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Effect of persistence on trend detection via regression Nicholas C. Matalas

Summary: Effect of persistence on trend detection via regression
Nicholas C. Matalas
Vienna, Virginia, USA
A. Sankarasubramanian
International Research Institute for Climate Prediction, Lamont-Doherty Earth Observatory, Columbia University, Palisades,
New York, USA
Received 28 April 2003; revised 13 August 2003; accepted 28 August 2003; published 5 December 2003.
[1] Trends in hydrologic sequences may be assessed in various ways. The coefficient of
regression of flow on time may be used, particularly if the sequences are very long. Under
the assumption of stationarity the variance of the regression coefficient is expressed as
a function of sequence length and the autocorrelation coefficients of relevant order. Thus
the variance inflation factor for assessing the statistical significance of estimated
regression coefficients may be readily determined for any given stationary process. The
variance inflation factor is determined for four stationary processes: independent, Markov,
autoregressive-moving average of order (1, 1), and fractional Gaussian noise. The
effectiveness of prewhitening observed sequences with a Markov process is nearly the
same whether the first order autocorrelation coefficient is known per se or through
estimation. INDEX TERMS: 1869 Hydrology: Stochastic processes; 1860 Hydrology: Runoff and
streamflow; 1833 Hydrology: Hydroclimatology; KEYWORDS: persistence, stationarity, trends
Citation: Matalas, N. C., and A. Sankarasubramanian, Effect of persistence on trend detection via regression, Water Resour. Res.,


Source: Arumugam, Sankar - Department of Civil, Construction, and Environmental Engineering, North Carolina State University


Collections: Environmental Sciences and Ecology; Engineering