Description Usage Arguments Details Value References See Also Examples

This function extends the maximum entropy bootstrap procedure
implemented in `meboot`

to allow for for a flexible trend up, flat or down.

1 |

`x` |
vector of data, |

`reps` |
number of replicates to generate. |

`segment` |
block size. |

`forc` |
logical. If TRUE the ensemble is forced to satisfy the central limit theorem.
See |

`myseq` |
directions for trend within a block of data is chosen randomly with the user's choice
limited by the range of values given by myseq. For example, |

`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:

Choose block size

`segment`

denoted here as*m*(default equal to*m=5*) and divide the original time series`x`

of 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.Regress each block having m observations as subsets of

`x`

on the set*τ = 1, 2,..., m*, and store the intercept*b0*, the slope*b1*of*τ*and the residuals*r*.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.Reconstruct all time series blocks as:

*b0 + b1 * w * τ + r*, by adding back the residual*r*of the regression on*τ*.The next step applies the function

`meboot`

to 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.Sequentially join the

*J*replicates of all*k*blocks or subsets together.

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

.

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

1 2 3 4 | ```
set.seed(235)
myseq <- seq(-1, 1, by = 0.5)
xx <- flexMeboot(x = AirPassengers, myseq = myseq, reps = 3)
matplot(cbind(AirPassengers, xx), type = "l")
``` |

```
Loading required package: dynlm
Loading required package: zoo
Attaching package: 'zoo'
The following objects are masked from 'package:base':
as.Date, as.Date.numeric
Loading required package: nlme
```

meboot documentation built on May 2, 2019, 9:13 a.m.

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