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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)?

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  • $\begingroup$ What's your objective? There's no way to go from monthly to daily returns, assuming you don't have the underlying daily returns, without it being some manner of simulation $\endgroup$
    – Chris
    Sep 22 '20 at 3:59
  • $\begingroup$ If it is a matter if simulation, how can simulated daily returns even be inferred from the properties of monthly returns? $\endgroup$
    – develarist
    Sep 22 '20 at 4:21
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    $\begingroup$ That's what I'm saying, they'd be constructed based on some assumptions to match monthly returns. It's not something I'd advise, which is why I asked about objective $\endgroup$
    – Chris
    Sep 22 '20 at 5:15
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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.

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