meboot.default {meboot}R Documentation

Generate Maximum Entropy Bootstrapped Time Series Ensemble

Description

This function generates maximum entropy bootstrap replicates for dependent data. (See details.)

Usage

    meboot.default (x, reps=999, trim=0.10, reachbnd=TRUE,
  expand.sd=TRUE, force.clt=TRUE, elaps=FALSE, ...)
  

Arguments

x a vector of data or a time series object.
reps number of replicates to generate.
trim the trimming proportion.
reachbnd logical. If TRUE potentially reached bounds (xmin = smallest value - trimmed mean and xmax=largest value + trimmed mean) are given when the random draw happens to be equal to 0 and 1, respectively.
expand.sd logical. If TRUE the standard deviation in the ensemble in expanded. See expand.sd.
force.clt logical.If TRUE the ensemble is forced to satisfy the central limit theorem. See force.clt.
elaps logical. If TRUE elapsed time during computations is displayed.
... possible argument fiv to be passed to expand.sd.

Details

Seven-steps algorithm:

  1. Sort the original data in increasing order and store the ordering index vector.
  2. Compute intermediate points on the sorted series.
  3. Compute lower limit for left tail (xmin) and upper limit for right tail (xmax). This is done by computing the trim (e.g. 10
  4. Compute the mean of the maximum entropy density within each interval in such a way that the mean preserving constraint is satisfied. (Denoted as m_t in the reference paper.) The first and last interval means have distinct formulas. See Theil and Laitinen (1980) for details.
  5. Generate random numbers from the [0,1] uniform interval and compute sample quantiles at those points.
  6. Apply to the sample quantiles the correct order to keep the dependence relationships of the observed data.
  7. Repeat the previous steps several times (e.g. 999).

Value

x original data provided as input.
ensemble maximum entropy bootstrap replicates.
xx sorted order stats (x[1] is minimum value).
z class intervals limits.
dv deviations of consecutive data values.
dvtrim trimmed mean of dv.
xmin data minimum for ensemble=x[1]-dvtrim.
xmax data x maximum for ensemble=x[n]+dvtrim.
desintxb desired inteval means.
ordxx ordered x values.
elaps elapsed time.

References

Vinod, H.D. (2006), Maximum Entropy Ensembles for Time Series Inference in Economics, Journal of Asian Economics, 17(6), pp. 955-978

Vinod, H.D. (2004), Ranking mutual funds using unconventional utility theory and stochastic dominance, Journal of Empirical Finance, 11(3), 353-377.

See Also

slider.mts.

Examples

    ## Ensemble for the AirPassenger time series data
    set.seed(345)
    out <- meboot(x=AirPassengers, reps=100, trim=0.10, elaps=TRUE)

    ## Ensemble for T=5 toy time series used in Vinod (2004)
    set.seed(345)
    out <- meboot(x=c(4, 12, 36, 20, 8), reps=999, trim=0.25, elaps=TRUE)
    mean(out$ens)  # ensemble mean should be close to sample mean 16
  

[Package meboot version 1.0-0 Index]