Evaluation of goodness of fit criterion in time series analysis

Abstract

The order determination of appropriate model type among various models is one of the most important problems in stochastic hydrology. In the presented study, various types of testing the goodness of fit criterion are compared by using observed annual mean flow and synthetic data sets. For this purpose, AR(1), AR(2), AR(3), ARMA(1,1) and ARMA(1,2) models which are mostly used in hydrology are investigated. In the presented study, Tanir/ Gözlerüstü (2015/25) annual mean runoff series of Ceyhan basin and corresponding synthetic series are used. The results based on the performance analysis for criterions versus observation length showed that, testing the goodness of fit criterion performance improved with increasing data length. In the second part of the synthetic series evaluation, the performance of the criterion was tested on the thirty generated samples with well known statistical and population characteristics.