Leave·k·out Diagnostics for Time Series

We propose diagnostics for ARIMA model fitting for time series formed by deleting observations from the data and measuring the change in the estimates of the parameters. The use of leave-one-out diagnostics is a well established tool in regression analysis. We demonstrate the efficacy of observation deletion based diagnostics for ARIMA models, addressing issues special to the time diagnostics based on the innovations variance. It is shown that the dependency aspect of time series data gives rise to a "smearing" effect, which confounds the diagnostics for the coefficients. It is also shown that the diagnostics based on the innovations variance are much clearer and more sensitive than those for the coefficients. A "Ieave-k-out" diagnostics approachis proposed to deal with patches of outliers, and problems caused by "masking" are handled by use of iterative deletion. An overall strategy for ARIMA model fitting is given, and applied to two data sets. Research supported by NASC Contract N00014-86-K-08l9, APL Contract N00014-84-K0599, and ONR Contract N00014-84-C-0169.