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Generate an AR(1) lognormal FLQuant time-series

Source: R/oem.R
rlnormar1.Rd

Simulate one or more iterated log-normal AR(1) series across specified years and return the results as an FLQuant.

Usage

rlnormar1(
  n = NULL,
  meanlog = 0,
  sdlog = 1,
  rho = 0,
  years,
  bias.correct = FALSE
)

Arguments

n

Integer. Number of iterations to generate. If NULL (default) n is set to the maximum length of meanlog, sdlog and rho.

meanlog

Numeric. Mean(s) of the normal (log) distribution for the innovations. Recycled to length n if necessary.

sdlog

Numeric. Standard deviation(s) of the normal (log) distribution for the innovations. Recycled to length n if necessary.

rho

Numeric. AR(1) autocorrelation parameter(s) in -1, 1. Recycled to length n if necessary.

years

Integer or character vector. Years (time dimension) for the returned FLQuant (length determines number of time steps).

bias.correct

Logical. If TRUE (default FALSE) subtract 0.5 * sdlog^2 from the log-series before exponentiation to correct for the lognormal bias.

Value

An object of class FLQuant with dimensions year x iter containing the simulated log-normal AR(1) series.

Details

The function first draws independent normal samples with given meanlog and sdlog, constructs an AR(1) process with correlation parameter rho, and finally exponentiates the series. If bias.correct = TRUE the log-normal bias (0.5 * sdlog^2) is removed on the log-scale so that the resulting series have the requested meanlog on the log-scale.

The simulation proceeds as follows:

  1. Draw independent normal innovations: eps_t,i ~ N(meanlog_i, sdlog_i^2).

  2. Build the AR(1) process: x_t,i = rho_i * x_t-1,i + sqrt(1 - rho_i^2) * eps_t,i, with x_1,i = eps_1,i.

  3. Optionally apply bias correction on the log scale, then exponentiate: y_t,i = exp(x_t,i - 0.5 * sdlog_i^2) (if bias.correct = TRUE).

References

Thorson, J. T. Predicting recruitment density dependence and intrinsic growth rate for all fishes worldwide using a data-integrated life-history model. Fish Fish. 2020; 21: 237– 251. https://doi-org.ezproxy.library.wur.nl/10.1111/faf.12427

See also

rlnorm

Author

Iago Mosqueira (WMR), Henning Winker (JRC).

Examples

# 6 years, 5 iterations, rho = 0.5, default meanlog/sdlog
rlnormar1(n = 5, rho = 0.5, years = 2000:2005)
#> An object of class "FLQuant"
#> iters:  5 
#> 
#> , , unit = unique, season = all, area = unique
#> 
#>      year
#> quant 2000          2001          2002          2003          2004         
#>   all 0.549(0.6036) 0.649(0.3214) 0.570(0.3084) 0.363(0.0362) 0.470(0.6211)
#>      year
#> quant 2005         
#>   all 1.112(0.2548)
#> 
#> units:  NA 

# varying sdlog per iteration
rlnormar1(n = 3, sdlog = c(0.5, 1, 1.5), rho = 0.3, years = 1990:1994)
#> An object of class "FLQuant"
#> iters:  3 
#> 
#> , , unit = unique, season = all, area = unique
#> 
#>      year
#> quant 1990         1991         1992         1993         1994        
#>   all 0.979(0.443) 1.785(0.537) 1.623(2.108) 1.211(0.188) 0.933(0.981)
#> 
#> units:  NA