Fig. 10

Autocorrelation coefficient estimates. The horizontal axis shows the estimate of autocorrelation coefficient. The vertical axis shows the length of the time series. The five vertical columns display the results for different values of autocorrelation ranging from 0 to 0.8 (the value of autocorrelation is shown by a vertical red line). Each coloured curve shows the distribution of autocorrelation coefficient estimates from 10,000 simulations. Each subset of four curves shows the results from a different analysis method for a given combination of time series length and autocorrelation. The simulation combination presented is for a level change of 2 and slope change of 0.1; however, other combinations give similar results. From top to bottom the methods are autoregressive integrated moving average (ARIMA) (purple), Prais-Winsten (PW) (green) and restricted maximum likelihood (REML) (orange)