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Abstract:
In the aftermath of the burst of the "new economy" bubble in 2000, the Federal Reserve aggressively reduced short-term rates yields in less than two years from 6 1/2 to 1 1/4 % in an attempt to coax forth a stronger recovery of the US economy. But, there is growing apprehension that this is creating a new bubble in real estate, as strong housing demand is fuelled by historically low mortgage rates. Are we going from Charybdis to Scylla? This question is all the more excruciating at a time when many other indicators suggest a significant deflationary risk. Using economic data, Federal Reserve Chairman A. Greenspan and Governor D.L. Kohn dismissed recently this possibility. Using the theory of critical phenomena resulting from positive feedbacks in markets, we confirm this view point for the US but find that mayhem may be in store for the UK: we unearth the unmistakable signatures (log-periodicity and power law super-exponential acceleration) of a strong unsustainable bubble there, which could burst before the end of the year 2003.

Real estate, Bubble, Econophysics

Abstract:
Previous analyses of a large ensemble of stock markets have demonstrated that a log-periodic power law (LPPL) behavior of the prices constitutes a qualifying signature of speculative bubbles that often land with a crash. We detect such a LPPL signature in the foreign capital inflow during the bubble on the US markets culminating in March 2000. We detect a weak synchronization and lag with the NASDAQ 100 LPPL pattern. We propose to rationalize these observations by the existence of positive feedback loops between market-appreciation / increased-spending / increased-deficit-of-balance-of-payment / larger-foreign-surplus / increased-foreign-capital-inflows and so on. Our analysis suggests that foreign capital inflow have been following rather than causing the bubble.

We then 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 conclude that the low interest rates and depreciating dollar are the indispensable ingredients for a lower sustainable burden of the global US debt structure and for allowing the slow rebuilding of an internationally competitive economy. This will probably be accompanied by a weak stock market on the medium term as the growing Federal deficit is consuming a large part of the foreign surplus dollars and the stock market is remaining a very risky and unattractive investment. Notwithstanding strong surge of liquidity in recent months orchestrated by the Federal Reserve, this macroeconomic analysis which incorporates an element of collective behavior is in line with our recent analyses of the bearish market that started in 2000 in terms of a LPPL "anti-bubble." We project this LPPL anti-bubble to continue at least for another year. On the short term, increased availability of liquidity (M1) and self-fulfilling bullish anticipations may hold the stock market for a while.

Foreign capital inflow, speculative bubble, new economy, dollar depreciation, depression

Abstract:
Our analysis of financial data, in terms of super-exponential growth, suggests that the seed of the 2002/03 crisis of the Dutch supermarket giant AHOLD was planted in 1996. It became quite visible in 1999 when the post-bubble destabilization regime was well-developed and acted as the precursor of an inevitable collapse fueled by raising expectations of investors to maintain strong herding pressures. We have adapted Weidlich's theory of opinion formation to describe the formation of buy or sell decisions among investors, based on a competition between the mechanisms of herding and of personal opinion opposing the herd. Among four typical patterns of stock price evolution, we have identified a "critical zone" in the model characterized by a strong sensitivity of the price trajectory on the herding and personal inclination parameters. The critical zone describes the maturation of a systemic instability forewarning of an inevitable crash. Classification and recognition of the spontaneous emergence of patterns of stock market evolution based on Weidlich's theory of complex systems, and in particular our discovery of the post-bubble destabilization regime which acts as a precursor to a subsequent crash or antibubble, not only presents the possibility of developing early warning signals but also suggests to top management ways of dealing with the coming crisis.

