Bootstrapped Data using Stoffer and Wall's Algorithm

Creates bootstrap data via sampling from the standardized innovations matrix. This is an internal function in the MARSS-package and is not exported. Users should access this with MARSSboot.

Usage

MARSSinnovationsboot(MLEobj, nboot = 1000, minIndx = 3)

Arguments

MLEobj: An object of class marssMLE. This object must have a $par element containing MLE parameter estimates from e.g. MARSSkem() or MARSS(). This algorithm may not be used if there are missing datapoints in the data.
nboot: Number of bootstraps to perform.
minIndx: Number of innovations to skip. Stoffer & Wall suggest not sampling from innovations 1-3.

Details

Stoffer and Wall (1991) present an algorithm for generating CIs via a non-parametric bootstrap for state-space models. The basic idea is that the Kalman filter can be used to generate estimates of the residuals of the model fit. These residuals are then standardized and resampled and used to generate bootstrapped data using the MARSS model and its maximum-likelihood parameter estimates. One of the limitations of the Stoffer and Wall algorithm is that it cannot be used when there are missing data, unless all data at time $t$ are missing.

Value

A list containing the following components:

boot.states: Array (dim is m x tSteps x nboot) of simulated state processes.
boot.data: Array (dim is n x tSteps x nboot) of simulated data.
marss: marssMODEL object element of the marssMLE object (marssMLE$marss) in "marss" form.
nboot: Number of bootstraps performed.

m is the number state processes (x in the MARSS model) and n is the number of observation time series (y in the MARSS model).

References

Stoffer, D. S., and K. D. Wall. 1991. Bootstrapping state-space models: Gaussian maximum likelihood estimation and the Kalman filter. Journal of the American Statistical Association 86:1024-1033.

Author

Eli Holmes and Eric Ward, NOAA, Seattle, USA.

Examples

dat <- t(kestrel)
dat <- dat[2:3, ]
fit <- MARSS(dat, model = list(U = "equal", Q = diag(.01, 2)))
#> Success! algorithm run for 15 iterations. abstol and log-log tests passed.
#> Alert: conv.test.slope.tol is 0.5.
#> Test with smaller values (<0.1) to ensure convergence.
#> 
#> MARSS fit is
#> Estimation method: kem 
#> Convergence test: conv.test.slope.tol = 0.5, abstol = 0.001
#> Algorithm ran 15 (=minit) iterations and convergence was reached. 
#> Log-likelihood: -11.12704 
#> AIC: 30.25409   AICc: 30.78742   
#>  
#>                       Estimate
#> R.diag                 0.04958
#> U.1                   -0.00783
#> x0.X.British.Columbia  0.78786
#> x0.X.Alberta           0.73740
#> Initial states (x0) defined at t=0
#> 
#> Standard errors have not been calculated. 
#> Use MARSSparamCIs to compute CIs and bias estimates.
#> 
boot.obj <- MARSSinnovationsboot(fit)