Abstract
Time series models are often used in hydrology and meteorology studies to model streamflows series in order to make forecasting and generate synthetic series which are inputs for the analysis of complex water resources systems. In thispaper we introduce a new modeling approach for hydrologic and meteorological time series assuming a continuous distribution for the data, where both the conditional mean and conditional varianceparameters are modeled. Bayesian methods using standard MCMC (Markov Chain Monte Carlo Methods) are used to simulate samples for the joint posterior distribution of interest. Two applications to real data sets illustrate the proposedmethodology, assuming that the observations come from a normal, a gamma or a beta distribution. A first example is given by a time series of monthly averages of natural streamflows, measured in the year period ranging from1931 to 2010 in Furnas hydroelectric dam, Brazil. A second example is given with a time series of 313 air humidity data measured in a weather station of Rio Claro, a Brazilian city located in southeastern of Brazil. These applications motivate us to introduce new classes of models to analyze hydrological and meteorological time series
Highlights
Time series models are often used in hydrology studies to model streamflow series in order to make predictions and to generate synthetic series which are inputs for the analysis of complex water resources systems
4.2 Gamma seasonal time series we present the results of the Bayesian analysis for the time series for monthly averages of natural streamflows, measured in the period 1931 to 2010, in Furnas hydroelectric dam, assuming joint modeling for the mean and variance autoregressive gamma models, that is, we assume that the observations of the interest are generated from a conditional gamma density function given by f, where Ht-1) is the information up to time t − 1 and Yt has conditional mean and conditional variance given respectively by μt = E(Yt | Ht-1) and σt2 = Var(Yt | Ht-1), and defined by (10) and (11)
We introduce a new class of time series models assuming continuous random variables within the exponential family applied to hydrological and meteorological data
Summary
Time series models are often used in hydrology studies to model streamflow series in order to make predictions and to generate synthetic series which are inputs for the analysis of complex water resources systems (see, for example, Salas et al, 1980, 1982; Hosking, 1984; Hipel& McLeod, 1994; Montanari et al, 1997; Hasebe et al, 2000). Considering hydrological time series, the monthly streamflow series typically have a periodic behavior in the mean and variance and in general, periodic autoregressive models are used in de analysis of the data (see, for example, Modal & Wasimi, 2006). In this situation, usually it is assumed that the series flow has a normal or log-normal distribution (see for example, Tesfaye et al, 2006; Wang et al, 2009). From this Figure, we observe that the streamflow series have a periodic behavior in the mean and variance and in this case, general periodic autoregressive models are usually assumed in the analysis of the time series data (Modal & Wasimi, 2006)
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