8 research outputs found
Goodness-of-Fit tests with Dependent Observations
We revisit the Kolmogorov-Smirnov and Cram\'er-von Mises goodness-of-fit
(GoF) tests and propose a generalisation to identically distributed, but
dependent univariate random variables. We show that the dependence leads to a
reduction of the "effective" number of independent observations. The
generalised GoF tests are not distribution-free but rather depend on all the
lagged bivariate copulas. These objects, that we call "self-copulas", encode
all the non-linear temporal dependences. We introduce a specific, log-normal
model for these self-copulas, for which a number of analytical results are
derived. An application to financial time series is provided. As is well known,
the dependence is to be long-ranged in this case, a finding that we confirm
using self-copulas. As a consequence, the acceptance rates for GoF tests are
substantially higher than if the returns were iid random variables.Comment: 26 page
Individual and collective stock dynamics: intra-day seasonalities
We establish several new stylised facts concerning the intra-day
seasonalities of stock dynamics. Beyond the well known U-shaped pattern of the
volatility, we find that the average correlation between stocks increases
throughout the day, leading to a smaller relative dispersion between stocks.
Somewhat paradoxically, the kurtosis (a measure of volatility surprises)
reaches a minimum at the open of the market, when the volatility is at its
peak. We confirm that the dispersion kurtosis is a markedly decreasing function
of the index return. This means that during large market swings, the
idiosyncratic component of the stock dynamics becomes sub-dominant. In a
nutshell, early hours of trading are dominated by idiosyncratic or sector
specific effects with little surprises, whereas the influence of the market
factor increases throughout the day, and surprises become more frequent.Comment: 9 pages, 7 figure
Dependency structure and scaling properties of financial time series are related
We report evidence of a deep interplay between cross-correlations hierarchical properties and multifractality of New York Stock Exchange daily stock returns. The degree of multifractality displayed by different stocks is found to be positively correlated to their depth in the hierarchy of cross-correlations. We propose a dynamical model that reproduces this observation along with an array of other empirical properties. The structure of this model is such that the hierarchical structure of heterogeneous risks plays a crucial role in the time evolution of the correlation matrix, providing an interpretation to the mechanism behind the interplay between cross-correlation and multifractality in financial markets, where the degree of multifractality of stocks is associated to their hierarchical positioning in the cross-correlation structure. Empirical observations reported in this paper present a new perspective towards the merging of univariate multi scaling and multivariate cross-correlation properties of financial time series