Overlapping Annual Changes and the Limits of Tail-Risk Samples

Summary

The document asks whether a daily series spanning more than two decades can be expanded into many overlapping one-year changes to estimate annual variability and tail risk. It recognizes that this transformation yields a daily series of changes in the rolling annual measure, rather than a collection of independent annual observations. That distinction matters when interpreting a distribution or using it to assess risk.

The text presents the sampling question but includes no answers, calculations, or evidence that the overlapping approach produces reliable tail estimates. Overlapping windows share most of their underlying data, so the apparent increase in observations does not provide the same increase in independent information. The document is therefore useful as a prompt to distinguish the target quantity from the transformed series and to account for dependence when estimating uncertainty. It does not establish a preferred estimator or explain how to correct tail-risk estimates.

Key ideas

• Overlapping annual windows create a daily series of changes in the rolling annual measure.
• The transformed series does not directly represent independent annual observations.
• Shared data between adjacent windows induces dependence that affects interpretation.
• A larger count of overlapping observations does not by itself provide more independent tail information.
• The document raises the estimation question but offers no tested solution.

Tags

# Overlapping Data


# Overlapping Data












I have a daily time series data spanning over 22 years. I need to compute some meaningful yearly standard deviation statistics / generate probability distribution and estimate tail risk. 22 years obviously is not enough, so was wondering about perhaps generating overlapping 1-year change time series and analyzing the daily change in it - that would give me around 5200 observations. Struggling a bit on how to interpret the distribution that I generated - it appears to be a daily change of the yearly change, so was wondering if it could be used at all or if there is a better way to use overlapping data?

Thanks a lot for the inputs,

D>

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