15,983 research outputs found
Maximum Entropy Production Principle for Stock Returns
In our previous studies we have investigated the structural complexity of
time series describing stock returns on New York's and Warsaw's stock
exchanges, by employing two estimators of Shannon's entropy rate based on
Lempel-Ziv and Context Tree Weighting algorithms, which were originally used
for data compression. Such structural complexity of the time series describing
logarithmic stock returns can be used as a measure of the inherent (model-free)
predictability of the underlying price formation processes, testing the
Efficient-Market Hypothesis in practice. We have also correlated the estimated
predictability with the profitability of standard trading algorithms, and found
that these do not use the structure inherent in the stock returns to any
significant degree. To find a way to use the structural complexity of the stock
returns for the purpose of predictions we propose the Maximum Entropy
Production Principle as applied to stock returns, and test it on the two
mentioned markets, inquiring into whether it is possible to enhance prediction
of stock returns based on the structural complexity of these and the mentioned
principle.Comment: 14 pages, 5 figure
An interacting-agent model of financial markets from the viewpoint of nonextensive statistical mechanics
In this paper we present an interacting-agent model of stock markets. We
describe a stock market through an Ising-like model in order to formulate the
tendency of traders getting to be influenced by the other traders' investment
attitudes [1], and formulate the traders' decision-making regarding investment
as the maximum entropy principle for nonextensive entropy. We demonstrate that
the equilibrium probability distribution function of the traders' investment
attitude is the {\it q-exponential distribution}. We also show that the
power-law distribution of the volatility of price fluctuations, which is often
demonstrated in empirical studies, can be explained naturally by our model
which is based on the collective crowd behavior of many interacting agents.Comment: 7 pages, forthcoming into Physica A (2006
Information measure for financial time series: quantifying short-term market heterogeneity
A well-interpretable measure of information has been recently proposed based
on a partition obtained by intersecting a random sequence with its moving
average. The partition yields disjoint sets of the sequence, which are then
ranked according to their size to form a probability distribution function and
finally fed in the expression of the Shannon entropy. In this work, such
entropy measure is implemented on the time series of prices and volatilities of
six financial markets. The analysis has been performed, on tick-by-tick data
sampled every minute for six years of data from 1999 to 2004, for a broad range
of moving average windows and volatility horizons. The study shows that the
entropy of the volatility series depends on the individual market, while the
entropy of the price series is practically a market-invariant for the six
markets. Finally, a cumulative information measure - the `Market Heterogeneity
Index'- is derived from the integral of the proposed entropy measure. The
values of the Market Heterogeneity Index are discussed as possible tools for
optimal portfolio construction and compared with those obtained by using the
Sharpe ratio a traditional risk diversity measure
Predicting stock market movements using network science: An information theoretic approach
A stock market is considered as one of the highly complex systems, which
consists of many components whose prices move up and down without having a
clear pattern. The complex nature of a stock market challenges us on making a
reliable prediction of its future movements. In this paper, we aim at building
a new method to forecast the future movements of Standard & Poor's 500 Index
(S&P 500) by constructing time-series complex networks of S&P 500 underlying
companies by connecting them with links whose weights are given by the mutual
information of 60-minute price movements of the pairs of the companies with the
consecutive 5,340 minutes price records. We showed that the changes in the
strength distributions of the networks provide an important information on the
network's future movements. We built several metrics using the strength
distributions and network measurements such as centrality, and we combined the
best two predictors by performing a linear combination. We found that the
combined predictor and the changes in S&P 500 show a quadratic relationship,
and it allows us to predict the amplitude of the one step future change in S&P
500. The result showed significant fluctuations in S&P 500 Index when the
combined predictor was high. In terms of making the actual index predictions,
we built ARIMA models. We found that adding the network measurements into the
ARIMA models improves the model accuracy. These findings are useful for
financial market policy makers as an indicator based on which they can
interfere with the markets before the markets make a drastic change, and for
quantitative investors to improve their forecasting models.Comment: 13 pages, 7 figures, 3 table
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