ARIMA Models

Using FAST TRACK PLUS data, we analyzed how auto insurance claims change over time. In this report, we identify which state-level claims are unexpectedly extreme. Using an ARIMA model, we forecast the Q2 2019 value for each state, metric (frequency, severity and loss cost), and coverage (bodily injury, property damage, comprehensive, collision, and personal injury protection). ARIMA models allow us to account for both the quarter-to-quarter trends and any trends across years (for example if all the Q3 values are higher than any other quarters in the year). The state maps show the accuracy of the Q2 prediction. Blue states indicate that the true Q2 metric was significantly less than expected, and red states indicate that the true Q2 metric was significantly greater than expected.

Below each state map, full time series plots are displayed for the states that had a Q2 metric fall outside of the 10%-90% prediction interval. The green dot represents the true Q2 value. The blue dot represents the point forecast with a surrounding grey area representing the 10%-90% prediction interval.

Some states and metrics experienced an extreme or abnormal observation due to weather or other events; these outliers decreased the accuracy of the ARIMA model. The time series with outliers were smoothed as to improve the Q2 prediction accuracy. These smoothed outliers are marked with an orange square on the time series plots.

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