551 research outputs found
A memory-based method to select the number of relevant components in Principal Component Analysis
We propose a new data-driven method to select the optimal number of relevant
components in Principal Component Analysis (PCA). This new method applies to
correlation matrices whose time autocorrelation function decays more slowly
than an exponential, giving rise to long memory effects. In comparison with
other available methods present in the literature, our procedure does not rely
on subjective evaluations and is computationally inexpensive. The underlying
basic idea is to use a suitable factor model to analyse the residual memory
after sequentially removing more and more components, and stopping the process
when the maximum amount of memory has been accounted for by the retained
components. We validate our methodology on both synthetic and real financial
data, and find in all cases a clear and computationally superior answer
entirely compatible with available heuristic criteria, such as cumulative
variance and cross-validation.Comment: 29 pages, publishe
Quasar Clustering in Cosmological Hydrodynamic Simulations: Evidence for mergers
We examine the clustering properties of a population of quasars drawn from
fully hydrodynamic cosmological simulations that directly follow black hole
growth. We find that the black hole correlation function is best described by
two distinct components: contributions from BH pairs occupying the same dark
matter halo ('1-halo term') which dominate at scales below 300 kpc/h, and
contributions from BHs occupying separate halos ('2-halo term') which dominate
at larger scales. From the 2-halo BH term we find a typical host halo mass for
faint-end quasars (those probed in our simulation volumes) ranging from 10^11
to a few 10^12 solar masses from z=5 to z=1 respectively (consistent with the
mean halo host mass). The BH correlation function shows a luminosity dependence
as a function of redshift, though weak enough to be consistent with
observational constraints. At small scales, the high resolution of our
simulations allows us to probe the 1-halo clustering in detail, finding that
the 1-halo term follows an approximate power law, lacking the characteristic
decrease in slope at small scales found in 1-halo terms for galaxies and dark
matter. We show that this difference is a direct result of a boost in the
small-scale quasar bias caused by galaxies hosting multiple quasars (1-subhalo
term) following a merger event, typically between a large central subgroup and
a smaller, satellite subgroup hosting a relatively small black hole. We show
that our predicted small-scale excess caused by such mergers is in good
agreement with both the slope and amplitude indicated by recent small-scale
measurements. Finally, we note the excess to be a strong function of halo mass,
such that the observed excess is well matched by the multiple black holes of
intermediate mass (10^7-10^8 solar masses) found in hosts of 4-8*10^11 solar
masses, a range well probed by our simulations.Comment: 12 pages, 10 figures. Submitted to MNRA
Relation between Financial Market Structure and the Real Economy: Comparison between Clustering Methods
We quantify the amount of information filtered by different hierarchical
clustering methods on correlations between stock returns comparing it with the
underlying industrial activity structure. Specifically, we apply, for the first
time to financial data, a novel hierarchical clustering approach, the Directed
Bubble Hierarchical Tree and we compare it with other methods including the
Linkage and k-medoids. In particular, by taking the industrial sector
classification of stocks as a benchmark partition, we evaluate how the
different methods retrieve this classification. The results show that the
Directed Bubble Hierarchical Tree can outperform other methods, being able to
retrieve more information with fewer clusters. Moreover, we show that the
economic information is hidden at different levels of the hierarchical
structures depending on the clustering method. The dynamical analysis on a
rolling window also reveals that the different methods show different degrees
of sensitivity to events affecting financial markets, like crises. These
results can be of interest for all the applications of clustering methods to
portfolio optimization and risk hedging.Comment: 31 pages, 17 figure
True and Apparent Scaling: The Proximity of the Markov- Switching Multifractal Model to Long-Range Dependence
In this paper, we consider daily financial data of a collection of different stock market indices, exchange rates, and interest rates, and we analyze their multi-scaling properties by estimating a simple specification of the Markov- switching multifractal model (MSM). In order to see how well the estimated models capture the temporal dependence of the data, we estimate and compare the scaling exponents H(q) (for q = 1; 2) for both empirical data and simulated data of the estimated MSM models. In most cases the multifractal model appears to generate `apparent' long memory in agreement with the empirical scaling laws. --Scaling,Generalized Hurst exponent,Multifractal model,GMM estimation
Multifractality and long-range dependence of asset returns: The scaling behaviour of the Markov-switching multifractal model with lognormal volatility components
In this paper we consider daily financial data from various sources (stock market indices, foreign exchange rates and bonds) and analyze their multi-scaling properties by estimating the parameters of a Markov-switching multifractal model (MSM) with Lognormal volatility components. In order to see how well estimated models capture the temporal dependency of the empirical data, we estimate and compare (generalized) Hurst exponents for both empirical data and simulated MSM models. In general, the Lognormal MSM models generate ?apparent? long memory in good agreement with empirical scaling provided one uses sufficiently many volatility components. In comparison with a Binomial MSM specification [7], results are almost identical. This suggests that a parsimonious discrete specification is flexible enough and the gain from adopting the continuous Lognormal distribution is very limited. --Markov-switching multifractal , scaling , return volatility
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