Filippo Petroni

First and second order semi-Markov chains for wind speed modeling

The increasing interest in renewable energy, particularly in wind, has given rise to the necessity of accurate models for the generation of good synthetic wind speed data. Markov chains are often used for this purpose but better models are needed to reproduce the statistical properties of wind speed data. We downloaded a database, freely available from the web, in which are included wind speed data taken from L.S.I. -Lastem station (Italy) and sampled every 10 min. With the aim of reproducing the statistical properties of this data we propose the use of three semi-Markov models. We generate synthetic time series for wind speed by means of Monte Carlo simulations. The time lagged autocorrelation is then used to compare statistical properties of the proposed models with those of real data and also with a synthetic time series generated through a simple Markov chain.

Wind speed and energy forecasting at different time scales: A nonparametric approach

The prediction of wind speed is one of the most important aspects when dealing with renewable energy. In this paper we show a new nonparametric model, based on semi-Markov chains, to predict wind speed and the energy produced by a commercial blade. Particularly, we use an indexed semi-Markov model, that reproduces accurately the statistical behavior of wind speed. The model is used to forecast future wind speed and the energy produced through a 10 kW Aircon wind turbine. We forecast one step ahead and for different time scales. In order to check the main features of the model we show, as indicator of goodness, the root mean square error between real data and predicted ones. We compare our forecasting results with those of a persistence model and of an autoregressive model.

Malagasy dialects and the peopling of Madagascar

The origin of Malagasy DNA is half African and half Indonesian, nevertheless the Malagasy language, spoken by the entire population, belongs to the Austronesian family. The language most closely related to Malagasy is Maanyan (Greater Barito East group of the Austronesian family), but related languages are also in Sulawesi, Malaysia and Sumatra. For this reason, and because Maanyan is spoken by a population which lives along the Barito river in Kalimantan and which does not possess the necessary skill for long maritime navigation, the ethnic composition of the Indonesian colonizers is still unclear. There is a general consensus that Indonesian sailors reached Madagascar by a maritime trek, but the time, the path and the landing area of the first colonization are all disputed. In this research, we try to answer these problems together with other ones, such as the historical configuration of Malagasy dialects, by types of analysis related to lexicostatistics and glottochronology that draw upon the automated method recently proposed by the authors. The data were collected by the first author at the beginning of 2010 with the invaluable help of Joselinà Soafara Néré and consist of Swadesh lists of 200 items for 23 dialects covering all areas of the island.

Statistical dynamics of religion evolutions

A religion affiliation can be considered as a “degree of freedom” of an agent on the human genre network. A brief review is given on the state of the art in data analysis and modelization of religious “questions” in order to suggest and if possible initiate further research, after using a “statistical physics filter”. We present a discussion of the evolution of 18 so-called religions, as measured through their number of adherents between 1900 and 2000. Some emphasis is made on a few cases presenting a minimum or a maximum in the investigated time range—thereby suggesting a competitive ingredient to be considered, besides the well accepted “at birth” attachment effect. The importance of the “external field” is still stressed through an Avrami late stage crystal growth-like parameter. The observed features and some intuitive interpretations point to opinion based models with vector, rather than scalar, like agents.

A semi-Markov model with memory for price changes

We study the high frequency price dynamics of traded stocks by a model of returns using a semi-Markov approach. More precisely we assume that the intraday returns are described by a discrete time homogeneous semi-Markov which depends also on a memory index. The index is introduced to take into account periods of high and low volatility in the market. First of all we derive the equations governing the process and then theoretical results have been compared with empirical findings from real data. In particular we analyzed high frequency data from the Italian stock market from first of January 2007 until end of December 2010.

Measures of lexical distance between languages

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 geographical division of the Pacific, he proposed a method for measuring the degree of relation among languages. The method used by modern glottochronology, developed by Morris Swadesh in the 1950s, measures distances from the percentage of shared cognates, which are words with a common historical origin. Recently, we proposed a new automated method which uses the normalized Levenshtein distances among words with the same meaning and averages on the words contained in a list. Recently another group of scholars, Bakker et al. (2009) [8] and Holman et al. (2008) [9], proposed a refined version of our definition including a second normalization. In this paper we compare the information content of our definition with the refined version in order to decide which of the two can be applied with greater success to resolve relationships among languages.

A semi-Markov model for price returns

We study the high frequency price dynamics of traded stocks by a model of returns using a semi-Markov approach. More precisely we assume that the intraday returns are described by a discrete time homogeneous semi-Markov process and the overnight returns are modeled by a Markov chain. Based on this assumptions we derived the equations for the first passage time distribution and the volatility autocorrelation function. Theoretical results have been compared with empirical findings from real data. In particular we analyzed high frequency data from the Italian stock market from 1 January 2007 until the end of December 2010. The semi-Markov hypothesis is also tested through a nonparametric test of hypothesis.

Weighted-indexed semi-Markov models for modeling financial returns

In this paper we propose a new stochastic model based on a generalization of semi-Markov chains to study the high frequency price dynamics of traded stocks. We assume that the financial returns are described by a weighted indexed semi-Markov chain model. We show, through Monte Carlo simulations, that the model is able to reproduce important stylized facts of financial time series as the first passage time distributions and the persistence of volatility. The model is applied to data from Italian and German stock market from first of January 2007 until end of December 2010.

Reliability Measures of Second-Order Semi-Markov Chain Applied to Wind Energy Production

We consider the problem of wind energy production by using a second-order semi-Markov chain in state and duration as a model of wind speed. The model used in this paper is based on our previous work where we have shown the ability of second-order semi-Markov process in reproducing statistical features of wind speed. Here we briefly present the mathematical model and describe the data and technical characteristics of a commercial wind turbine (Aircon HAWT-10 kW). We show how, by using our model, it is possible to compute some of the main dependability measures such as reliability, availability, and maintainability functions. We compare, by means of Monte Carlo simulations, the results of the model with real energy production obtained from data available in the Lastem station (Italy) and sampled every 10 minutes. The computation of the dependability measures is a crucial point in the planning and development of a wind farm. Through our model, we show how the values of this quantity can be obtained both analytically and computationally.

Spot foreign exchange market and time series

Abstract.We investigate high frequency price dynamics in foreign exchange market using data from Reuters information system (the dataset has been provided to us by Olsen and Associates). In our analysis we show that a naïve approach to the definition of price (for example using the spot mid price) may lead to wrong conclusions on price behavior as for example the presence of short term correlations for returns. For this purpose we introduce an algorithm which only uses the non arbitrage principle to estimate real prices from the spot ones. The new definition leads to returns which are not affected by spurious correlations. Furthermore, any apparent information (defined by using Shannon entropy) contained in the data disappears.