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WATER RESOURCES RESEARCH, VOL. 42, W01419, doi:10.1029/2004WR003772, 2006

Identification of periodic autoregressive moving average models and their application to the modeling of river flows

Yonas Gebeyehu Tesfaye

Graduate Program of Hydrologic Sciences, University of Nevada, Reno, Nevada, USA


Mark M. Meerschaert

Department of Mathematics and Statistics, University of Otago, Dunedin, New Zealand


Paul L. Anderson

Department of Mathematics and Computer Science, Albion College, Albion, Michigan, USA


Abstract

The generation of synthetic river flow samples that can reproduce the essential statistical features of historical river flows is useful for the planning, design, and operation of water resource systems. Most river flow series are periodically stationary; that is, their mean and covariance functions are periodic with respect to time. This article develops model identification and simulation techniques based on a periodic autoregressive moving average (PARMA) model to capture the seasonal variations in river flow statistics. The innovations algorithm is used to obtain parameter estimates. An application to monthly flow data for the Fraser River in British Columbia is included. A careful statistical analysis of the PARMA model residuals, including a truncated Pareto model for the extreme tails, produces a realistic simulation of these river flows.

Received 28 October 2004; accepted 18 October 2005; published 31 January 2006.

Keywords: innovation algorithm; model identification; parameter estimation; PARMA model; river flows; simulation study.

Index Terms: 1869 Hydrology: Stochastic hydrology; 1860 Hydrology: Streamflow; 1817 Hydrology: Extreme events; 1872 Hydrology: Time series analysis (3270, 4277, 4475).

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Citation: Tesfaye, Y. G., M. M. Meerschaert, and P. L. Anderson (2006), Identification of periodic autoregressive moving average models and their application to the modeling of river flows, Water Resour. Res., 42, W01419, doi:10.1029/2004WR003772.