# 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. Commented Sep 28, 2015 at 9:15
• What is the criterion of this importance? Commented Sep 28, 2015 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? Commented Sep 28, 2015 at 9:30
• I want to estimate a number of days passed since the beginning of sample when cumulative return passes threshold Commented Sep 28, 2015 at 9:31
• Yes, but that does neither require bootstrapping nor the autocorrelation. You can directly measure it. Commented Sep 28, 2015 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 $Ω$.