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Πλοήγηση ανά Επιβλέπων "Pavlopoulos, Charalampos"

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  • Μικρογραφία εικόνας
    Τεκμήριο
    Stochastic modeling of time series with intermittency, persistence and extreme variability, with application to spatio-temporal averages of rainfall fields
    (21-06-2018) Chronis, George A.; Χρόνης, Γεώργιος Α.; Athens University of Economics and Business, Department of Statistics; De Michele, Carlo; Picek, Jan; Dellaportas, Petros; Karlis, Dimitrios; Zazanis, Michael; Ioannidis, Evaggelos; Pavlopoulos, Charalampos
    Motivated by rainfall research, this thesis contributes new insights on mechanisms of precipitation. This is accomplished through a stochastic modelling approach of time series representing intermittency and variability of precipitation cumulatively at large spatial scales. Our objective is to obtain a parsimonious but flexible stochastic model that can capture adequately the spectral power distribution and the marginal probability distribution of time series of spatio-temporal averages of rain rate (STARR) at such large spatial scales, presumably under stationarity conditions. The model conceived and presented in this thesis treats intermittency and variability as two stochastically independent multiplicative components, each contributing partially to the overall persistence of memory or dependence of the model. Specifically, we model intermittency by a stationary renewal process in discrete time, where instants of renewals are marked with the value {1} and otherwise the process attains the value {0}. In particular, we model the probability distribution of waiting (discrete) time between successive renewals by the family of Riemann's zeta-distributions, whose parameter allows for the possibility of heavy tails (i.e. infinite variance), which in turn is an event associated with persistence (i.e. long memory) of the renewal process. Subsequently, conditionally on raining, the overall amount of rain is modelled as a log-infinitely divisible noise process, independent of the zeta-renewal process. Specifically, positive values of STARR during spells of successive renewals are modelled as exponential values of (unitary-lag) stationary increments of a self-similar process known as Linear Fractional Stable Motion, which is obtained by stochastic integration of a certain deterministic kernel with respect to a suitable alpha-stable random measure. That is, conditionally on raining, log-STARR is modelled as Linear Fractional Stable Noise. The contemporaneous product of the stationary zeta-renewal process with the stationary log-LFSN process, provides the stationary model proposed in this dissertation.