15,904 research outputs found

### Non-Parametric Analyses of Log-Periodic Precursors to Financial Crashes

We apply two non-parametric methods to test further the hypothesis that
log-periodicity characterizes the detrended price trajectory of large financial
indices prior to financial crashes or strong corrections. The analysis using
the so-called (H,q)-derivative is applied to seven time series ending with the
October 1987 crash, the October 1997 correction and the April 2000 crash of the
Dow Jones Industrial Average (DJIA), the Standard & Poor 500 and Nasdaq
indices. The Hilbert transform is applied to two detrended price time series in
terms of the ln(t_c-t) variable, where t_c is the time of the crash. Taking all
results together, we find strong evidence for a universal fundamental
log-frequency $f = 1.02 \pm 0.05$ corresponding to the scaling ratio $\lambda =
2.67 \pm 0.12$. These values are in very good agreement with those obtained in
past works with different parametric techniques.Comment: Latex document 13 pages + 58 eps figure

### Comment on "Are financial crashes predictable?"

Comment on "Are financial crashes predictable?", L. Laloux, M. Potters, R.
Cont, J.P Aguilar and J.-P. Bouchaud, Europhys. Lett. 45, 1-5 (1999)Comment: 2 pages including 2 figures. Subm. to Eur. Phys Lett. Previous error
in fig. 1 correcte

### Twisting of N=1 SUSY Gauge Theories and Heterotic Topological Theories

It is shown that $D=4$ $N=1$ SUSY Yang-Mills theory with an appropriate
supermultiplet of matter can be twisted on compact K\"ahler manifold. The
conditions of cancellation of anomalies of BRST charge are found. The twisted
theory has an appropriate BRST charge. We find a non-trivial set of physical
operators defined as classes of the cohomology of this BRST \op . We prove that
the physical correlators are independent on external K\"ahler metric up to a
power of a ratio of two Ray-Singer torsions for the Dolbeault cohomology
complex on a K\"ahler manifold. The correlators of local physical \op s turn
out to be independent of anti-holomorphic coordinates defined with a complex
structure on the K\"ahler manifold. However a dependence of the correlators on
holomorphic coordinates can still remain. For a hyperk\"ahler metric the
physical correlators turn out to be independent of all coordinates of
insertions of local physical \op s.Comment: Latex, 35 pages, FERMILAB-PUB-93/062-T. More extended arguments, 7
references added, some misprints are remove

### Financial ``Anti-Bubbles'': Log-Periodicity in Gold and Nikkei collapses

We propose that imitation between traders and their herding behaviour not
only lead to speculative bubbles with accelerating over-valuations of financial
markets possibly followed by crashes, but also to ``anti-bubbles'' with
decelerating market devaluations following all-time highs. For this, we propose
a simple market dynamics model in which the demand decreases slowly with
barriers that progressively quench in, leading to a power law decay of the
market price decorated by decelerating log-periodic oscillations. We document
this behaviour on the Japanese Nikkei stock index from 1990 to present and on
the Gold future prices after 1980, both after their all-time highs. We perform
simultaneously a parametric and non-parametric analysis that are fully
consistent with each other. We extend the parametric approach to the next order
of perturbation, comparing the log-periodic fits with one, two and three
log-frequencies, the latter one providing a prediction for the general trend in
the coming years. The non-parametric power spectrum analysis shows the
existence of log-periodicity with high statistical significance, with a
prefered scale ratio of $\lambda \approx 3.5$ for the Nikkei index $\lambda
\approx 1.9$ for the Gold future prices, comparable to the values obtained for
speculative bubbles leading to crashes.Comment: 14 pages with 4 figure

