Quantitative understanding of human behaviors provides elementary
comprehension of the complexity of many human-initiated systems. In this paper,
we investigate the behavior of people on the $BBS$ forum by the statistical
analysis of the amounts of view and reply of posts. According to our
statistics, we find that the amounts of view and reply of posts follow the
power law distributions with different power exponent. Furthermore, we discover
that the amounts of view and reply of posts have nonlinear relationship. They
are related by power function and show us straight line in log-log plot. Based
on the estimation of slope and intercept of the line, we can characterize the
behaviors quantitatively and know that people of Chinese forum and those of
foreign forum have different preference towards replying to and viewing the
posts. At last, we analyze the burstiness and memory in replying time series.
They show some universal properties among different forum. All of them locate
themselves in the high-$B$, low-$M$ region.
Prediction markets show considerable promise for developing flexible
mechanisms for machine learning. Here, machine learning markets for
multivariate systems are defined, and a utility-based framework is established
for their analysis. This differs from the usual approach of defining static
betting functions. It is shown that such markets can implement model
combination methods used in machine learning, such as product of expert and
mixture of expert approaches as equilibrium pricing models, by varying agent
utility functions. They can also implement models composed of local potentials,
and message passing methods. Prediction markets also allow for more flexible
combinations, by combining multiple different utility functions. Conversely,
the market mechanisms implement inference in the relevant probabilistic models.
This means that market mechanism can be utilized for implementing parallelized
model building and inference for probabilistic modelling.
We introduce a new measure of activity of financial markets that provides a
direct access to their level of endogeneity. This measure quantifies how much
of price changes are due to endogenous feedback processes, as opposed to
exogenous news. For this, we calibrate the self-excited conditional Poisson
Hawkes model, which combines in a natural and parsimonious way exogenous
influences with self-excited dynamics, to the E-mini S&P 500 futures contracts
traded in the Chicago Mercantile Exchange from 1998 to 2010. We find that the
level of endogeneity has increased significantly from 1998 to 2010, with only
70% in 1998 to less than 30% since 2007 of the price changes resulting from
some revealed exogenous information. Analogous to nuclear plant safety
concerned with avoiding "criticality", our measure provides a direct
quantification of the distance of the financial market to a critical state
defined precisely as the limit of diverging trading activity in absence of any
external driving.
This paper deals with the disciplinary dimensions of a very new field called econphysics and shows that despite the fact that econophysics is regularly described as an interdisciplinary approach, it is in fact a multidisciplinary field. Beyond this observation, we note that recent developments suggests that econophysics could evolve into a more integrated field. We have therefore taken a prospective approach by analyzing how this field could become more transdisciplinary. We show that a common echeme is attainable and we investigate the possibilities of transdisciplinary econophysics.
Tim R. L. Fry (Department of Econometrics and Business
Statistics Monash University) ; Mark N
posted by editor
(28 February 2002)
pdf
(235 views, 322 downloads, 0 comments)
[show abstract]
[hide abstract]
There is no qualitative dependent model that can
simultaneously
account for data sets in which the variable of interest has both a
multi-modal distribution and is potentially ordered. Such a
multimodal distribution may be the result of individuals being
captive to particular choices. Such a case arises when there is digit
preferencing (particular numbers, such as 0, 5 and 101 are often
favored in many survey-based data sets). This paper introduces a new
discrete choice model, the Dogit Ordered Extreme Value (DOGEV), that
does account for both ordering and digit preferencing in the data,
and applies it to an Australian Inflationary Expectations data set
In this paper we develop an evidential force aggregation method intended for classification of evidential intelligence into recognized force structures. We assume that the intelligence has already been partitioned into clusters and use the classification method individually in each cluster. The classification is based on a measure of fitness between template and fused intelligence that makes it possible to handle intelligence reports with multiple nonspecific and uncertain propositions. With this measure we can aggregate on a level-by-level basis, starting from general intelligence to achieve a complete force structure with recognized units on all hierarchical levels.
