Non stationary multifractality in stock returns

We perform an extensive empirical analysis of scaling properties of equity returns, suggesting that financial data show time varying multifractal properties. This is obtained by comparing empirical observations of the weighted generalised Hurst exponent (wGHE) with time series simulated via Multifractal Random Walk (MRW) by Bacry \textit{et al.} [\textit{E.Bacry, J.Delour and J.Muzy, Phys.Rev.E \,{\bf 64} 026103, 2001}]. While dynamical wGHE computed on synthetic MRW series is consistent with a scenario where multifractality is constant over time, fluctuations in the dynamical wGHE observed in empirical data are not in agreement with a MRW with constant intermittency parameter. We test these hypotheses of constant multifractality considering different specifications of MRW model with fatter tails: in all cases considered, although the thickness of the tails accounts for most of anomalous fluctuations of multifractality, still cannot fully explain the observed fluctuations.Comment: 27 pages, 10 figure

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

Anomalous volatility scaling in high frequency financial data

Volatility of intra-day stock market indices computed at various time horizons exhibits a scaling behaviour that differs from what would be expected from fractional Brownian motion (fBm). We investigate this anomalous scaling by using empirical mode decomposition (EMD), a method which separates time series into a set of cyclical components at different time-scales. By applying the EMD to fBm, we retrieve a scaling law that relates the variance of the components to a power law of the oscillating period. In contrast, when analysing 22 different stock market indices, we observe deviations from the fBm and Brownian motion scaling behaviour. We discuss and quantify these deviations, associating them to the characteristics of financial markets, with larger deviations corresponding to less developed markets.Comment: 25 pages, 11 figure, 5 table

Il ruolo dell'Arcipelago di la Maddalena (Sardegna) nella circolazione di materiali e idee dal V al III Millenio A.C.

Molte evidenze archeologiche confermano l’importanza del ruolo dell’Arcipelago di La Maddalena dal V al III millennio a.C. Le principali categorie sono le seguenti: 1) molti ritrovamenti di ossidiana e selce; 2) varie forme di megalitismo; 3) un grande complesso produttivo nell’isola di Caprera; questo complesso, delimitato da un muro rettangolare, mostra un’impressionante somiglianza con quello di Ferrandell-Oleza, nell’isola di Maiorca. Tale documentazione offre un importante contributo su forme, tempi e direzionalità della circolazione di persone, cose e idee nel Mediterraneo occidentale

Hierarchical information clustering by means of topologically embedded graphs

We introduce a graph-theoretic approach to extract clusters and hierarchies in complex data-sets in an unsupervised and deterministic manner, without the use of any prior information. This is achieved by building topologically embedded networks containing the subset of most significant links and analyzing the network structure. For a planar embedding, this method provides both the intra-cluster hierarchy, which describes the way clusters are composed, and the inter-cluster hierarchy which describes how clusters gather together. We discuss performance, robustness and reliability of this method by first investigating several artificial data-sets, finding that it can outperform significantly other established approaches. Then we show that our method can successfully differentiate meaningful clusters and hierarchies in a variety of real data-sets. In particular, we find that the application to gene expression patterns of lymphoma samples uncovers biologically significant groups of genes which play key-roles in diagnosis, prognosis and treatment of some of the most relevant human lymphoid malignancies

Analysis of isoenzymes and isoforms of human alkaline phosphatase, hexosaminidase and transferrin by micro column chromatography

The main objective of this study was to develop a micro column chromatographic system (MCC) for the separation, detection and quantitation of isoenzymes and isoforms of proteins in human plasma. Three proteins (hexosaminidase, alkaline phosphatase and transferrin) were chosen, as they presented different clinical and analytical problems. Developmental work showed that a 5 mm x 4.6 mm column, packed with a strong polymer-based anion exchanger, used with a step-gradient and a slow flow rate (< 0.55 ml/min) was capable of resolving the different forms of the three proteins. A rapid post-column detection system was designed for the analysis of hexosaminidase and alkaline phosphatase. Transferrin was detected at 460 nm which is specific for iron. The chromatography was found to be reproducible; the coefficient of variation (CV) for the retention times of the various forms of the three proteins generally being approximately 2%. The precision for the within-batch and between-batch quantitation of individual isoenzymes and isoforms varied greatly from one protein to another (from a CV of 1.2% for hexosaminidase to 48.56% for alkaline phosphatase). This appeared to result principally from problems with the software of the commercial integration system. When MCC was compared with appropriate reference methods such as agarose electrophoresis and isoelectric focusing (IEF), the following conclusions were made. The percentage contribution of the various forms of hexosaminidase and transferrin following MCC was comparable with that obtained using electrophoresis and IEF respectively. MCC therefore, provided a rapid and easy method for the clinical analysis of these proteins. For alkaline phosphatase, however, MCC and electrophoresis gave poor agreement, particularly in neonatal samples, which may have resulted from different method specificities. The optimised methods (MCC, IEF and electrophoresis) for the analysis of hexosaminidase and transferrin were applied to a study of patients with Carbohydrate Deficient Glycoprotein Syndrome

Understanding the source of multifractality in financial markets

In this paper, we use the generalized Hurst exponent approach to study the multi- scaling behavior of different financial time series. We show that this approach is robust and powerful in detecting different types of multiscaling. We observe a puzzling phenomenon where an apparent increase in multifractality is measured in time series generated from shuffled returns, where all time-correlations are destroyed, while the return distributions are conserved. This effect is robust and it is reproduced in several real financial data including stock market indices, exchange rates and interest rates. In order to understand the origin of this effect we investigate different simulated time series by means of the Markov switching multifractal (MSM) model, autoregressive fractionally integrated moving average (ARFIMA) processes with stable innovations, fractional Brownian motion and Levy flights. Overall we conclude that the multifractality observed in financial time series is mainly a consequence of the characteristic fat-tailed distribution of the returns and time-correlations have the effect to decrease the measured multifractality