### Liouville theory and special coadjoint Virasoro orbits

We describe the Hamiltonian reduction of the coajoint Kac-Moody orbits to the
Virasoro coajoint orbits explicitly in terms of the Lagrangian approach for the
Wess-Zumino-Novikov-Witten theory. While a relation of the coajoint Virasoro
orbit $Diff \; S^1 /SL(2,R)$ to the Liouville theory has been already studied
we analyse the role of special coajoint Virasoro orbits $Diff \;
S^1/\tilde{T}_{\pm ,n}$ corresponding to stabilizers generated by the vector
fields with double zeros. The orbits with stabilizers with single zeros do not
appear in the model. We find an interpretation of zeros $x_i$ of the vector
field of stabilizer $\tilde{T}_{\pm ,n}$ and additional parameters $q_i$, $i =
1,...,n$, in terms of quantum mechanics for $n$ point particles on the circle.
We argue that the special orbits are generated by insertions of "wrong sign"
Liouville exponential into the path integral. The additional parmeters $q_i$
are naturally interpreted as accessory parameters for the uniformization map.
Summing up the contributions of the special Virasoro orbits we get the
integrable sinh-Gordon type theory.Comment: preprint ITEP-67-1993,16 p.,Latex fil

### Significance of log-periodic precursors to financial crashes

We clarify the status of log-periodicity associated with speculative bubbles
preceding financial crashes. In particular, we address Feigenbaum's [2001]
criticism and show how it can be rebuked. Feigenbaum's main result is as
follows: ``the hypothesis that the log-periodic component is present in the
data cannot be rejected at the 95% confidence level when using all the data
prior to the 1987 crash; however, it can be rejected by removing the last year
of data.'' (e.g., by removing 15% of the data closest to the critical point).
We stress that it is naive to analyze a critical point phenomenon, i.e., a
power law divergence, reliably by removing the most important part of the data
closest to the critical point. We also present the history of log-periodicity
in the present context explaining its essential features and why it may be
important. We offer an extension of the rational expectation bubble model for
general and arbitrary risk-aversion within the general stochastic discount
factor theory. We suggest guidelines for using log-periodicity and explain how
to develop and interpret statistical tests of log-periodicity. We discuss the
issue of prediction based on our results and the evidence of outliers in the
distribution of drawdowns. New statistical tests demonstrate that the 1% to 10%
quantile of the largest events of the population of drawdowns of the Nasdaq
composite index and of the Dow Jones Industrial Average index belong to a
distribution significantly different from the rest of the population. This
suggests that very large drawdowns result from an amplification mechanism that
may make them more predictable than smaller market moves.Comment: Latex document of 38 pages including 16 eps figures and 3 tables, in
press in Quantitative Financ

### Stock market crashes are outliers

We call attention against what seems to a widely held misconception according
to which large crashes are the largest events of distributions of price
variations with fat tails. We demonstrate on the Dow Jones Industrial index
that with high probability the three largest crashes in this century are
outliers. This result supports suggestion that large crashes result from
specific amplification processes that might lead to observable pre-cursory
signatures.Comment: 8 pages, 3 figures (accepted in European Physical Journal B

### Stochastics theory of log-periodic patterns

We introduce an analytical model based on birth-death clustering processes to
help understanding the empirical log-periodic corrections to power-law scaling
and the finite-time singularity as reported in several domains including
rupture, earthquakes, world population and financial systems. In our
stochastics theory log-periodicities are a consequence of transient clusters
induced by an entropy-like term that may reflect the amount of cooperative
information carried by the state of a large system of different species. The
clustering completion rates for the system are assumed to be given by a simple
linear death process. The singularity at t_{o} is derived in terms of
birth-death clustering coefficients.Comment: LaTeX, 1 ps figure - To appear J. Phys. A: Math & Ge

### The Higgs Penguin and its Applications : An overview

We review the effective Lagrangian of the Higgs penguin in the Standard Model
and its minimal supersymmetric extension (MSSM). As a master application of the
Higgs penguin, we discuss in some detail the B-meson decays into a
lepton-antilepton pair. Furthermore, we explain how this can probe the Higgs
sector of the MSSM provided that some of these decays are seen at Tevatron Run
II and B-factories. Finally, we present a complete list of observables where
the Higgs penguin could be strongly involved.Comment: 22 pages, 6 figures, Invited review article to appear in Mod. Phys.
Lett. A, v2: Table 1 updated, comments and references adde

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