Syngernetics, Royal Ahold, Bubble, Critical Zone, Crash

Abstract:
We introduce a novel non-parametric methodology to test for the dynamical time evolution of the lag-lead structure between two arbitrary time series. The method consists in constructing a distance matrix based on the matching of all sample data pairs between the two time series. Then, the lag-lead structure is searched as the optimal path in the distance matrix landscape that minimizes the total mismatch between the two time series, and that obeys a one-to-one causal matching condition. To make the solution robust to the presence of large noise that may lead to spurious structures in the distance matrix landscape, we then generalize this optimal search by introducing a fuzzy search by sampling over all possible paths, each path being weighted according to a multinomial logit or equivalently Boltzmann factor proportional to the exponential of the global mismatch of this path. We present the efficient transfer matrix method that solves the problem and test it on simple synthetic examples to demonstrate its properties and usefulness compared with the standard running-time cross-correlation method. We then apply our Optimal Thermal Causal Path method to the question of the causality between the US stock market and the treasury bond yields and confirm our earlier results on a causal arrow of the stock markets preceding the Federal Reserve Funds adjustments, as well as the yield rates at short maturities in the period 2000-2003. Our application of this technique to inflation, inflation change, GDP growth rate and unemployment rate unearths non-trivial causal relationships: the GDP changes lead inflation especially since the 1980s, inflation changes leads GDP only in the 1980 decade, and inflation leads unemployment rates since the 1970s. In addition, our approach seems to detect multiple competing causality paths in which one can have inflation leading GDP with a certain lag time and GDP feeding back/leading inflation with another lag time.

Econophysics, causality, correlation, thermal average, time series

Abstract:
Following a long tradition of physicists who have noticed that the Ising model provides a general background to build realistic models of social interactions, we study a model of financial price dynamics resulting from the collective aggregate decisions of agents. This model incorporates imitation, the impact of external news and private information. It has the structure of a dynamical Ising model in which agents have two opinions (buy or sell) with coupling coefficients which evolve in time with a memory of how past news have explained realized market returns. We study two versions of the model, which differ on how the agents interpret the predictive power of news. We show that the stylized facts of financial markets are reproduced only when agents are over-confident and mis-attribute the success of news to predict return to herding effects, thereby providing positive feedbacks leading to the model functioning close to the critical point. Our model exhibits a rich multifractal structure characterized by a continuous spectrum of exponents of the power law relaxation of endogenous bursts of volatility, in good agreement with previous analytical predictions obtained with the multifractal random walk model and with empirical facts.

Ising model, overconfidence, imitation and herding, econophysics

Abstract:
Since August 2000, the USA as well as most other western markets have depreciated almost in synchrony according to complex patterns of drops and local rebounds. In a paper published in the December 2002 issue of Quantitative Finance, we have proposed to describe this phenomenon using the concept of a log-periodic power law (LPPL) antibubble, characterizing behavioral herding between investors leading to a competition between positive and negative feedbacks in the pricing process. An online monthly prediction for the future evolution of the US S&P 500 index has been issued, monitored and updated. Here, we test the possible existence of a regime switching in the US S&P 500 antibubble. First, we find some evidence that the antibubble might be on its way to cross-over to a shift in log-periodicity described by a so-called second-order log-periodicity previously documented for the Japanese Nikkei index in the 1990s. Second, we develop a battery of tests to detect a possible end of the antibubble which suggest that the antibubble is still alive and may still continue well in the future. Our tests provide quantitative measures to diagnose the end of the antibubble, when it will come. Such diagnostic is not instantaneous and requires probably three to six months within the new regime before assessing its existence with confidence. In conclusion, our prediction that the S&P 500 is going to plunge progressively from the summer 2003 to bottom in 2004 seems to remain basically intact, possibly with a few month delay extending almost to the end of 2003 if the shift to the second-order log-periodicity is confirmed.

Econophysics, Prediction, Log-periodic power law, Antibubble, Hypothesis test

Abstract:
We analyze 27 house price indexes of Las Vegas from Jun. 1983 to Mar. 2005, corresponding to 27 different zip codes. These analyses confirm the existence of a real-estate bubble, defined as a price acceleration faster than exponential, which is found however to be confined to a rather limited time interval in the recent past from approximately 2003 to mid-2004 and has progressively transformed into a more normal growth rate comparable to pre-bubble levels in 2005. There has been no bubble till 2002 except for a medium-sized surge in 1990. In addition, we have identified a strong yearly periodicity which provides a good potential for fine-tuned prediction from month to month. A monthly monitoring using a model that we have developed could confirm, by testing the intra-year structure, if indeed the market has returned to "normal" or if more turbulence is expected ahead. We predict the evolution of the indexes one year ahead, which is validated with new data up to Sep. 2006. The present analysis demonstrates the existence of very significant variations at the local scale, in the sense that the bubble in Las Vegas seems to have preceded the more global USA bubble and has ended approximately two years earlier (mid 2004 for Las Vegas compared with mid-2006 for the whole of the USA).

