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Identification of periodic autoregressive moving average models and their application to the modeling of river flows
Author(s) -
Tesfaye Yonas Gebeyehu,
Meerschaert Mark M.,
Anderson Paul L.
Publication year - 2006
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/2004wr003772
Subject(s) - autoregressive model , autoregressive–moving average model , generalized pareto distribution , flow (mathematics) , series (stratigraphy) , streamflow , identification (biology) , time series , moving average , covariance , environmental science , hydrology (agriculture) , meteorology , computer science , statistics , mathematics , geology , geography , extreme value theory , ecology , cartography , drainage basin , geotechnical engineering , biology , paleontology , geometry
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.