Non-linear constraints forecast reconciliation

This function performs optimal (in least squares sense) forecast reconciliation for a multiple time series with \(C\) linear and non-linear constraints.

Usage

csnlc(base, g_fun, g_grad = NULL, comb = "ols", res = NULL, start = NULL,
      nn = FALSE, settings = NULL, ...)

Arguments

base

A (\(h \times n\)) numeric matrix or multivariate time series (mts class) containing the base forecasts to be reconciled; \(h\) is the forecast horizon, and \(n\) is the total number of time series.

g_fun

A multivariate constraint function \(g:\mathbb{R}^n \rightarrow \mathbb{R}^{C}\). It may consist of both linear and non-linear constraints.

g_grad

Gradient of the constraints function \(g\).

comb

A string specifying the reconciliation method: ols, wls or shr. (see for more details FoReco::cscov).

res

An (\(N \times n\)) optional numeric matrix containing the in-sample residuals/validation errors. This matrix is used to compute some covariance matrices.

start

Optional starting values of the non-linear optimisation.

nn

Logical value: TRUE (default) if non-negative reconciled forecasts are wished.

settings

Settings for (nloptr). The default options are: algorithm = "NLOPT_LD_SLSQP", xtol_rel = 1.0e-6, xtol_abs = 1.0e-6. For details, see the (nloptr) documentation.

...

Arguments passed on to FoReco::cscov.

Value

A (\(h \times n\)) numeric matrix of cross-sectional reconciled forecasts.

References

Girolimetto, D., Panagiotelis, A., Di Fonzo, T., Li, H. (2024), Forecast reconciliation with non-linear constraints, arXiv. doi:10.48550/arXiv.2510.21249

Johnson, S. (2008), The NLopt non-linear optimization package. https://github.com/stevengj/nlopt

Examples

bf <- c(1, 2, 4)
g_fun <- function(x) x[1]-x[2]/x[3]
g_grad <- function(x){
  c(1, -1/x[3], x[2]/(x[3]^2))
}
reco <- csnlc(base = bf, g_fun = g_fun, g_grad = g_grad, comb = "ols")
#> Warning: Argument `res` is ignored.
#> ℹ When `res` is provided, `comb = 'shr'` is suggested.
FoReco::recoinfo(reco)$info
#> ✔  Cross-sectional Forecast Reconciliation
#> ℹ FoReco function: `csnlc`
#> ℹ Covariance approximation: `ols`
#> ℹ Non-negative forecasts: `TRUE`
#>     obj_val iter ineq_cons eq_cons status
#> 1 0.1156807    5         0       1      4