With the daily and minutely data of the German DAX and Chinese indices, we
investigate how the return-volatility correlation originates in financial
dynamics. Based on a retarded volatility model, we may eliminate or generate
the return-volatility correlation of the time series, while other
characteri
83b
stics, such as the probability distribution of returns and long-range
time-correlation of volatilities etc., remain essentially unchanged. This
suggests that the leverage effect or anti-leverage effect in financial markets
arises from a kind of feedback return-volatility interactions, rather than the
long-range time-correlation of volatilities and asymmetric probability
distribution of returns. Further, we show that large volatilities dominate the
return-volatility correlation in financial dynamics.
To investigate the universal structure of interactions in financial dynamics,
we analyze the cross-correlation matrix C of price returns of the Chinese stock
market, in comparison with those of the American and Indian stock markets. As
an important emerging market, the Chinese market exhibits much stronger
correlations than the developed markets. In the Chinese market, the
interactions between the stocks in a same business sector are weak, while extra
interactions in unusu
6b9
al sectors are detected. Using a variation of the
two-factor model, we simulate the interactions in financial markets.
We present conditions under which positive alpha exists in the realm of active portfolio management–
in contrast to the controversial result in (Jarrow, 2010, pg. 20) which implicates delegated portfolio
management by surmising that positive alphas are illusionary. Specifically, we show that the critical
assumption used in (Jarrow, 2010, pg. 20), to derive the illusionary alpha result, is based on
a zero set for CAPM with Lebesgue measure zero. So conclusions based on the assumption may
well have probability measure zero of occurrence. Technically, the existence of [Tanaka] local time
on that set implies existence of positive alphas. In fact, we show that positive alpha exists under
the same scenarios of ”perpetual event swap” and ”market systemic event” Jarrow (2010) used to
formulate the illusionary positive alpha result. First, we prove that as long as asset price volatility
is greater than zero, systemic events like market crash will occur in finite time almost surely. Thus
creating an opportunity to hedge against that event. Second, we find that Jarrow’s ”false positive
alpha” variable constitutes portfolio manager reward for trading strategy. For instance, we show
that positive alpha exists if portfolio managers develop hedging strategies based on either (1) an
exotic [barrier] option on the underlying asset–with barrier hitting time motivated by the ”market
systemic” event, or (2) a swaption strategy for the implied interest rate risk inherent in Jarrow’s
triumvirate of riskless rate of return, factor sensitivity exposure, and constant risk premium for a
perpetual event swap.
74c
We show how random matrix theory can be applied to develop new algorithms to
extract dynamic factors from macroeconomic time series. In particular, we
consider a limit where the number of random variables N and the number of
consecutive time measurements T are large but the ratio N / T is fixed. In this
regime the underlying random matrices are asymptotically equivalent to Free
Random Variables (FRV).Application of these methods for macroeconomic
indicators for Poland economy is also presented.
We provide direct evidence of market manipulation at the beginning of the
financial crisis in November 2007. The type of manipulation, a "bear raid,"
would have been prevented by a regulation that was repealed by the Securities
and Exchange Commission in July 2007. The regulation, the uptick rule, was
designed to prevent manipulation and promote stability and was in force from
1938 as a key part of the government response to the 1929 market crash and its
aftermath. On November 1, 2007, Citigroup experienced an unusual increase in
trading volume and decrease in price. Our analysis of financial industry data
shows that this decline coincided with an anomalous increase in borrowed
shares, the selling of which would be a large fraction of the total trading
volume. The selling of borrowed shares cannot be explained by news events as
there is no corresponding increase in selling by share owners. A similar number
of shares were returned on a single day six days later. The magnitude and
coincidence of borrowing and returning of shares is evidence of a concerted
effort to drive down Citigroup's stock price and achieve a profit, i.e., a bear
raid. Interpretations and analyses of financial markets should consider the
possibility that the intentional actions of individual actors or coordinated
groups can impact market behavior. Markets are not sufficiently transparent to
reveal even major market manipulation events. Our results point to the need for
regulations that prevent intentional actions that cause markets to deviate from
equilibrium and contribute to crashes. Enforcement actions cannot reverse
severe damage to the economic system. The current "alternative" uptick rule
which is only in effect for stocks dropping by over 10% in a single day is
insufficient. Prevention may be achieved through improved availability of
market data and the original uptick rule or other transaction limitations.
