach” 11° and a “shallow beach” 0.5°.
    http://w3.salemstate.edu/~lhanson/gls214/gls214_beach2.htm

  57. This page gives the slope of two New Zealand beaches as 6 ½ degrees and 1 degree.

    http://rsnz.natlib.govt.nz/volume/rsnz_60/rsnz_60_02_005400.html

    A 1 degree rise, at the global average SLR of 3.2 mm/yr, would eat up 6 feet of beach per decade, if I did the math right this time.

  58. @David Appell
    “Evidence?”

    I’m assuming you’re familiar with the evidence as much as I am, but as I’ve pointed out in the past, cranks tend to pick and choose their evidence based on their beliefs. Any evidence you like you will believe, even if weak, such as based on models and proxies. Any evidence you dislike because it disagrees with your beliefs, such as empirical observations and measurements, you will think up reasons to hand wave away.

    There is little point ‘debating’ cranks. You’ve been debunked so many times in the past that I’ve lost count. When you can’t respond to an argument, you change topics. Then a week later you are repeating the same claims all over again somewhere else. No difference between your lot and the dragon slayers who don’t believe in the greenhouse effect. Same delusional thinking, only the topic is different.

  59. Again trying to ignore those kidnapping the thread and back to the original post: looking at the figure given by Briggs, as near as I can tell the predicted DJIA values are given by the black curve and the actual by the blue curve. Looking at this curve if you tried to do short
    options you’d be in much trouble… it predicts a fall, but much less steep than the actual (2009). Moreover, I can’t see how any such prediction would take account of up or down gaps at earnings–i.e. the effect of the real world.
    Let me turn to something else. I still don’t understand how chaos theory enters in, where the sensitivity to initial/boundary conditions comes from. I’ve Googled “chaos time series” and haven’t found anything that seems to answer that question; I understand the wikipedia article on Lyapunov exponents, but I don’t see how those enter into the chaotic behavior. Can anyone recommend a reasonable online reference?

  60. Actually, shorts would work out well–actual drop is steeper than predicted.

  61. Will: Your comment was completely devoid of evidence.

  62. Axioms do not require evidence as they cannot be proved and thus much be assumed. If you can predict something it is not unpredictable, so it follows that any and all things that can be predicted are not unpredictable. Thus, unless all predictions have been made and made correctly it can be assumed that there still exists unpredictable things. This is true even if you limit the thing to be predicted to the performance of the DJA or the path of a drunk walking across a field..

  63. Bob Kurland wrote:
    “Again trying to ignore those kidnapping the thread and back to the original post: looking at the figure.”

    Why don’t you comment about what you find interesting in the post, and let others comment on what they find interesting? Thank you.

  64. Here is a rather obvious clue as to why this is another junk science paper to be added the endless junk science stream. Their algorithm claims to be able to model temperature history. Those spikes and dips found at the end of the record (which they model more or less nearly perfectly) are temperature responses to El Nino and La Nina events. If you look at the entire record of ENSO events, you’ll see that they are random events. Even an extremely rare ‘super’ El Nino event gets predicted accurately, and right on que. What they are claiming is the ability to predict random effects with near perfection — not just the probability of any particular random event such as this occurring – they nail the timing too. Because the match is so close to perfect, it’s reasonable to assume that their findings are not just about extreme luck, but rather are likely faked.

  65. back to the point of the thread again. No data is shown for the retrodiction of epileptic seizures. Would the EEG of subjects be continuously monitored? Is there a periodicity to epileptic seizures that the new technique takes into account.
    And finally, how about a true prediction, not a retrodiction… it would be especially useful with the market at new highs; see:
    http://www.telegraph.co.uk/finance/comment/jeremy-warner/11269329/Five-reasons-why-markets-are-heading-for-a-crash.html

  66. Fletcher Christian

    December 3, 2014 at 6:16 am

    One problem with stock market prediction is that various changes can completely invalidate the model; political and technological changes could make a mess of even the most careful prediction. As an example, what would the introduction of a fusion reactor the size of a large refrigerator that puts out 5MW for $50,000 do to any stocks having anything to do with energy? And this isn’t a silly example; try googling “focus fusion”.

  67. “The US has had a cap-and-trade program for 20 years. How, specifically, has that constrained or reduced your freedom?”

    Any time you raise the cost of something I use, you take away my freedom to spend my money on things I value more.

  68. Paul W wrote:
    “Any time you raise the cost of something I use, you take away my freedom to spend my money on things I value more.”

    So in your opinion you can do whatever you want to the environment, without regard for anyone else at all?

    Do you dump you trash over the bank at the end of the street? That’d be much cheaper than paying for weekly trash pickup. Do you drain your sewage into the street?

