Guglielmo D’Amico

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.

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.

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.

Statistical inference for Markov chain European option : estimating the price, the bare risk and the theta by historical distributions of Markov chain

Abstract In this paper we assume that the underlying asset follows an ergodic Markov chain with finite state space E, we observe the asset for m times and using this information we estimate the value of an European option, the associated “bare” risk and the theta too. We show that the proposed estimators are uniformly strongly consistent and properly centralized and normalized converge in distribution to normal random variables, then we give also the interval estimators.

Maintenance of Wind Turbine Scheduling Based on Output Power Data and Wind Forecast

Maintenance of a wind turbine is a combination of all technical, administrative and managerial actions intended to retain it in, or restore it to, a state in which the turbine is able to generate power. This paper presents an influence diagram to estimate the expected utility that represents wind turbine energy to be produced given period of time in the future. The conditional probability distribution of a chance node of the diagram is obtained relying on Bayesian networks, whereas the utilities of value node are calculated thanks to the second order semi-Markov chains. The example shows the application of the models in the real case of one wind turbine E48 by Enercon located in northern part of Poland. Both Bayesian network parameters and kernel of semi-Markov chain are derived from real data recorded by SCADA system of the turbine and weather forecast.

Downward Migration Credit Risk Problem: A Non-Homogeneous Backward Semi-Markov Reliability Approach

International organizations evaluate credit risk and rank firms according to risk by assigning them a ‘rating’. The time evolution of a rating can be studied by means of Markov models. Some papers have outlined the problem pertaining to the unsuitable fitting of Markov processes in a credit risk environment. This paper presents a model that overcomes the problems given by the Markov rating models. It includes non-homogeneity, the downward problem and the randomness of time in the transitions of states, thus making it possible to consider the duration inside a state in a complete way. In this paper, both, the transient and asymptotic analyses are presented. The asymptotic analysis is performed by using a mono-unireducible topological structure. Moreover, a real data application is conducted using the historical database of Standard & Poor’s as the source.

Copula based multivariate semi-Markov models with applications in high-frequency finance

We introduce a new multivariate model of multiple asset returns. Our model is based on weighted indexed semi-Markov chains to describe the single (marginals) asset returns, whereas the dependence structure among the considered assets is described by introducing copula functions. A real application of the proposed multivariate model is presented based on the evolution of 6 stocks from the Italian Stock Exchange. We provide empirical evidence that the model is able to correctly reproduce statistical regularities of multivariate real data such as the cross-correlation function, value-at-risk, marginal value-at-risk and conditional value-at-risk. The model is also used for volatility forecasting of each stock.

Decision Model of Wind Turbines Maintenance Planning

Performing a maintenance of wind energy system components under good wind conditions may lead to energy not served and finally – to financial losses. The best starting time of preventive maintenance will be, that reduces the energy not served in most. To find this time, a decision model is desired, where many circumstances should be taken into account, i.e. (i) the number and the order of components to be maintained, (ii) component maintenance duration, and (iii) wind turbine(s) output power prediction. Usually, preventive maintenance is planned a few days or weeks in advance. One of the decision problem representations can be influence diagram that enables choosing a decision alternative that has the lowest expected utility (energy not served). The paper presents an decision model that can support decisions-making on starting time of preventive maintenance and maintenance order of wind energy system components. The model relies on influence diagram. The conditional probability distribution of a chance nodes of the diagram are obtained relying on Bayesian networks (BN), whereas the utilities of value node in the diagram are calculated thanks to the second order semi-Markov chains (SMC). The example shows the application of the model in real case of two wind turbines located in Poland. Both the parameters of Bayesian network nodes and semi-Markov chain are derived from real data recorded by SCADA system of the both turbines and weather forecast.