Estimate stochastic model parameters by matching wavelet variance

Fits a time_series_model or sum_model to data by minimizing the weighted distance between empirical and theoretical wavelet variance. Optimization is performed in real (unconstrained) space and transformed to the model's parameter domain internally.

Usage

gmwm2(x, model, omega = NULL, method = "L-BFGS-B", control = list(), ...)

Arguments

x: Numeric vector, or a generated_time_series / generated_composite_model_time_series object (its series is used).
model: A time_series_model or sum_model.
omega: Optional weighting matrix. If NULL, a default based on the empirical WV confidence intervals is used.
method: Optimization method passed to stats::optim.
control: Optional list of control parameters for stats::optim.
...: Additional arguments passed to stats::optim.

Value

An object of class gmwm2_fit with elements: theta_hat (real space), theta_domain (constrained space), model, empirical_wvar, theoretical_wvar, optim, and n.

Details

The default weighting matrix is diagonal with entries proportional to the inverse squared width of the empirical WV confidence intervals. Provide omega to use a custom weighting (e.g., from a theoretical covariance).

Examples

model <- wn(sigma2 = 1) + ar1(phi = 0.8, sigma2 = 0.5)
x <- generate(model, n = 1000, seed = 123)
plot(x)

fit <- gmwm2(x, model = wn()+ar1())
fit
#> GMWM fit
#> 
#> Stochastic model
#>   Sum of 2 processes
#> 
#>   [1] White Noise
#>       Parameters : sigma2
#> 
#>   [2] AR(1)
#>       Parameters : phi, sigma2
#> 
#> Initial parameters
#>   1) White Noise: sigma2 = 2.424
#>   2) AR(1): phi = -0.1953, sigma2 = 2.424
#> 
#> Estimated parameters
#>   1) White Noise: sigma2 = 0.9147
#>   2) AR(1): phi = 0.7744, sigma2 = 0.5982
#> 
#> Optimization
#>   Convergence : converged (code 0)
#>   Iterations  : 38
#>   Loss        : 0.03692