We introduce a new method for detection of long-range cross-correlations and
multifractality - multifractal height cross-correlation analysis (MF-HXA) -
based on scaling of qth order covariances. MF-HXA is a bivariate generalization
of the height-height correlation analysis of Barabasi & Vicsek [Barabasi, A.L.,
Vicsek, T.: Multifractality of self-affine fractals, Physical Review A 44(4),
1991]. The method can be used to analyze long-range cross-correlations and
multifractality between two simultaneously recorded series. We illustrate a
power of the method on both simulated and real-world time series.
In this paper, we use the ge
8ac
neralized Hurst exponent approach to study the
multi- scaling behavior of different financial time series. We show that this
approach is robust and powerful in detecting different types of multiscaling.
We observe a puzzling phenomenon where an apparent increase in multifractality
is measured in time series generated from shuffled returns, where all
time-correlations are destroyed, while the return distributions are conserved.
This effect is robust and it is reproduced in several real financial data
including stock market indices, exchange rates and interest rates. In order to
understand the origin of this effect we investigate different simulated time
series by means of the Markov switching multifractal (MSM) model,
autoregressive fractionally integrated moving average (ARFIMA) processes with
stable innovations, fractional Brownian motion and Levy flights. Overall we
conclude that the multifractality observed in financial time series is mainly a
consequence of the characteristic fat-tailed distribution of the returns and
time-correlations have the effect to decrease the measured multifractality.
Different network models have been suggested for the topology underlying
complex interactions in natural systems. These models are aimed at replicating
specific statistical features encountered in real-world networks. However, it
is rarely considered to which degree the results obtained for one particular
network class can be extrapolated to real-world networks. We address this issue
by comparing different classical and more recently developed network models
with respect to their generalisation power, which we identify with large
structural variability and absence of constraints imposed by the construction
scheme. After having identified the most variable networks, we address the
issue of which constraints are common to all network classes and are thus
suitable candidates for being generic statistical laws of complex networks. In
fact, we find that generic, not model-related dependencies between different
network characteristics do exist. This allows, for instance, to infer global
features from local ones using regression models trained on networks with high
generalisation power. Our results confirm and extend previous findings
regarding the synchronisation properties of neural networks. Our method seems
especially relevant for large networks, which are difficult to map completely,
like the neural networks in the brain. The structure of such large networks
cannot be fully sampled with the present technology. Our approach provides a
method to estimate global properties of under-sampled networks with good
approximation. Finally, we demonstrate on three different data sets (C.
elegans' neuronal network, R. prowazekii's metabolic network, and a network of
synonyms extracted from Roget's Thesaurus) that real-world networks have
statistical relations compatible with those obtained using regression models.
We propose a stochastic process driven by memory effect with novel
distributions including both exponential and leptokurtic heavy-tailed
distributions. A class of distribution is analytically derived from the
continuum limit of the discrete binary process with the renormalized
auto-correlation and the closed form moment generating function is obtained,
thus the cumulants are calculated and shown to be convergent. The other class
of distributions are numerically investigated. The concoction of the two
stochastic processes of the different s
527
igns of memory under regime switching
mechanism does incarnate power-law decay behavior, which strongly implies that
memory is the alternative origin of heavy-tail.
In evaluating prediction markets (and other crowd-prediction mechanisms),
investigators have repeatedly observed a so-called "wisdom of crowds" effect,
which roughly says that the average of participants performs much better than
the average participant. The market price---an average or at least aggregate of
traders' beliefs---offers a better estimate than most any individual trader's
opinion. In this paper, we ask a stronger question: how does the market price
compare to the best trader's belief, not just the average trader. We measure
the market's worst-case log regret, a notion common in machine learning theory.
To arrive at a meaningful answer, we need to assume something about how traders
behave. We suppose that every trader optimizes according to the Kelly criteria,
a strategy that provably maximizes the compound growth of wealth over an
(infinite) sequence of market interactions. We show several consequences.
