Effect of persistence on trend detection via regression

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.