I have data from a natural archive (lake sediment). For various reasons it is usually impossible to sample the archive equally in time, and we end up with a time series where essentially we have observations at
random[*] time points. (In other words we are not sampling a regular process and missing some of the regular observations - we have a continuous process [sediment accumulates constantly over time] and we observe something from that process essentially randomly in time.)
For normal time series data one might employ a block bootstrap when applying the bootstrap to problems of confidence interval generation etc. Does the block bootstrap depend on equal sampling intervals or would it be appropriate to apply it to the unevenly-sampled data I describe?
[*] Apologies, the use of "random" here is wrong. We sample the mud evenly in terms of depth (or distance from the mud-water interface, larger distances == older samples). However, the accumulation rate of the sediment is rarely constant, and even if it was there is the issue of compaction of the sediments, hence each, say 0.5cm, slice of mud represents a slightly different amount of time. Then, in general, we might only analyse at best every other slice of mud, and usually at coarser resolutions. Hence the unequal sampling in time of our resulting observations.