For a general presentation of the underlying concepts, theory, empirical tests and concrete applications, with a discussion of previous predictions, see Why Stock Market Crash?.Posted on 08/02/2003 11:04:34 PM PDT by ThePythonicCow
Based on a theory of cooperative herding and imitation working both in bullish as well as in bearish regimes, we have detected the existence of a clear signature of herding in the decay of the US S&P500 index since August 2000 with high statistical significance, in the form of strong log-periodic components.
Please refer to the following paper for a detailed description: D. Sornette and W.-X. Zhou, The US 2000-2002 Market Descent: How Much Longer and Deeper? Quantitative Finance 2 (6), 468-481 (2002) (e-print at http://arXiv.org/abs/cond-mat/0209065).
For a general presentation of the underlying concepts, theory, empirical tests and concrete applications, with a discussion of previous predictions, see Why Stock Market Crash?.
NEW: (Evidence of Fueling of the 2000 New Economy Bubble by Foreign Capital Inflow: Implications for the Future of the US Economy and its Stock Market ), this new paper attempts to construct a coherent analysis of the US stock market linking technical analysis of the type presented below to macroeconomic thinking. We combine a macroeconomic analysis of feedback processes occurring between the economy and the stock market with a technical analysis of more than two hundred years of the DJIA to investigate possible scenarios for the future, three years after the end of the bubble and deep into a bearish regime. We also detect a log-periodic power law (LPPL) accelerating bubble on the EURO against the US dollar and the Japanese Yen. In sum, our analyses is in line with our previous work on the LPPL "anti-bubble" representing the bearish market that started in 2000.
This figure shows 8 years of the evolution of the Japanese Nikkei index and 7 years of the USA S&P500 index, compared to each other after a translation of 11 years has been performed. The years are written on the horizontal axis (and marked by a tick on the axis) where January 1 of that year occurs. This figure illustrates an analogy noted by several observers that our work has made quantitative. The oscillations with decreasing frequency which decorate an overall decrease of the stock markets are observed only in very special stock markets regimes, that we have terms log-periodic "anti-bubbles". By analyzing the mathematical structure of these oscillations, we quantify them into one (or several) mathematical formula(s) that can then be extrapolated to provide the prediction shown in the two following figures. Note that extrapolating is often a risky endeavor and needs to be justified. In our case, the extrapolations, which give the forecasts, are based on the belief that these equations offered below embody the major forces in the market at the macroscopic scale. This leads to the possibility of describing several probable scenarios. We do not believe in the existence of deterministic trajectories but we aim at targetting the most probable future paths.
Fig. 1 shows the predictions of the future of the US S&P 500 index performed on Aug.24,2002. The continuous line is the fit and its extrapolation, using our theory capturing investor herding and crowd behavior. The theory takes into account the competition between positive feedback (self-fulfilling sentiment), negative feedbacks (contrariant behavior and fundamental/value analysis) and inertia (everything takes time to adjust). Technically, we use what we call a "super-exponential power-law log-periodic function" derived from a first order Landau expansion of the logarithm of the price. The dashed line is the fit and its extrapolation by including in the function a second log-periodic harmonic. The two fits are performed using the index data from Aug.9,2000 to Aug.24 2002 that are marked as black dots. The blue dots show the daily price evolution from Aug.25,2002 to July 17,2003. The large (respectively small) ticks in the abscissa correspond to January 1st (respectively to the first day of each quarter of each year.
Fig. 2 shows the new predictions of the future of the US S&P 500 index using all the data from Aug.9,2000 to Jul.17,2003, illustrated by (continuous and dashed) black lines. Again, the continuous line is the fit and its extrapolation using the super-exponential power-law log-periodic function derived from the first order Landau expansion of the logarithm of the price, while the dashed line is the fit and its extrapolation by including in the function a second log-periodic harmonic. We also present the two previous fits (red lines) performed on Aug.24,2002 (shown in Fig. 1) for comparison, so as to provide an estimation of the sensitivity of the prediction and of its robustness as the price evolves. The blue dots show the daily price evolution from Aug.9,2000 to Jul.17,2003. The large (respectively small) ticks in the abscissa correspond to January 1st (respectively to the first day of each quarter) of each year.