  69. CO2 is not pollution. It’s effects are more likely positive than negative. If the negative consequences of an action are less likely than positive consequences, taxing that action does indeed impede people’s rights. The Appell ‘argument’ only works if you begin with false assumptions and then apply the wrong analogy.

  70. Will Nitschke wrote:
    “CO2 is not pollution.”

    In Massachusetts v. EPA (2007), the US Supreme Court held that GHGs are “air pollutants” under the Clean Air Act and its amendments:
    http://www.law.cornell.edu/supct/html/05-1120.ZS.html

    It also meets the common definition of “pollutant” — a substance that in excess quantity is harmful and/or unwanted.

    “It’s effects are more likely positive than negative.”

    Another grand claim with no backing evidence whatsoever. Must be nice to be able to do science by pronouncement. Do these things come to you in dreams?

  71. Sander van der Wal

    December 4, 2014 at 1:24 am

    So, oxygen is a pollutant then, too.

    BTW, last time I looked the Clean Air Act wasn’t law in Europe, of anywhere else.

  72. You have to appreciate that internet trolls and cranks have a desperate need to make ‘converts’. That’s why they spam forums like this with endless postings. Best not to encourage them, as they only multiply their output if shown the slightest interest in what they are trying to sell.

    When presenting arguments, they have their own inner circle of cranks that cite each other. If you’re a psychoanalytic practitioner, you have dedicated journals you can quote from to support your position. If someone skeptically raises an eye brow over the assertion that Mary Jane’s psychological problems boil down to bad case of penis envy, you’ll be flooded with links to authoritative looking peer reviewed publications exhaustively discussing penis envy and its many obtuse manifestations. If you’re a chiropractor and someone dare question your rather magical views about the human body, well, a few authoritative citations from the American Chiropractic Association will fix you up!

    Appell of course, has all the links. If he wants to present some bizarre ideas on climate change, he has a long list of speculative junk science papers he can present. If he wants to argue economics, he has got all sorts of links from the works of ‘environmental economists’. That is how cranks play the game. It doesn’t matter that the vast majority of academic psychologists think of psychoanalysts as ‘nutters’ or that the vast majority of serious economists think of environmental economists (or ecological economists or whatever they are calling themselves today) as bonkers. It’s all about presentation over substance.

  73. @Appell “So in your opinion you can do whatever you want to the environment, without regard for anyone else at all?

    Do you dump you trash over the bank at the end of the street? That’d be much cheaper than paying for weekly trash pickup. Do you drain your sewage into the street?”

    It doesn’t follow that spending my money how I want leads to sewage in the streets or a lack of regard for others. I may freely donate to charity with great regard to my fellow man, but then again I may not. Neither should be of the slightest interest to you or anyone else. How you took freedom to spend my money as I see fit to spewing raw sewage is something you can only solve through a little introspection.

    There seems to be a lot of jumping back and forth between climate change and pollution trying to evoke an emotional response. It’s interesting that you regard your fellow man as rampant polluters if left to their own devices. Perhaps you should cut your fellow man a little slack. However, in the meantime, if garbage in the street is a big problem to you then you should probably take that fight to those countries that spew the least amount of CO2 into the atmosphere.

  74. Paul W commented:
    “It doesn’t follow that spending my money how I want leads to sewage in the streets or a lack of regard for others. I may freely donate to charity with great regard to my fellow man, but then again I may not. Neither should be of the slightest interest to you or anyone else.”

    Others shouldn’t be interested in you dispose of your sewage in the street??? How can you possibly say such a thing — ever hear of cholera?

    “There seems to be a lot of jumping back and forth between climate change and pollution trying to evoke an emotional response. ”

    No, it’s the same issue. The sewage example just makes it clear and places it in a historical context.

    “It’s interesting that you regard your fellow man as rampant polluters if left to their own devices.”

    Has not history shown that to be true — up to the present, when everyone is using the atmosphere as a free dump for CO2 pollution? Why do you think people stopped running their sewage and wash water and dish water into the street? Your choice/action has a consequence that affects the entire community. Do you have NO responsibility towards your community? And if you do choose to be responsible about it, what about the people who don’t choose that?

    “However, in the meantime, if garbage in the street is a big problem to you then you should probably take that fight to those countries that spew the least amount of CO2 into the atmosphere?”

    Huh??? I’m sorry, this makes no sense to me. Why wouldn’t you take the fight to those who’ve spewed the MOST amount of CO2 into the atmosphere? (The USA.)

  75. Sander van der Wal wrote:
    “So, oxygen is a pollutant then, too.”

    It once was, yes. It once killed many of the being on the planet 2.5 B yrs ago. But it does not have that effect today, nor is it threatening to increase to values that cause damage.

    “BTW, last time I looked the Clean Air Act wasn’t law in Europe, of anywhere else.”

