arXiv subjects

W. -X. Zhou

Publications and source records attributed to W. -X. Zhou.

25 records · Page 2Linked to original sources

arXiv2003

Renormalization Group Analysis of the 2000-2002 anti-bubble in the US S&P 500 index: Explanation of the hierarchy of 5 crashes and Prediction

We propose a straightforward extension of our previously proposed log-periodic power law model of the ``anti-bubble'' regime of the USA market since the summer of 2000, in terms of the renormalization group framework to model critical points. Using a previous work by Gluzman and Sornette (2002) on the classification of the class of Weierstrass-like functions, we show that the five crashes that occurred since August 2000 can be accurately modelled by this approach, in a fully consistent way with no additional parameters. Our theory suggests an overall consistent organization of the investors forming a collective network which interact to form the pessimistic bearish ``anti-bubble'' regime with intermittent acceleration of the positive feedbacks of pessimistic sentiment leading to these crashes. We develop retrospective predictions, that confirm the existence of significant arbitrage opportunities for a trader using our model. Finally, we offer a prediction for the unknown future of the US S&P500 index extending over 2003 and 2004, that refines the previous prediction of Sornette and Zhou (2002).

physics.soc-ph↗

arXiv2003

2000-2003 Real Estate Bubble in the UK but not in the USA

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 6.5% to 1.25% 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.

physics.soc-ph↗

arXiv2003

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

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 also detect a 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.

cond-mat.stat-mech↗

arXiv2003

The US 2000-2003 Market Descent: Clarifications

In a recent comment (Johansen A 2003 An alternative view, Quant. Finance 3: C6-C7, cond-mat/0302141), Anders Johansen has criticized our methodology and has questioned several of our results published in [Sornette D and Zhou W-X 2002 The US 2000-2002 market descent: how much longer and deeper? Quant. Finance 2: 468-81, cond-mat/0209065] and in our two consequent preprints [cond-mat/0212010, physics/0301023]. In the present reply, we clarify the issues on (i) the analogy between rupture and crash, (ii) the Landau expansion, ``double cosine'' and Weierstrass-type solutions, (iii) the symmetry between bubbles and anti-bubbles and universality, (iv) the condition of criticality, (v) the meaning of ``bullish anti-bubbles'', (vi) the absolute value of t_c-t, (vii) the fractal log-periodic power law patterns, (viii) the similarity between the Nikkei index in 1990-2000 and the S&P500 in 2000-2002 and (ix) the present status of our prediction.

cond-mat.stat-mech↗

arXiv2003

Finite-Time Singularity Signature of Hyperinflation

We present a novel analysis extending the recent work of Mizuno et al. [2002] on the hyperinflations of Germany (1920/1/1-1923/11/1), Hungary (1945/4/30-1946/7/15), Brazil (1969-1994), Israel (1969-1985), Nicaragua (1969-1991), Peru (1969-1990) and Bolivia (1969-1985). On the basis of a generalization of Cagan's model of inflation based on the mechanism of ``inflationary expectation'' or positive feedbacks between realized growth rate and people's expected growth rate, we find that hyperinflations can be characterized by a power law singularity culminating at a critical time $t_c$. Mizuno et al.'s double-exponential function can be seen as a discrete time-step approximation of our more general nonlinear ODE formulation of the price dynamics which exhibits a finite-time singular behavior. This extension of Cagan's model, which makes natural the appearance of a critical time $t_c$, has the advantage of providing a well-defined end of the clearly unsustainable hyperinflation regime. We find an excellent and reliable agreement between theory and data for Germany, Hungary, Peru and Bolivia. For Brazil, Israel and Nicaragua, the super-exponential growth seems to be already contaminated significantly by the existence of a cross-over to a stationary regime.

physics.soc-ph↗

arXiv2002

The US 2000-2002 Market Descent: How Much Longer and Deeper?

A remarkable similarity in the behavior of the US S&P500 index from 1996 to August 2002 and of the Japanese Nikkei index from 1985 to 1992 (11 years shift) is presented, with particular emphasis on the structure of the bearish phases. Extending a previous analysis of Johansen and Sornette [1999, 2000] on the Nikkei index ``anti-bubble'' based on a theory of cooperative herding and imitation working both in bullish as well as in bearish regimes, we demonstrate the existence of a clear signature of herding in the decay of the S&P500 index since August 2000 with high statistical significance, in the form of strong log-periodic components. We offer a detailed analysis of what could be the future evolution of the S&P500 index over the next two years, according to three versions of the theory: we expect an overall continuation of the bearish phase, punctuated by local rallies; we predict an overall increasing market until the end of the year 2002 or at the beginning of 2003 (first quarter); we predict a strong following descent (with maybe one or two severe up and downs in the middle) which stops during the first semester of 2004. After this strong minimum, the market is expected to recover. Beyond, our prediction horizon is made fuzzy by the possible effect of additional nonlinear collective effects and of a real departure from the anti-bubble regime. The similarities between the two stock market indices may reflect deeper similarities between the fundamentals of two economies which both went through over-valuation with strong speculative phases preceding the transition to bearish phases characterized by a surprising number of bad surprises (bad loans for Japan and accounting frauds for the US) sapping investors' confidence.

cond-mat.stat-mech↗

arXiv2002

New Evidence of Discrete Scale Invariance in the Energy Dissipation of Three-Dimensional Turbulence: Correlation Approach and Direct Spectral Detection

We extend the analysis of [Zhou and Sornette, Physica D 165, 94-125, 2002] showing statistically significant log-periodic corrections to scaling in the moments of the energy dissipation rate in experiments at high Reynolds number ($\approx 2500$) of three-dimensional fully developed turbulence. First, we develop a simple variant of the canonical averaging method using a rephasing scheme between different samples based on pairwise correlations that confirms Zhou and Sornette's previous results. The second analysis uses a simpler local spectral approach and then performs averages over many local spectra. This yields stronger evidence of the existence of underlying log-periodic undulations, with the detection of more than 20 harmonics of a fundamental logarithmic frequency $f = 1.434 \pm 0.007$ corresponding to the preferred scaling ratio $γ= 2.008 \pm 0.006$.

cond-mat.stat-mech↗