In its simplest use, BOOT samples uniformly from the indicated range. This is appropriate when the observations are independent, or when you are resampling some component of the data (typically residuals), that have been transformed to be (approximately) independent. However, in some applications with correlated data, you may not have available a model which will transform the data to independent components (parametric or residual bootstrapping). In order to maintain the observed form of dependence, you need to resample the data in blocks. This is done using BOOT with the BLOCK=block size option.

 

There are three methods for doing block bootstrapping; you choose this using the METHOD option. The default is METHOD=OVERLAP. This will allow any block of block size entries from the resampling zone to be chosen. METHOD=NOOVERLAP partitions the resampling zone into disjoint blocks and only selects from those. METHOD=STATIONARY doesn’t sample by blocks. Instead, when sampling for an entry, it either takes the next item in the resampling zone, or (with probability) 1/block size, starts a new block. With this, the data are resampled with blocks with an expected size of  block size, while in the other two methods, they are exactly block size. See Politis and Romano (1994).

 

There are also some applications where it might be desired to oversample more recent values. You can do this with BOOT with the option GEOMETRIC=decay rate, where decay rate is the rate at which the probability of being chosen declines, with the last entry in the resampling zone having the highest probability. The closer decay rate is to 1, the closer this comes to uniform sampling.

 

An example which uses block bootstrapping is BOOTCOINTEGRATION.RPF, which does a bootstrapped distribution for a cointegrating vector.

 

 

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