    Countries in Europe don’t have clean air laws?

  76. Will, is this your 5th comment with no evidence or data, or your 6th? It’s difficult to keep up….

  77. Will N wrote:
    “If you look at the entire record of ENSO events, you’ll see that they are random events”

    And so, obviously unpredictable by climate models.

    Thanks for aiding the argument.

  78. Bob Kurland:

    Since you’re so sure AGW is wrong, why aren’t you refuting the papers by Harries et al, and several others, that show the greenhouse effect is increasing?

  79. I’m keeping to my resolve not to respond to trolls and those who argue with ad hominem attacks, but for the benefit of bystanders, I’ll announce a forthcoming post on my blog–“Why AGW isn’t science–the lessons of climategate.” Click on the sidebar link “Reflections of a Catholic Scientist”. It’ll be a couple of days.
    I apologize for this being off the thread topic.

  80. Bob K wrote:
    “I’m keeping to my resolve not to respond to trolls and those who argue with ad hominem attacks, but for the benefit of bystanders, I’ll announce a forthcoming post on my blog–“Why AGW isn’t science–the lessons of climategate.” ”

    This isn’t about Climategate — this is about observational evidence that the greenhouse effect is increasing.

    Until you address those specific observations, your blog post will (of course) mean nothing. Physics vs gossip.

    Bob, didn’t you say you were a scientist?

  81. Bob: I’m starting to realize you don’t HAVE a scientific case against AGW. Do you?

    That’s why you’ve instead gloomed onto the Climategate emails. They let you — you think — maintain your ideological beliefs without having to (you think) actually confront the evidence.

    How is that scientific??

    Tell you what: Grant me access to your private emails over the last year to two. OK? I **guarantee* you I can make you look like evil incarnate via selective release of your writing.

    Deal?

  82. Will Nitschke commented:
    “@David Appell
    “Evidence?”
    I’m assuming you’re familiar with the evidence as much as I am”

    I don’t think you are familiar with any evidence at all. You certainly haven’t presented any here. I think you pretend to say you know it as a way of avoiding having to actually present any. Your comments are among the most vacuous here, nothing more than name calling.

    You have spent far too much time commenting with people who agree with you, instead of seeking out forums where they do not. Typical.

  83. Fletcher Christian

    December 5, 2014 at 5:42 am

    David Appell – I can’t speak for the rest of Europe but the UK has fairly stringent clean air laws. However, they only apply in certain areas (mostly the crowded areas of cities) and relate to non-CO2 pollutants such as coal smoke.

    The laws were brought in in response to an incident in December 1952, in which smog lasted 5 days and killed 12,000 people by making existing lung problems worse.

    I believe that China is now having similar problems; also that LA used to have severe problems with photochemical smog until, yes, laws were brought in to sort it out. Apparently, Americans love their cars so much they are willing to breathe air turned into poison gas by those cars. Or at least some Americans – presumably some of them wanted clean air enough to do something about it.

  84. Briggs, why not do the obvious and Ban Apple. Give his martyrdom, so he can cash in his 72 virgins and grt busy with them

  85. Fletcher: Even before London there was the 1948 Denora smog incident in southwestern PA:
    http://en.wikipedia.org/wiki/1948_Donora_smog

    Clean air laws save money; it’s estimated the US Clean Air Act has saved the country between $5.6 and $49.4 trillion between 1970 and 1990:
    http://www.theatlantic.com/health/archive/2012/09/how-the-clean-air-act-has-saved-22-trillion-in-health-care-costs/262071/

    It’s the lack of pollution controls that inhibit economic growth.

  86. Bob: So then you’re going to completely ignore the half-dozen papers I listed above that directly show observatrions of an increase in the planet’s greenhouse effect?

    These measurements get at the heart of AGW at its most basic level. No one who questions AGW can ignore them and still be taken seriously.

  87. I do not understand how this paper was published; at a minimum I would have expected results for other easily available financial time series. It’s great the it works with the Dow Jones, for the provided time frames. How about the S&P500? The DAX? USD/JPY? Individual stocks? Would it predict the 1929 crash?

    These are all interesting questions, that with an implementation of the algorithm, can be answered with less than a day’s worth of work.

  88. @David Appell: You’re analogy with blood cholesterol is most apt. On the advice of activist scientists the US govt recommended people cut back on fatty foods and foods full of cholesterol, like eggs and prawns, and switch to a low fat diet. 35 years on with an obesity crisis caused by the switch from fatty foods to low fat foods in the US it turns our that this advice was pure bollards put out by scientists who sincerely thought they knew what they were talking about because they’re “scientists”. A little humility from the climate science activist community would help the human race a lot more than the hubristic posturing we see from some in that community.

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