Wats: Wrap Around Time Series Graphics

WATS Plots: Wrap Around Time Series

Raw monthly birth rates (General Fertility Rates; GFRs) for Oklahoma County, 1990-1999, plotted in a linear plot; the "bombing effect" is located ten months after the Oklahoma City bombing.

Smoothed monthly birth rates (General Fertility Rates; GFRs) for Oklahoma County, 1990-1999, plotted in a linear plot. The top plot shows the connected raw data with a February smoother; the middle plot shows smoothing with a 12-month moving average, blue/green line, superimposed on a February smoother, red line); the bottom plot shows the smoothers and confidence bands, which are H-spreads defined using the distribution of GFRs for the given month and 11 previous months.

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Cartesian plot of the GFR time series data in Oklahoma County, with H-spread Bands superimposed.

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Wrap Around Time Series (WATS Plot) of the Oklahoma City GFR data, 1990-1999

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WATS Plot with H-spread bands (top left), with data lines deleted (top right), and the original Cartesian plot (bottom)

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Comparison of Oklahoma County (where the bombing occurred) and four other urban counties. Cleveland County shows a smaller but relatively consistent increase; it is the southern neighbor of Oklahoma County from which many residents commute to work in Oklahoma City, and a number of whose residents were among those killed or injured. Tulsa County, which also shows a slight increase, is the other large metropolitan county besides Oklahoma county.

fig-7

Comparison of four different measures of spread for use in constructing WATS Plot error bands. WATS can accept an error band from most estimation procedures, including a full range (2nd row) and a parametric standard error (3rd row) error band. The bottom row error bands are constructed from a 66% bootstrap confidence interval, which can be asymmetric if the data are skewed (66% was chosen to be comparable to the parametric standard error band).

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