Bootstrapping in time series
Two methods are often used in bootstrapping of time series:
To estimate a model and draw from the residuals (see second last section on bootstrapping regression models by bootstrapping residuals)
Moving blocks bootstrap methods
We concentrate in the following, on the moving blocks bootstrap. It is a method that is often applied and mentioned in literature, but with limited success. To show the limitations of this approach is one goal of this section.
The idea is to divide the data in blocks and to sample with replacement within blocks. This allows us to not completely ignore the relationship between the observations. Relationships between observations are typically present in time series. For example, the next value will depend on the previous value. Think also on the trend, seasonality, and periodicity.
In principle, the time series can be divided in non-overlapping or overlapping blocks.
We will show an overlapping moving blocks bootstrap for estimating the autocorrelation...