First, the market prediction is a wealth-weighted average of the individual
participants' beliefs. Second, the market learns at the optimal rate, the
market price reacts exactly as if updating according to Bayes' Law, and the
market prediction has low worst-case log regret to the best individual
participant. We simulate a sequence of markets where an underlying true
probability exists, showing that the market converges to the true objective
frequency as if updating a Beta distribution, as the theory predicts. If agents
adopt a fractional Kelly criteria, a common practical variant, we show that
agents behave like full-Kelly agents with beliefs weighted between their own
and the market's, and that the market price converges to a time-discounted
frequency. Our analysis provides a new justification for fractional Kelly
betting, a strategy widely used in practice for ad-hoc reasons. Finally, we
propose a method for an agent to learn her own optimal Kelly fraction.
Human dynamical social networks encode information and are highly adaptive.
To characterize the information encoded in the fast dynamics of social
interactions, here we introduce the en
88a
tropy of dynamical social networks. By
analysing a large dataset of phone-call interactions we show evidence that the
dynamical social network has an entropy that depends on the time of the day in
a typical week-day. Moreover we show evidence for adaptability of human social
behavior showing data on duration of phone-call interactions that significantly
deviates from the statistics of duration of face-to-face interactions. This
adaptability of behavior corresponds to a different information content of the
dynamics of social human interactions. We quantify this information by the use
of the entropy of dynamical networks on realistic models of social
interactions.
Using Random Matrix Theory, we build a covariance matrix between stocks of
the BM&F-Bovespa (Bolsa de Valores, Mercadorias e Futuros de S\~ao Paulo) which
is cleaned of some of the noise due to the complex interactions between the
many stocks and the finiteness of available data, and use a regression model in
order to remove the market effect due to the common movement of all stocks.
These two procedures are then used in order to build portfolios of stocks based
on Markovitz's theory, trying to build better predictions of future risk based
on past data. This is done for years of both low and high volatility of the
Brazilian market, from 2004 to 2010.
In this paper, we show how the sampling properties of the Hurst exponent
methods of estimation change with the presence of heavy tails. We run extensive
Monte Carlo simulations to find out how rescaled range analysis (R/S),
multifractal detrended fluctuation analysis (MF-DFA), detrending moving average
(DMA) and generalized Hurst exponent approach (GHE) estimate Hurst exponent on
indepen
956
dent series with different heavy tails. For this purpose, we generate
independent random series from stable distribution with stability exponent
{\alpha} changing from 1.1 (heaviest tails) to 2 (Gaussian normal distribution)
and we estimate the Hurst exponent using the different methods. R/S and GHE
prove to be robust to heavy tails in the underlying process. GHE provides the
lowest variance and bias in comparison to the other methods regardless the
presence of heavy tails in data and sample size. Utilizing this result, we
apply a novel approach of the intraday time-dependent Hurst exponent and we
estimate the Hurst exponent on high frequency data for each trading day
separately. We obtain Hurst exponents for S&P500 index for the period beginning
with year 1983 and ending by November 2009 and we discuss the surprising result
which uncovers how the market's behavior changed over this long period.
class="descriptor">Abstract:</spa
af8
n> For fat tailed distributions (i.e. those that decay slower than an
exponential), large deviations not only become relatively likely, but the way
in which they are realized changes dramatically: A finite fraction of the whole
sample deviation is concentrated on a single variable: large deviations are not
the accumulation of many small deviations, but rather they are dominated to a
single large fluctuation. The regime of large deviations is separated from the
regime of typical fluctuations by a phase transition where the symmetry between
the points in the sample is {\em spontaneously broken}. This phenomenon has
been discussed in the context of mass transport models in physics, where it
takes the form of a condensation phase transition. Yet, the phenomenon is way
more general. For example, in risk management of large portfolios, it suggests
that one should expect losses to concentrate on a single asset: when extremely
bad things happen, it is likely that there is a single factor on which bad luck
concentrates. Along similar lines, one should expect that bubbles in financial
markets do not gradually deflate, but rather burst abruptly and that in the
most rainy day of a year, precipitation concentrate on a given spot.
Analogously, when applied to biological evolution, we're lead to infer that, if
fitness changes for individual mutations have a broad distribution, those large
deviations that lead to better fit species are not likely to result from the
accumulation of small positive mutations. Rather they are likely to arise from
large rare jumps.