The definition of time is still an open question when one deals with high frequency time series. If time is simply the calendar time, prices can be modeled as continuous random processes and values resulting from transactions or given quotes are discrete samples of this underlying dynamics. On...

We study the price dynamics of 65 stocks from the Dow Jones Composite Average from 1973 until 2014. We show that it is possible to define a Daily Market Volatility $\sigma(t)$ which is directly observable from data. This quantity is usually indirectly defined by $r(t)=\sigma(t) \omega(t)$ where...

The dynamics of prices in stock markets has been studied intensively both experimentally (data analysis) and theoretically (models). Nevertheless, while the distribution of returns of the most important indices is known to be a truncated Lévy, the behaviour of volatility correlations is still...

Prediction of events is a challenge in many different disciplines, from meteorology to finance: the more difficult this task is, the more complex the system is. Nevertheless, even according to this restricted definition, a general consensus on what should be the correct indicator for complexity...

In this paper we compute exactly the ground state energy and entropy of the dilute ferromagnetic Ising model. The two thermodynamic quantities are also computed when a magnetic field with random locations is present. The result is reached in the replica approach frame by a class of replica order...

In this paper we perform a quantitative check of long term correlations and multi-affinity in Deutsche Mark/US Dollar exchange rates using high frequency data. We show that the use of business time, i.e., the ranking of the quotes in the sequences, eliminates most of the seasonality in...

A quantitative check of efficiency in US dollar/Deutsche mark exchange rates is developed using high-frequency (tick by tick) data. The antipersistent Markov behavior of log-price fluctuations of given size implies, in principle, the possibility of a statistical forecast. We introduce and...

We consider a large population of asexually reproducing individuals in absence of selective pressure. The population size is maintained constant by the environment. We find out that distances between individuals (time from the last common ancestor) exhibit highly non-trivial properties. In...

The idea of measuring distance between languages seems to have its roots in the work of the French explorer Dumont D’Urville (1832) [13]. He collected comparative word lists for various languages during his voyages aboard the Astrolabe from 1826 to 1829 and, in his work concerning the...

The dynamics of prices in financial markets has been studied intensively both experimentally (data analysis) and theoretically (models). Nevertheless, a complete stochastic characterization of volatility is still lacking. What it is well known is that absolute returns have memory on a long time...