Robustness of Time Delay Embedding to Sampling Interval Misspecification
Time delay embedding is a method that is often used when estimating continuous-time differential equation parameters from univariate and multivariate time series, and this method assumes equal time intervals between samples. But in much real-world social science data, time intervals between samples can vary widely. This chapter simulates several common types of time interval misspecification and compares three methods commonly used for accounting for unequal intervals against each other and against the case where no correction is made. Surprisingly, no correction performs almost as well as the best method: in most of the simulated conditions, there was no significant difference between no correction and a sophisticated full information maximum likelihood method where filter loadings were tailored to the actual intervals between samples for each row of data. Time delay embedding appears to be relatively robust to sampling interval misspecification. Reasons for this robustness are presented and discussed. Caveats are presented and discussed regarding cases when time misspecification may still induce bias in results from time delay embedding.
Funding for this work was provided in part by NIH Grant 1R21DA024304–01. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Institutes of Health.
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