Multivariate Stochastic Modeling of Monthly Streamflow of Rivers in the Sakarya Basin


Abstract: Mathematical expressions of multivariate periodic autoregressive (PAR) and periodic autoregressive-moving average (PARMA) models were obtained for monthly streamflow observations of 12 stations located in Sakarya Basin, Turkey. The methodology of both models was given in detail at five phases (preliminary analysis, estimation parameters, goodness of fit test, optional tests, and reliability of estimated parameters). For the purpose of methodological to be easily understood, the methodological procedures of annual multivariate AR and ARMA models were firstly presented. Because of being more practical PAR(1) model was initially considered in the analyses, but it was found that this model did not preverse the cross-correlation structure of historical series. Since a long-term dependency structure was observed in the correlograms of historical series in the phase of preliminary analysis, the modeling procedures were continued with the multivariate ARMA(1,1) model. This model was proven to be suitable for Sakarya Basin due to the fact that statistical moments of individual stations as well as cross correlation structures of all stations were satisfactorily preserved in the generated synthetic series.

Keywords: Multivariate autoregressive model, multivariate autoregressive-moving average model, Sakarya basin, stochastic modeling

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