Fig. 3 shows the predictions of the future of the US S&P 500 index applying the so-called 'zero-phase' Weierstrass-type function, which is another child of our general theory of imitation and herding between investors. As for the previous figures, our theory takes into account the competition between positive feedback (self-fulfilling sentiment), negative feedbacks (contrariant behavior and fundamental/value analysis) and inertia (everything takes time to adjust). This 'zero-phase' Weierstrass-type function adds one additional ingredient: it attempts to capture the existence of 'critical' points within the anti-bubble, corresponding to accelerating waves of imitation within the large scale unraveling of the herding anti-bubble. The continuous black line is the forward prediction using all the data from Aug.9,2000 to July, 17,2003, while the dashed black line is the retroactive prediction using the data from Aug.9,2000 to Aug.24,2002. Both lines are reconstructed and extrapolated from the fits to a six-term zero-phase Weierstrass-type function. We also present the two previous fits (red lines) performed on Aug.24,2002 (shown in Fig. 1) for comparison. The blue dots show the daily price evolution from Aug.9,2000 to July, 17,2003. The large (respectively small) ticks in the abscissa correspond to January 1st (respectively to the first day of each quarter) of each year.
The striking development observed in the last update on June, 19, is confirmed. The 'zero-phase' Weierstrass-type function, which up to May, 18, 2003 included selected a series of downward critical crashes, is now selecting as the dominant critical points the bullish accelerations. The formula is thus deciphering the coexistence of two sets of critical points: (i) the crashes previously recognized which have punctuated the descent in the last three years and (ii) the bursts of upward accelerating rallies. This formula is however not rich enough in its present version to capture these two sets simultaneously and has to choose between the two, as a result of their relative strengths. This new twist does not change fundamentally our prediction of a drastic turn in the very near future towards a systematic downward trajectory till the summer of 2004. The question posed by the insight provided by this figure 3 is whether this will turn out as a result of a crash following a strong rally in the next two months or so. This crash will then be followed by a longer and continuous price depreciation.
Fig. 3bis is a modification of the 'zero-phase' Weierstrass-type function, which contains only odd-terms in the expansion (this will be elaborated upon in a future technical communication). By this trick, the odd-zero-phase Weierstrass-type function is able to describe simultaneously the two sets of critical points. The continuous black line is the forward prediction using all the data from Aug.9,2000 to July, 17,2003, while the dashed black line is the retroactive prediction using the data from Aug.9,2000 to Aug.24,2002. Both lines are reconstructed and extrapolated from the fits to a six-term odd-zero-phase Weierstrass-type function. We also present the two previous fits (red lines) performed on Aug.24,2002 (shown in Fig. 1) for comparison. The blue dots show the daily price evolution from Aug.9,2000 to July 17,2003. The large (respectively small) ticks in the abscissa correspond to January 1st (respectively to the first day of each quarter) of each year.
In conclusion, the coexistence of the strong downward crashes and upward rallies in the overall anti-bubble regime suggests to us that the market is completely dominated by sentiment, confidence and lack thereof and byherding. These mechanisms are amplifying any news, perturbation or rumor spreading in the network of investors.
Fig. 4 extends figures 1 and 2 by performing a sensitivity analysis on the simple log-periodic formula (continuous lines in figures 1 and 2), in order to assess the reliability and range of uncertainty of the prediction. Using the fit shown in black solid lines in figure 2, we have generated 10 realizations of an artificial S&P500 by adding GARCH noise to the black solid line. GARCH means "generalized auto-regressive conditional heteroskedasticity". It is a process often taken as a benchmark in the financial industry and describes the fact that volatility is persistent. The innovations of the used GARCH noise have been drawn from a Student distribution with 3 degrees of freedom with a variance equal to that of the residuals of the fit of the real data by the black continuous curve, to ensure the agreement between these synthetic time series and the known properties of the empirical distribution of returns. Using the GARCH noise improves on our previous synthetic tests of last month by using a more realistic correlated noise process. The fits are shown as the bundle of 10 curves in magenta. This bundle of predictions is coherent and suggests a good robustness of the prediction. The typical width of the blue dots give a sense of the variability that can be expected around this most probable scenario. The real S&P500 price trajectory is shown as the red wiggly line.
Fig. 5 extends figures 1 and 2 by performing a sensitivity analysis on the log-periodic formula with a second log-periodic harmonic (dashed lines in figures 1 and 2), in order to assess the reliability and range of uncertainty of the prediction. Using the fit shown in dashed solid lines in figure 2, we have generated 10 realizations of an artificial S&P500 by adding the GARCH noise (described in the previous caption of Fig. 5) to the dashed solid line. We have then fitted each of these 10 synthetic noisy clones of the S&P500 by our log-periodic formula. This yields the 10 curves shown here in magenta. This test shows that the log-periodic formula with a second log-periodic harmonic (dashed lines in figures 1 and 2) is also providing stable scenarios: the precise timing of the highs and lows remain robust with respect to the realization of the noise. The real S&P500 price trajectory is shown as the red wiggly line.
