# Bootstrapping Time Series Data

I have daily time series for returns on currency exchange rate. I want to estimate the frequency of crossing certain level for cumulative return, that is, how often cumulative return over several days exceeds some level.

I have checked for autocorrelation and found that coefficients are insignificant. Can I use simple bootstrap in this case or do I need to use block bootstrap or sort of? I know that correlation is not a measure of dependece and it simply shows linear dependence.

Also, should I choose a number of drawings from sample for bootstrap equal to a size of sample or it can be less?

• In time series ordering is important then you cannot use simple bootstrap in this case. – TPArrow Sep 28 '15 at 9:15
• What is the criterion of this importance? – Andrew Sep 28 '15 at 9:17
• I fail to understand what you want to do: What evaluation are you running? What does the autocorrelition have to do with how often the time series summed over some days (or moving average) exceeds some level? – Wrzlprmft Sep 28 '15 at 9:30
• I want to estimate a number of days passed since the beginning of sample when cumulative return passes threshold – Andrew Sep 28 '15 at 9:31
• Yes, but that does neither require bootstrapping nor the autocorrelation. You can directly measure it. – Wrzlprmft Sep 28 '15 at 9:43

Assuming that this is correct, i.e., that the temporal information is irrelevant, you can treat your time series information as independent samples from some distribution $Ω$. Thus your problem of finding how frequently the sum of $n$ consecutive values of your time series exceeds a certain value $ϑ$ is equivalent to the problem of finding how often the sum of $n$ random samples from $Ω$ exceeds $ϑ$.
Therefore you can boostrap your findings by randomising your time series order, which is equivalent to taking another sample from $Ω$.