![]() ![]() So that all blocks have the same length (L) */ n = nrow (Pred ) /* length of series */ The length of the series (n) must be divisible by the number of blocks (k) * Restriction for Simple Block Bootstrap: * MOVING BLOCK BOOTSTRAP */ %let L = 12 The following SAS/IML program reads the data and defines a matrix ( R) such that the i_th row contains the residuals with indices i:i+L-1. The OutReg data set contains three variables of interest: Time, Pred, and Resid.Īs before, I will choose the block size to be L=12. Sashelp.Air data set and used PROC AUTOREG to form an additive model Predicted + Residuals. The previous article extracted 132 observations from the To demonstrate the moving block bootstrap in SAS, let's use the same data that I analyzed in the previous article about the simple block bootstrap. In the figure, the time series has been reshaped into a k x L matrix, where each row is a block. The process of forming one bootstrap sample is illustrated in the following figure. Repeat the process many times and you have constructed a batch of bootstrap resamples. You then add these residuals to the predicted values to create a "new" time series. To form a bootstrap resample, you randomly choose k=n/L blocks (with replacement) and concatenate them. ![]() The indices 1: L define the first block of residuals, the indices 2: L+1 define the second block, and so forth until the last block, which contains the residuals n-L+1:n. The following figure illustrates the overlapping blocks when L=3. In the moving block bootstrap, every block has the same block length but the blocks overlap. This article describes a better alternative: the moving block bootstrap. If so, the bootstrap resamples do not capture enough variation for the bootstrap method to make correct inferences. One reason is that the total number of blocks ( k=n/L) is often small. ![]() The simple block bootstrap is not often used in practice. Each bootstrap resample is generated by randomly choosing from among the non-overlapping n/L blocks of residuals, which are added to the predicted model. You then choose a block length ( L) that divides the total length of the series ( n). The first step is to decompose the series into additive components: Y = Predicted + Residuals. As I discussed in a previous article, the simple block bootstrap is a way to perform a bootstrap analysis on a time series. ![]()
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