Resampling a timeseries I have a list of stock returns (say computed from the historical data) and would like to resample the historical return distribution. Naively doing bootstrapping means the samples are iid. I'm particularly interested in correlation between consecutive returns (a large return should be more likely to be followed by a large return of either sign)
Is there any standard way we can do this? I had a stab of this myself -


*Assume the return of the day t is dependent on t-1

*Break the return into (arbitary) buckets.

*Estimate the probability day t return is belongs to a certain bucket, based on which bucket t-1 is from.

*For every t, first sample which bucket it belongs to conditional t-1 using estimated probability then pick a sample from this bucket uniformly.

Is there any reference someone suggests where is such techniques are discussed. Thanks!

These returns are not iid, because:

*

*they aren't identically distributed (have different variances, even if having the same absolute or scaled mean),

*nor independent (the latter because their variances sort of depend on each other).

Instead of resampling, I would suggest that you take a look at autoregressive conditional heteroskedasticity models (there are many of them).
