meboot (version 1.3-0)

flexMeboot: Flexible Extension of the Maximum Entropy Bootstrap Procedure

Description

This function extends the maximum entropy bootstrap procedure implemented in meboot to allow for for a flexible trend up, flat or down.

Usage

flexMeboot (x, reps = 9, segment = 5, forc = FALSE, myseq = seq(-1, 1, by = 1))

Value

A matrix containing by columns the bootstrapped replicated of the original data x.

Details

flexMeboot uses non-overlapping blocks having only m observations. A trend $a + bt$ is replaced by $a + Bt$, where B = sample(myseq) * b.

Its steps are as follows:

1. Choose block sizesegmentdenoted here as$m$(default equal to$m=5$) and divide the original time seriesxof length$T$into$k = floor(T/m)$blocks or subsets. Note that when$T/m$is not an integer the$k$-th block will have a few more than$m$items. Hence let us denote the number of observations in each block as$m$which equals$m$for most blocks, except the$k$-th.
2. Regress each block having m observations as subsets ofxon the set$\tau = 1, 2,..., m$, and store the intercept$b0$, the slope$b1$of$\tau$and the residuals$r$.
3. Note that the positive (negative) sign of the slope$b1$in this regression determines the up (down) direction of the time series in that block. Hence the next step of the algorithm replaces$b1$by$B1 = b1 * w$, defined by a randomly chosen weight$w in (-1, 0, 1)$. For example, when the random choice yields$w = -1$, the sign of$b1$is reversed. Our weighting independently injects some limited flexibility to the directions of values block segments of the original time series.
4. Reconstruct all time series blocks as:$b0 + b1 * w * \tau + r$, by adding back the residual$r$of the regression on$\tau$.
5. The next step applies the functionmebootto each block of time serie-now having a modified trend-and create a large number,$J$, of resampled time series for each of the$k$blocks.
6. Sequentially join the$J$replicates of all$k$blocks or subsets together.

References

Vinod, H.D. (2012), Constructing Scenarios of Time Heterogeneous Series for Stress Testing, Available at SSRN: http://ssrn.com/abstract=1987879.

See Also

meboot.

Examples

set.seed(235)
myseq <- seq(-1, 1, by = 0.5)
xx <- flexMeboot(x = AirPassengers, myseq = myseq, reps = 3)
matplot(cbind(AirPassengers, xx), type = "l")