Fig. 6 extends figure 3 by performing a sensitivity analysis on the 'zero-phase' Weierstrass-type function, in order to assess the reliability and range of uncertainty of the prediction. Using the fit shown in black solid lines in figure 3, we have generated 10 realizations of an artificial S&P500 by adding A GARCH noise to the black solid line. GARCH means "generalized auto-regressive conditional heteroskedasticity". It is a process often taken as a benchmark in the financial industry and describes the fact that volatility is persistent. The innovations of the used GARCH noise have been drawn from a Student distribution with 3 degrees of freedom with a variance equal to that of the residuals of the fit of the real data by the black continuous curve, to ensure the agreement between these synthetic time series and the known properties of the empirical distribution of returns. Using the GARCH noise improves on our previous synthetic tests of last month by using a more realistic correlated noise process. We have then fitted each of these 10 synthetic noisy clones of the S&P500 (shown as the blue dots) by our 'zero-phase' Weierstrass-type function. This yields the narrow bundle of 10 curves shown here in magenta. This bundle of predictions is very coherent and suggests a good robustness of the prediction. The typical width of the blue dots give a sense of the variability that can be expected around this most probable scenario. The real S&P500 price trajectory is shown as the red wiggly line.
Fig. 6bis is the same as Fig. 6 but for the odd-zero-phase Weierstrass function shown in Fig. 3bis.
Fig. 7 analyses the VIX index by fitting it with our simple log-periodic formula. The VIX index is one of the world's most popular measures of investors' expectations about future stock market volatility (that is, risk). See http://www.cboe.com/micro/vixvxn/introduction.asp. For historical data, see http://www.cboe.com/micro/vixvxn/specifications.asp. The VIX time series is shown as the red wiggly curve. We have followed the same procedure as for figures 4-6: (i) we fit the real VIX data with our simple log-periodic formula; (ii) we then generate 10 synthetic time series by adding GARCH noise to the fit; (iii) we redo a fit of each of the 10 synthetic time series by the simple log-periodic formula and thus obtain the bundle of 10 predictions shown as the magenta lines. Strikingly, we first observe that our log-periodic formula is able to account quite well for the behavior of the VIX index, strengthening the evidence that the market is presently in a strong herding (anti-bubble) phase. Note also the rather good stability of the predictions, suggesting a reasonable reliability.
Yes, but these guys are using a very weak and naive predictive model. It is the kind of "analysis" that you expect someone with no experience in market prediction to come up with. Nobody in the business uses these kinds of models because they are known to give really lousy results in the general case. The kinds of mathematics actually used for state-of-the-art financial prediction are much more technologically sophisticated than what these guys are doing, and have MUCH better track records for accurate forecasting and prediction.
BTW, the best models to date are suggesting a slow-but-steady several year growth period. Nothing explosive, but good for business and the economy.
And, yes, if I were using a model to help manage large sums of money, or to help forecasting for a large corporation, I would not use this model. This model is too academic, too single-flavored, too monochrome. It does a cute job of pointing out one thing.
BTW - did the best models predict the crashes of 1929, 1987 or 2000, or at least, do they, when backtested?
Yes, they did. And not with backtesting, but projecting a decade or more out. Note that the first fully predicted boom-crash was the late 1990s one, because it takes some significant computing horsepower to build really good models, crunch that wasn't really available and cost-effective prior to the 1980s.
I saw models in the late 1980s that predicted not only the timing and magnitude of the 1990s stock boom, but the crash as well. Actually, they put the crash in the late 2001 timeframe IIRC, but I give'em an "A" for effort; in the intervening years they may have done a model update that revised the actual downside date. The further out the projection, the bigger the error margin on magnitude and timing. The models are occasionally checkpointed with reality to reduce the error margin; models that have drifted more than a certain amount at the checkpoint need to be rebuilt, which is expensive. Among the many reasons that cash flow into the stock market from institutions liberalized a few months ago is that several big models checkpointed okay, which basically confirmed that we were past the bottom as the models predicted and that the models (which almost universally stated we should be on a long upside) were still reasonably valid predictors.
I was skeptical when I saw some of the reports generated by these models in the mid- to late-1980s, but over the years I've become a believer because those models delivered despite my skepticism. I've since involved myself in the actual science and theory of large-scale predictive models of complex dynamic systems. Most big financial institutions and hedge funds have close guarded predictive models of the markets and economy. Some are better than others, but I can state for a fact that most are vastly better than most people generally believe. Also, the factors that go into even simple models are unbelievably diverse. All the most important factors are largely unrelated to finance and the stock market, yet they are remarkably good at predicting finance and markets.
I design predictor technologies for hedge funds among other clients. Good predictors are heavy duty trade secrets and are worth quite a bit of bank to those that can produce something just a few percent better than the institution down the street.
