1,893 research outputs found
Long-range correlations and nonstationarity in the Brazilian stock market
We report an empirical study of the Ibovespa index of the Sao Paulo Stock
Exchange in which we detect the existence of long-range correlations. To
analyze our data we introduce a rescaled variant of the usual Detrended
Fluctuation Analysis that allows us to obtain the Hurst exponent through a
one-parameter fitting. We also compute a time-dependent Hurst exponent H(t)
using three-year moving time windows. In particular, we find that before the
launch of the Collor Plan in 1990 the curve H(t) remains, in general, well
above 1/2, while afterwards it stays close to 1/2. We thus argue that the
structural reforms set off by the Collor Plan has lead to a more efficient
stock market in Brazil. We also suggest that the time dependence of the
Ibovespa Hurst exponent could be described in terms of a multifractional
Brownian motion.Comment: 19 pages with 11 figures, submitted to Physica
Long-term correlations and multifractal nature in the intertrade durations of a liquid Chinese stock and its warrant
Intertrade duration of equities is an important financial measure
characterizing the trading activities, which is defined as the waiting time
between successive trades of an equity. Using the ultrahigh-frequency data of a
liquid Chinese stock and its associated warrant, we perform a comparative
investigation of the statistical properties of their intertrade duration time
series. The distributions of the two equities can be better described by the
shifted power-law form than the Weibull and their scaled distributions do not
collapse onto a single curve. Although the intertrade durations of the two
equities have very different magnitude, their intraday patterns exhibit very
similar shapes. Both detrended fluctuation analysis (DFA) and detrending moving
average analysis (DMA) show that the 1-min intertrade duration time series of
the two equities are strongly correlated. In addition, both multifractal
detrended fluctuation analysis (MFDFA) and multifractal detrending moving
average analysis (MFDMA) unveil that the 1-min intertrade durations possess
multifractal nature. However, the difference between the two singularity
spectra of the two equities obtained from the MFDMA is much smaller than that
from the MFDFA.Comment: 10 latex pages, 4 figure
Detrended cross-correlations between returns, volatility, trading activity, and volume traded for the stock market companies
We consider a few quantities that characterize trading on a stock market in a
fixed time interval: logarithmic returns, volatility, trading activity (i.e.,
the number of transactions), and volume traded. We search for the power-law
cross-correlations among these quantities aggregated over different time units
from 1 min to 10 min. Our study is based on empirical data from the American
stock market consisting of tick-by-tick recordings of 31 stocks listed in Dow
Jones Industrial Average during the years 2008-2011. Since all the considered
quantities except the returns show strong daily patterns related to the
variable trading activity in different parts of a day, which are the best
evident in the autocorrelation function, we remove these patterns by detrending
before we proceed further with our study. We apply the multifractal detrended
cross-correlation analysis with sign preserving (MFCCA) and show that the
strongest power-law cross-correlations exist between trading activity and
volume traded, while the weakest ones exist (or even do not exist) between the
returns and the remaining quantities. We also show that the strongest
cross-correlations are carried by those parts of the signals that are
characterized by large and medium variance. Our observation that the most
convincing power-law cross-correlations occur between trading activity and
volume traded reveals the existence of strong fractal-like coupling between
these quantities
Emergence of long memory in stock volatility from a modified Mike-Farmer model
The Mike-Farmer (MF) model was constructed empirically based on the
continuous double auction mechanism in an order-driven market, which can
successfully reproduce the cubic law of returns and the diffusive behavior of
stock prices at the transaction level. However, the volatility (defined by
absolute return) in the MF model does not show sound long memory. We propose a
modified version of the MF model by including a new ingredient, that is, long
memory in the aggressiveness (quantified by the relative prices) of incoming
orders, which is an important stylized fact identified by analyzing the order
flows of 23 liquid Chinese stocks. Long memory emerges in the volatility
synthesized from the modified MF model with the DFA scaling exponent close to
0.76, and the cubic law of returns and the diffusive behavior of prices are
also produced at the same time. We also find that the long memory of order
signs has no impact on the long memory property of volatility, and the memory
effect of order aggressiveness has little impact on the diffusiveness of stock
prices.Comment: 6 pages, 6 figures and 1 tabl
- …