meboot (version 1.4-6)

meboot: Generate Maximum Entropy Bootstrapped Time Series Ensemble

Description

Generates maximum entropy bootstrap replicates for dependent data. (See details.)

Usage

meboot (x, reps=999, trim=list(trim=0.10, xmin=NULL, xmax=NULL), reachbnd=TRUE, expand.sd=TRUE, force.clt=TRUE, scl.adjustment = FALSE, sym = FALSE, elaps=FALSE, colsubj, coldata, coltimes, ...)

Arguments

x

vector of data, ts object or pdata.frame object.

reps

number of replicates to generate.

trim

a list object containing the elements: trim, the trimming proportion; xmin, the lower limit for left tail and xmax, the upper limit for right tail.

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.

scl.adjustment

logical. If TRUE scale adjustment is performed to ensure that the population variance of the transformed series equals the variance of the data.

sym

logical. If TRUE an adjustment is peformed to ensure that the ME density is symmetric.

elaps

logical. If TRUE elapsed time during computations is displayed.

colsubj

the column in x that contains the individual index. It is ignored if the input data x is not a pdata.frame object.

coldata

the column in x that contains the data of the variable to create the ensemble. It is ignored if the input data x is not a pdata.frame object.

coltimes

an optional argument indicating the column that contains the times at which the observations for each individual are observed. It is ignored if the input data x is not a pdata.frame object.

...

possible argument fiv to be passed to expand.sd.

Value

x

original data provided as input.

ensemble

maximum entropy bootstrap replicates.

xx

sorted order stats (xx[1] is minimum value).

z

class intervals limits.

dv

deviations of consecutive data values.

dvtrim

trimmed mean of dv.

xmin

data minimum for ensemble=xx[1]-dvtrim.

xmax

data x maximum for ensemble=xx[n]+dvtrim.

desintxb

desired interval means.

ordxx

ordered x values.

kappa

scale adjustment to the variance of ME density.

elaps

elapsed time.

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).

The scale and symmetry adjustments are described in Vinod (2013) referenced below.

In some applications, the ensembles must be ensured to be non-negative. Setting trim$xmin = 0 ensures positive values of the ensembles. It also requires force.clt = FALSE and expand.sd = FALSE. These arguments are set to FALSE if trim$xmin = 0 is defined and a warning is returned to inform that the value of those arguments were overwritten. Note: The choice of xmin and xmax cannot be arbitrary and should be cognizant of range(x) in data. Otherwise, if there are observations outside those bounds, the limits set by these arguments may not be met. If the user is concerned only with the trimming proportion, then it can be passed as argument simply trim = 0.1 and the default values for xmin and xmax will be used.

References

Vinod, H.D. (2013), Maximum Entropy Bootstrap Algorithm Enhancements. http://ssrn.com/abstract=2285041.

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), pp. 353-377.

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