Leave-K-Out Diagnostics for Time Series

SUMMARY We propose diagnostics for autoregressive integrated moving average (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 series setting. 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 ‘leave-k-out’ diagnostics approach is 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.