Fig. 11

Autocorrelation coefficient estimates. The horizontal axis shows the length of the time series. The vertical axis shows the mean estimate of the autocorrelation coefficient across 10,000 simulations. The five plots display the results for different values of autocorrelation ranging from 0 to 0.8 (the true value of autocorrelation is shown by a horizontal black line). Each coloured point shows the mean autocorrelation estimate for a given combination of true autocorrelation coefficient and number of points in the data series. The simulation combination presented is for a level change of 2 and slope change of 0.1; however, other combinations give similar results. Abbreviations: ARIMA, autoregressive integrated moving average; OLS, ordinary least squares; PW, Prais-Winsten; REML, restricted maximum likelihood