So I suspect that you'd say that Sornette's analysis is a one trick pony, suitable mostly for "predicting" the couple years of charts prior to when it was published. Which is, as someone noted above, useless BS.
hmmm ...
I do not have access to the models of which you speak. But if they are as you say, then this is most impressive.
We shall soon enough see. I've been quite happy with the very dark, pro-Gold, anti-stock, advisors I've been following for the last three years, such as James Dines, Elliott Wave and bits and pieces such as Sornette's analysis above.
But I pulled out of Gold earlier this week, and currently am only invested in my health, my profession and my children. I think I will stay on the sidelines for a bit until I see which way this is playing out.
As I've explained repeatedly (in other threads), gold is a very bad investment unless you subscribe to the dotcom theory of economics. The total cost of production for the average ounce of gold is $190 give or take $10. And that number is expected to fall, possibly as low as $150 for reasons that are beyond scope here relating to some excellent new resource models. Due to improvements in gold extraction and discovery, the production of gold has been very flexible for at least a couple decades now. At $300/oz, the mining companies could easily increase production ten-fold and still be profitable. In other words, it has become a purely commodity market that doesn't act like a commodity because people still act like gold has inherently inflexible production, which was true for most of its history but isn't true now due to the state of gold mining technology.
Some day sooner than later, the price of gold will collapse from its currently absurd price to a level reflecting a genuine commodity market. When that happens, a lot of people banking on gold will be very unhappy and the gold mining companies won't be remotely as profitable.
For those really interested in metals, I suggest avoiding metals that have flexible commodity production capability, which includes both gold and silver. In this sense, gold and silver should be treated the same as copper or iron production. All metals of this resource type are subject to a slow but steady decrease in value with the current state of mining and extraction technology, even ones that were formerly "rare" and "precious".
If I was going to stock up on physical storage implements of dense value, I usually suggest platinum. It has much more value industrially than gold or silver, has high value density (dollars/oz), the production is still relatively inflexible, and the market price reflects the actual commodity cost of production. Platinum will likely retain its value very well for economically sound reasons.
Or should I make it a habit of scanning FR for your posts every few weeks <grin>?
And, post Black Friday of '29, the markets rallied ; that's right, they went up. It was Joe Kennedy and his little band of shorters, who, against the masses and masses of money being poured in, by the likes of Morgan, etc. created the backwash and did it ILLEGALLY ! This can no longer happen, BTW, since so many rules /laws have been changed since then.
One CAN make pots of money, if one knows that the market is going down and can guesstimate for how long.
A little factual history re THE SOUTH SEA BUBBLE. Yes, it was a BUBBLE, yes, the mania of the crowds ( as with ALL "BUBBLES" )fed it, what makes this one atypical, is that the Bank of England AND the government was involved in it, corruption was on a massive scale and it almost brought down the government, dethroned the monarchy, AND made a nation totally insolvent.
The nascent English Stock Exchange was so far removed from what was around in America, on Wall Street, in the 1920s, as to be almost totally unrecognizable.The swindles, that went down back then, make ENRON, Arthur Anderson, et al , look like kindergarten stuff, penny ante child's play. It even makes the dot.com stuff look honest .
What anyone, who finds the article "useful " should do, is to adjust their tinfoil.
Historically, excepting THE GREAT DEPRESSION ( more on that later ), our crashes/depressions ( we haven't had one since the that one )/resessions don't last all that long. The above chart, is therefore misleading to utterly bogus. The ONLY reasons that the one sort of begun in '29 lasted as long as it did, was because there was a worldwide depression, which was the direct aftermath of WW I and the Treaty of Versailles, Wilson's inepttitude, the Taft-Hartley garbage, and the rise of Hitler; not to mention FDR's Socialistic stupidities.
Oh yes, and the authors of the charts, based at least some of it, on charts from the CBOE ( Chicago Board Otions Exchange ), whose charts do NOT relate to ALL markets; not even in general. Since I am probably the ONLY person on FR ( well, the only one who types to it ... LOL ) who happens to be part of a company that is a FOUNDING member of the CBOE, I am also the ONLY one on this thread, who is talking about something they actually know about.
I can't complain. But one must stay on one's toes; the market enjoys making fools of us all, sooner or later.
Yes, of course there are others here, who actually know about markets; that isn't the point. LOL
I'm still convinced that bad times are a comin'. I just don't know when or how to play it. If we still have big bubbles, we can still have big crashes. The laws of human nature have not been repealed, last I looked.
Maybe the feds managed to pour enough gas er eh debt on the fire to keep it from going out for now ... but the systemic problems in the worlds banking, investment and financial arenas keep growing.
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