Ware, AntonyBadescu, AlexandruAsadzadeh, Ilnaz2016-06-232016-06-2320162016http://hdl.handle.net/11023/3076We consider the problem of measuring reliability of a hydro reservoir over a finite horizon with a stochastic optimal control technique. To apply this technique, we need to model the underlying stochastic process which is the inflow of water to the reservoir. Typical time series models for such problems only capture linear dependency (simple correlation) in the data. Alternative approaches include artificial neural network methods but these lack a theoretical foundation and a systematic procedure for the construction of the model. To overcome both of these limitations, we propose a new framework based on the application of copulas to univariate time series modelling. Our model shows that some important statistical characteristics of hydrological time series, such as upper and lower tail dependencies, persistence, etc., can be described with the aid of copulas. In turn, this provides insight regarding the qualitative properties of the underlying time series. Our main contribution is a new method of estimation based on a semi-parametric technique. By semi-parametric we mean using empirical autocopula (copula of a time series with itself with different lags), and parametric marginal distributions. Goodness of fit analysis is carried out and numerical results are illustrated with variety of concrete examples and sample data sets. We then benchmark and compare our scheme to alternative methods such as parametric models and various other time series modelling techniques. The final part of the dissertation proposes an application of stochastic optimal control to measure the reliability function (the probability that a system will perform the required function for a specified period of time under stated conditions) of the reservoir. For this section, we work with both uncorrelated and correlated inflow time series. For the first case, we generate independent inflow series using some probability distribution and for the second assumption, correlated inflow series, we employ the values of inflow generated using the autocopula method.engUniversity of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.Education--MathematicsHydrologyStatisticsEngineering--Operations ResearchCopulasStochastic Dynamic ProgrammingUpper and Lower Tail Dependencedoctoral thesis10.11575/PRISM/26404