Parameter estimation for symmetric correlation functions for an mcgf object.

Parameter estimation for symmetric correlation functions for an mcgf object.

Usage

# S3 method for mcgf
fit_base(
  x,
  lag,
  horizon = 1,
  model = c("spatial", "temporal", "sep", "fs", "none"),
  method = c("wls", "mle"),
  optim_fn = c("nlminb", "optim", "other"),
  par_fixed = NULL,
  par_init,
  lower = NULL,
  upper = NULL,
  other_optim_fn = NULL,
  dists_base = NULL,
  scale_time = 1,
  ...
)

Arguments

x

An mcgf object containing attributes dists, acfs, ccfs, and sds.

lag

Integer time lag.

horizon

Integer forecast horizon.

model

Base model, one of spatial, temporal, sep, fs, none. Only sep and fs are supported when method = mle. If none, NULLs are returned.

method

Parameter estimation methods, weighted least square (wls) or maximum likelihood estimation (mle).

optim_fn

Optimization functions, one of nlminb, optim, other. When optim_fn = other, supply other_optim_fn.

par_fixed

Fixed parameters.

par_init

Initial values for parameters to be optimized.

lower

Optional; lower bounds of parameters.

upper

Optional: upper bounds of parameters.

other_optim_fn

Optional, other optimization functions. The first two arguments must be initial values for the parameters and a function to be minimized respectively (same as that of optim and nlminb).

dists_base

List of distance matrices. If NULL, dists(x) is used. Must be a matrix or an array of distance matrices.

scale_time

Scale of time unit, default is 1. lag is divided by scale_time for parameter estimation.

...

Additional arguments passed to optim_fn.

Value

A list containing outputs from optimization functions of optim_fn.

Details

This function fits the separable and fully symmetric models using weighted least squares and maximum likelihood estimation. Optimization functions such as nlminb and optim are supported. Other functions are also supported by setting optim_fn = "other" and supplying other_optim_fn. lower and upper are lower and upper bounds of parameters in par_init and default bounds are used if they are not specified.

Note that both wls and mle are heuristic approaches when x contains observations from a subset of the discrete spatial domain, though estimation results are close to that using the full spatial domain for large sample sizes.

See also

Other functions on fitting an mcgf: add_base.mcgf(), add_lagr.mcgf(), fit_lagr.mcgf(), krige.mcgf(), krige_new.mcgf()

Examples

data(sim1)
sim1_mcgf <- mcgf(sim1$data, dists = sim1$dists)
#> `time` is not provided, assuming rows are equally spaced temporally.
sim1_mcgf <- add_acfs(sim1_mcgf, lag_max = 5)
sim1_mcgf <- add_ccfs(sim1_mcgf, lag_max = 5)

# Fit a pure spatial model
fit_spatial <- fit_base(
    sim1_mcgf,
    model = "spatial",
    lag = 5,
    par_init = c(c = 0.001, gamma = 0.5),
    par_fixed = c(nugget = 0)
)
fit_spatial$fit
#> $par
#>           c       gamma 
#> 0.001145201 0.500000000 
#> 
#> $objective
#> [1] 1.385845
#> 
#> $convergence
#> [1] 0
#> 
#> $iterations
#> [1] 7
#> 
#> $evaluations
#> function gradient 
#>       18       17 
#> 
#> $message
#> [1] "both X-convergence and relative convergence (5)"
#> 

# Fit a pure temporal model
fit_temporal <- fit_base(
    sim1_mcgf,
    model = "temporal",
    lag = 5,
    par_init = c(a = 0.3, alpha = 0.5)
)
fit_temporal$fit
#> $par
#>         a     alpha 
#> 0.6534102 0.7572530 
#> 
#> $objective
#> [1] 0.004445817
#> 
#> $convergence
#> [1] 0
#> 
#> $iterations
#> [1] 16
#> 
#> $evaluations
#> function gradient 
#>       18       38 
#> 
#> $message
#> [1] "relative convergence (4)"
#> 

# Fit a separable model
fit_sep <- fit_base(
    sim1_mcgf,
    model = "sep",
    lag = 5,
    par_init = c(
        c = 0.001,
        gamma = 0.5,
        a = 0.3,
        alpha = 0.5
    ),
    par_fixed = c(nugget = 0)
)
fit_sep$fit
#> $par
#>           c       gamma           a       alpha 
#> 0.001139264 0.500000000 0.627518829 0.734384140 
#> 
#> $objective
#> [1] 3.196846
#> 
#> $convergence
#> [1] 0
#> 
#> $iterations
#> [1] 25
#> 
#> $evaluations
#> function gradient 
#>       46      113 
#> 
#> $message
#> [1] "relative convergence (4)"
#>