Analysis of fragmented time series data using box-jenkins models

Abstract

Throughout ecology, fragmented time series data have remained largely unanalyzed even though numerous methods exist for both structural and Box-Jenkins time series models. We evaluated four fragmented-data techniques for Box-Jenkins models using a data set of Peromyscus leucopus densities that spans 248 months and contains 15% missing data. We (1) approximated missing data using a linear interpolation between available observations (interpolation model), (2) estimated missing data according to the autocorrelation pattern identified with available data (estimation model), (3) forecasted missing data and re-estimated the model until the forecasts converged using an estimation maximization algorithm (maximization model), and (4) omitted missing data during parameter estimation (omission model). We compared overall model fit using the Schwarz information criterion and outlieranalysis. We found that the estimation and omission models fit the data better than the maximization model and far better than the interpolation model. In addition, the estimation model created more biologically realistic estimates of missing data than either the interpolation or maximization model. These results are directly applicable to multivariate Box-Jenkins time series models.