An ARMA(1,1) model for monthly stream flows

Abstract

The partial auto-correlation coefficients of most of the series of monthly stream flows recorded in Turkey of lag greater than one are within the 99% confidence band while the lag-one partial correlation coefficient is highly significant. An ARMA(1,1) model to compute synthetic monthly flows up to 5000 years is developed, which is different from the ones presented in relevant sources. Having observed mostly skewed standardized variates, they are normalized by the 3-parameter log-normal distribution whose parameters are computed by the method of maximum-likelihood (LN3-ML). The two parameters of the ARMA(1,1) model are computed so as to minimize the sum of squares of differences of the observed and computed standardized–normalized variates rather than minimizing the sum of squares of the random component terms. Application of the developed model on the 64-year-long monthly flow series of the unregulated Kizilirmak River in Turkey is given here as an example, which reveals plausible results.