Interpreting the Adapted Roll Measure’s Lagged Returns and Window

Summary

The document asks how to implement the adapted Roll measure attributed to Easley and coauthors using daily cryptocurrency OHLCV data. Its main questions concern the meaning of lagged price changes such as ΔP at t−w and t−w+1, whether the lookback window W is a count of observations or an average, and how to interpret grouping symbols in the formula.

The document does not include the formula itself, an implementation, or an answer to these questions. It therefore identifies practical ambiguities a researcher would need to resolve before coding the estimator, but gives no evidence about how those choices affect estimates. The cited source may define the notation, yet the document does not explain how to map its inputs to daily OHLCV data or address whether that data is suitable for the measure.

Key ideas

• The document concerns implementation of an adapted Roll measure using cryptocurrency OHLCV data.
• It asks how lagged price changes should be computed across a lookback window.
• It is unclear whether W denotes the number of observations or an averaged quantity.
• The document provides no formula details or worked implementation to resolve the questions.

Tags

# Adapted Roll measure implementation


# Adapted Roll measure implementation












I'm currently trying to implement the roll measure adapted by Easley et al. (2020, p. 22). https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3345183

The adapted roll measure is given by the eq below.

However, I do not understand how to implement it. Firstly looking at Delta Pt, I am under the understanding the delta (small) pt is a regular change in value from the day before until "this" day. How should I implement the Delta_Pt-w and Delta pt-w+1?

Would the lookback window W, in this case, be a number such as 10? or is it the avg value of the days in those ten days? Do the brackets in this case mean I should add all of the variables together?

The data used for this project is crypto currency OHLCV retrived from Coinapi.oi. (Sample below)

Thanks for the assistance.

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