Skip to contents

NNS meboot

Source: R/NNS_meboot.R
NNS.meboot.Rd

Adapted maximum entropy bootstrap routine from meboot https://cran.r-project.org/package=meboot.

Usage

NNS.meboot(
  x,
  reps = 999,
  rho = NULL,
  type = "spearman",
  drift = TRUE,
  target_drift = NULL,
  target_drift_scale = NULL,
  trim = 0.1,
  xmin = NULL,
  xmax = NULL,
  reachbnd = TRUE,
  expand.sd = TRUE,
  force.clt = TRUE,
  scl.adjustment = FALSE,
  sym = FALSE,
  elaps = FALSE,
  digits = 6,
  colsubj,
  coldata,
  coltimes,
  ...
)

Arguments

x

vector of data.

reps

numeric; number of replicates to generate.

rho

numeric [-1,1] (vectorized); A rho must be provided, otherwise a blank list will be returned. The dependence target is applied to each individual replicate (every replicate is mixed to the requested dependence with the original series); it is not applied to the ensemble. See Note.

type

options("spearman", "pearson", "NNScor", "NNSdep"); type = "spearman"(default) dependence metric desired.

drift

logical; drift = TRUE (default) preserves the drift of the original series.

target_drift

numerical; target_drift = NULL (default) Specifies the desired drift when drift = TRUE, i.e. a risk-free rate of return.

target_drift_scale

numerical; instead of calculating a target_drift, provide a scalar to the existing drift when drift = TRUE.

trim

numeric [0,1]; The mean trimming proportion, defaults to trim = 0.1.

xmin

numeric; the lower limit for the left tail.

xmax

numeric; the upper limit for the 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 is expanded. See expand.sd in meboot::meboot.

force.clt

logical; If TRUE the ensemble is forced to satisfy the central limit theorem. See force.clt in meboot::meboot.

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 performed to ensure that the ME density is symmetric.

elaps

logical; If TRUE elapsed time during computations is displayed.

digits

integer; 6 (default) number of digits to round output to.

colsubj

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

coldata

numeric; 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

numeric; 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

Returns the following row names in a matrix:

  • x original data provided as input.

  • replicates maximum entropy bootstrap replicates.

  • ensemble average observation over all replicates. Being a per-observation mean it is a central summary, not a single series carrying the target dependence; a rank or linear correlation taken directly on the ensemble tends to read higher than rho (averaging amplifies the shared order), so assess rho on the 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.

Note

Vectorized rho and drift parameters will not vectorize both simultaneously. Also, do not specify target_drift = NULL.

The rho dependence alignment is calibrated on each individual replicate: every replicate is mixed so that its dependence on the original series matches rho, in the metric implied by type. Assess a result in that same metric – a "NNSdep" target with NNS.dep$Dependence (unsigned) and a "spearman"/"pearson" target with rank/linear correlation – because a signed correlation taken on an unsigned "NNSdep" target is not comparable to rho (it can even read negative while the dependence target is met). Separately, the ensemble is the per-observation mean of the replicates – a central summary, not a single series carrying the target dependence – so a rank or linear correlation computed directly on the ensemble tends to read higher than the per-replicate rho (averaging amplifies the shared order). Verify rho on the replicates, in the metric implied by type, rather than on the ensemble.

References

  • Vinod, H.D. and Viole, F. (2020) Arbitrary Spearman's Rank Correlations in Maximum Entropy Bootstrap and Improved Monte Carlo Simulations. doi:10.2139/ssrn.3621614

  • Vinod, H.D. (2013), Maximum Entropy Bootstrap Algorithm Enhancements. doi:10.2139/ssrn.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

if (FALSE) { # \dontrun{
# To generate an orthogonal rank correlated time-series to AirPassengers
boots <- NNS.meboot(AirPassengers, reps = 100, rho = 0, xmin = 0)

# Verify correlation of replicates ensemble to original
cor(boots["ensemble",]$ensemble, AirPassengers, method = "spearman")

# Plot all replicates
matplot(boots["replicates",]$replicates , type = 'l')

# Plot ensemble
lines(boots["ensemble",]$ensemble, lwd = 3)

# Plot original
lines(1:length(AirPassengers), AirPassengers, lwd = 3, col = "red")

### Vectorized drift with a single rho
boots <- NNS.meboot(AirPassengers, reps = 10, rho = 0, xmin = 0, target_drift = c(1,7))
matplot(do.call(cbind, boots["replicates", ]), type = "l")
lines(1:length(AirPassengers), AirPassengers, lwd = 3, col = "red")

### Vectorized rho with a single target drift
boots <- NNS.meboot(AirPassengers, reps = 10, rho = c(0, .5, 1), xmin = 0, target_drift = 3)
matplot(do.call(cbind, boots["replicates", ]), type = "l")
lines(1:length(AirPassengers), AirPassengers, lwd = 3, col = "red")

### Vectorized rho with a single target drift scale
boots <- NNS.meboot(AirPassengers, reps = 10, rho = c(0, .5, 1), xmin = 0, target_drift_scale = 0.5)
matplot(do.call(cbind, boots["replicates", ]), type = "l")
lines(1:length(AirPassengers), AirPassengers, lwd = 3, col = "red") 
} # }