33,520 research outputs found
An Information-Theoretic Test for Dependence with an Application to the Temporal Structure of Stock Returns
Information theory provides ideas for conceptualising information and
measuring relationships between objects. It has found wide application in the
sciences, but economics and finance have made surprisingly little use of it. We
show that time series data can usefully be studied as information -- by noting
the relationship between statistical redundancy and dependence, we are able to
use the results of information theory to construct a test for joint dependence
of random variables. The test is in the same spirit of those developed by
Ryabko and Astola (2005, 2006b,a), but differs from these in that we add extra
randomness to the original stochatic process. It uses data compression to
estimate the entropy rate of a stochastic process, which allows it to measure
dependence among sets of random variables, as opposed to the existing
econometric literature that uses entropy and finds itself restricted to
pairwise tests of dependence. We show how serial dependence may be detected in
S&P500 and PSI20 stock returns over different sample periods and frequencies.
We apply the test to synthetic data to judge its ability to recover known
temporal dependence structures.Comment: 22 pages, 7 figure
Point estimation with exponentially tilted empirical likelihood
Parameters defined via general estimating equations (GEE) can be estimated by
maximizing the empirical likelihood (EL). Newey and Smith [Econometrica 72
(2004) 219--255] have recently shown that this EL estimator exhibits desirable
higher-order asymptotic properties, namely, that its bias is small
and that bias-corrected EL is higher-order efficient. Although EL possesses
these properties when the model is correctly specified, this paper shows that,
in the presence of model misspecification, EL may cease to be root n convergent
when the functions defining the moment conditions are unbounded (even when
their expectations are bounded). In contrast, the related exponential tilting
(ET) estimator avoids this problem. This paper shows that the ET and EL
estimators can be naturally combined to yield an estimator called exponentially
tilted empirical likelihood (ETEL) exhibiting the same bias and the
same variance as EL, while maintaining root n convergence under
model misspecification.Comment: Published at http://dx.doi.org/10.1214/009053606000001208 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
A statistical physics perspective on criticality in financial markets
Stock markets are complex systems exhibiting collective phenomena and
particular features such as synchronization, fluctuations distributed as
power-laws, non-random structures and similarity to neural networks. Such
specific properties suggest that markets operate at a very special point.
Financial markets are believed to be critical by analogy to physical systems
but few statistically founded evidence have been given. Through a data-based
methodology and comparison to simulations inspired by statistical physics of
complex systems, we show that the Dow Jones and indices sets are not rigorously
critical. However, financial systems are closer to the criticality in the crash
neighborhood.Comment: 23 pages, 19 figure
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