Using a Brownian Bridge to Upsample Monthly Returns

Summary

The question asks whether monthly returns can be expanded into plausible daily returns, noting that aggregation from daily data is straightforward but reversing it seems underdetermined. The response points to a Brownian bridge approach, which can construct an intermediate path conditioned on the observed endpoints. Such a method may help fill missing time-series observations or support backtests of path-dependent strategies when only coarse data are available.

The document does not provide the procedure, assumptions, or an empirical example; it only refers readers to another answer. Upsampled daily values are therefore modeled paths, not recovered historical observations. Any use in research or backtesting should account for the assumptions of the bridge and the uncertainty in the unobserved path.

Key ideas

• Monthly observations do not uniquely determine the daily path within each month.
• A Brownian bridge is suggested for generating an intermediate path conditioned on observed endpoints.
• The method may be relevant to missing data and path-dependent backtests.
• The document omits implementation details and evidence, so the resulting daily returns should be treated as modeled estimates.

Tags

# How to up-sample monthly returns into daily returns?


# How to up-sample monthly returns into daily returns?












I know how to down-sample daily returns (large-sample data) to monthly returns (small-sample data) by using rolling windows, which feels like estimating a sub-sample from the population (something that makes sense based on what's given), but for some reason don't think it's as easy to go the reverse direction if starting from monthly returns and wanting to up-sample to daily returns, which sounds like estimating the population from a sub-sample (something that does not make sense based on what's given).

Is there a step-by-step procedure for up-sampling monthly returns (small-sample data) into daily returns (large-sample data)?

## Answer by RRL (score 1)

https://quant.stackexchange.com/a/58174

Despite the initial reaction, this is actually an interesting question. A related question arises naturally in the context of filling in missing financial time series data or perhaps in back-testing path dependent strategies again with data limitations.

An approach based on a Brownian bridge appears here.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.