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A Graphical Aid for Analyzing Autocorrelated Dynamical Systems 437

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FigurÄ™ 1. Scatterplot of a synthetic AR(1) time senes. The data was plotted against itself lagged by one time interval. NotÄ™ that the X_t+j axis has been inverted by the plotting software so that the X_t+j axis values increase from top to bottom.

name that has been used for this type of scatterplot is the univariate phase map or a State space map.

Another type of plot that is commonly used to view time series data is the time order plot as seen below in FigurÄ™ 2. In this case, the observations are plotted in time order and the observations are typically joined by lines.

Both of these plots have somewhat limited usefulness as graphical aids for the analysis of time series data. Either may be used to a limited extent to identify suspect observations that lie far from the observations. The time order plot may also be used to aid in the visual identification of trends and cycling or seasonality in the time series data.