Maximum Entropy Bootstrap for Time Series using Rcpp

Generates bootstrap replicates of a time series using the maximum entropy bootstrap algorithm with Rcpp implementation for improved performance. This method is particularly useful for non-stationary time series and preserves the dependence structure of the original data.

meboot(
  x,
  reps = 999,
  trim = list(trim = 0.1, xmin = NULL, xmax = NULL),
  reachbnd = TRUE,
  expand.sd = TRUE,
  force.clt = TRUE,
  scl.adjustment = FALSE,
  sym = FALSE,
  colsubj,
  coldata,
  coltimes,
  ...
)

Arguments

x

A numeric vector or time series object to be bootstrapped.

reps

Number of bootstrap replicates to generate (default: 999).

trim

Controls tail behavior. Can be a single numeric value specifying the trim proportion (e.g., 0.10 for 10% trimming), or a list with components:

trim: Trim proportion for tail calculation (default: 0.10)
xmin: Lower bound for generated values (optional)
xmax: Upper bound for generated values (optional)

reachbnd

Logical indicating whether to allow generated values to reach the boundaries xmin and xmax (default: TRUE).

expand.sd

Logical indicating whether to expand the standard deviation of the ensemble (default: TRUE).

force.clt

Logical indicating whether to force the central limit theorem compliance by centering each replicate (default: TRUE).

scl.adjustment

Logical indicating whether to adjust the scale of the ensemble to match the original data's variance (default: FALSE).

sym

Logical indicating whether to force symmetry in the maximum entropy density (default: FALSE).

colsubj

Deprecated parameter from original meboot (included for compatibility).

coldata

Deprecated parameter from original meboot (included for compatibility).

coltimes

Deprecated parameter from original meboot (included for compatibility).

...

Additional arguments passed to expansion functions.

Value

A list with the following components:

x: Original time series data
ensemble: Matrix of bootstrap replicates (n x reps)
xx: Sorted original data
z: Intermediate points between sorted values
dv: Absolute differences between consecutive observations
dvtrim: Trimmed mean of differences
xmin: Lower bound used for generation
xmax: Upper bound used for generation
desintxb: Interval means satisfying mean-preserving constraint
ordxx: Ordering index of original data
kappa: Scale adjustment factor (if scl.adjustment = TRUE)

Details

The maximum entropy bootstrap algorithm generates replicates that:

Preserve the dependence structure of the original time series
Can handle non-stationary time series
Satisfy the ergodic theorem and central limit theorem
Maintain the mean and autocorrelation structure

The Rcpp implementation provides significant performance improvements over the original R implementation, especially for large datasets and many replications.

References

Vinod, H. D., & Lopez-de-Lacalle, J. (2009). Maximum entropy bootstrap for time series: The meboot R package. Journal of Statistical Software, 29(5), 1-19.

Examples

# \donttest{
# Basic usage with a time series
set.seed(123)
x <- ts(rnorm(100), start = c(2000, 1), frequency = 12)
result <- meboot(x, reps = 1000)

# Plot first few replicates
matplot(result$ensemble[, 1:5], type = "l", lty = 1)
lines(result$x, col = "black", lwd = 2)


# With custom bounds
result_bounded <- meboot(x, reps = 100, 
                             trim = list(trim = 0.1, xmin = -3, xmax = 3))
#> Warning: expand.sd and force.clt were set to FALSE to enforce limits xmin/xmax.

# With scale adjustment
result_scaled <- meboot(x, reps = 100, scl.adjustment = TRUE)
# }