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Block bootstrap

Bootstrap resampling that draws contiguous blocks of observations rather than single points, preserving short-run structure like volatility clustering.

A plain bootstrap shuffles days independently, which destroys autocorrelation and volatility-clustering. Since calm days follow calm days and crash days cluster, a shuffled series understates drawdowns badly.

The block version picks a block length, say 20 days, and builds each synthetic series by stringing random 20-day blocks together. Internal structure inside each block survives; only the joins are artificial.

Choosing the block length is a judgement. Too short and you lose the clustering you were trying to keep; too long and you have only a handful of distinct blocks, so the synthetic paths are near-copies of the original. A rule of thumb is the cube root of the sample size, so about 13 for 2,500 days.

Related: bootstrap, monte-carlo-simulation

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