Econophysics, real estate market, periodicity, power law, prediction

Abstract:
By combining (i) the economic theory of rational expectation bubbles, (ii) behavioral finance on imitation and herding of investors and traders and (iii) the mathematical and statistical physics of bifurcations and phase transitions, the logperiodic power law (LPPL) model has been developed as a flexible tool to detect bubbles. The LPPL model considers the faster-than-exponential (power law with finite-time singularity) increase in asset prices decorated by accelerating oscillations as the main diagnostic of bubbles. It embodies a positive feedback loop of higher return anticipations competing with negative feedback spirals of crash expectations. We use the LPPL model in one of its incarnations to analyze two bubbles and subsequent market crashes in two important indexes in the Chinese stock markets between May 2005 and July 2009. Both the Shanghai Stock Exchange Composite index (US ticker symbol SSEC) and Shenzhen Stock Exchange Component index (SZSC) exhibited such behavior in two distinct time periods: 1) from mid-2005, bursting in October 2007 and 2) from November 2008, bursting in the beginning of August 2009. We successfully predicted time windows for both crashes in advance [24, 1] with the same methods used to successfully predict the peak in mid-2006 of the US housing bubble [37] and the peak in July 2008 of the global oil bubble [26]. The more recent bubble in the Chinese indexes was detected and its end or change of regime was predicted independently by two groups with similar results, showing that the model has been well-documented and can be replicated by industrial practitioners. Here we present more detailed analysis of the individual Chinese index predictions and of the methods used to make and test them. We complement the detection of log-periodic behavior with Lomb spectral analysis of detrended residuals and (H, q)-derivative of logarithmic indexes for both bubbles. We perform unit-root tests on the residuals from the log-periodic power law model to confirm the Ornstein-Uhlenbeck property of bounded residuals, in agreement with the consistent model of ‘explosive’ financial bubbles [16].

stock market crash, financial bubble, Chinese markets, rational expectation bubble, herding, log-periodic power law, Lomb spectral analysis, unit-root test

Abstract:
Using the descriptive method of log-periodic power laws (LPPL) based on a theory of behavioral herding, we use a battery of parametric and non-parametric tests to demonstrate the existence of an antibubble in the yields with maturities larger than 1 year since October 2000. The concept of "antibubble" describes the existence of a specific LPPL pattern that is thought to reflect collective herding effects. From the dependence of the parameters of the LPPL formula as a function of yield maturities and using lagged cross-correlation calculations between the S\&P 500 and bond yields, we find strong evidence for the following causality: Stock Market - Fed Reserve (Federal funds rate) - short-term yields - long-term yields (as well as a direct and instantaneous influence of the stock market on the long-term yields). Our interpretation is that the FRB is "causally slaved" to the stock market (at least for the studied period), because the later is (taken as) a proxy for the present and future health of the economy.

Econophysics, Antibubble, Causality, Yield, Stock market

Abstract:
The trade size $\omega$ has direct impact on the price formation of the stock traded. Econophysical analyses of transaction data for the US and Australian stock markets have uncovered market-specific scaling laws, where a master curve of price impact can be obtained in each market when stock capitalization $C$ is included as an argument in the scaling relation. However, the rationale of introducing stock capitalization in the scaling is unclear and the anomalous negative correlation between price change $r$ and trade size $\omega$ for small trades is unexplained. Here we show that these issues can be addressed by taking into account the aggressiveness of orders that result in trades together with a proper normalization technique. Using order book data from the Chinese market, we show that trades from filled and partially filled limit orders have very different price impact. The price impact of trades from partially filled orders is constant when the volume is not too large, while that of filled orders shows power-law behavior $r\sim \omega^\alpha$ with $\alpha\approx2/3$. When returns and volumes are normalized by stock-dependent averages, capitalization-independent scaling laws emerge for both types of trades. However, no scaling relation in terms of stock capitalization can be constructed. In addition, the relation $\alpha=\alpha_\omega/\alpha_r$ is verified, where $\alpha_\omega$ and $\alpha_r$ are the tail exponents of trade sizes and returns. These observations also enable us to explain the anomalous negative correlation between $r$ and $\omega$ for small-size trades. We anticipate that these regularities may hold in other order-driven markets.

Econophysics; Price impact function; Price-volume relation; Scaling laws; Data collapsing