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A Graphical Aid for Analyzing Autocorrelated Dynamical Systems

Autoregressive Time Senes AR(2), Coefficients Negative

AR02p9S Tin* Plot

Tim

FigurÄ™ 5. Left - the time order plot of the AR(2) synthetic time series with negative coefficients. Right - An extract, from the univariate phase map movie for the same series, of observations 150 to 170. NotÄ™ that the vertical axis for the plot on the right is inverted.

Autoregressive Time Series AR(3), Coefficients Negative

AR03p9S T1Plot

Tl M

FigurÄ™ 6. Left - the time order plot of the AR(3) synthetic time series with negative coefficients. Right - An extract, from the univariate phase map movie for the same series, of observations 150 to 170. NotÄ™ that the vertical axis for the plot on the right is inverted.

In addition there is another phenomena that appears, the movie contains a few short segments where the movie briefly takes on an uncharacteristic shape and