Select the FARMA orders

Selects the FARMA(p, q) orders of short-memory curves. Long-memory curves need to be fractionally differenced first, for example with frac_diff(). farfima() does this on the centred training curves and drops the first trim before selecting the orders.

Usage

# S3 method for class 'farfima_order'
plot(x, main = NULL, ...)

select_order(
  x,
  method = c("ic_full", "ic_auto", "bj", "cv"),
  p = 0:5,
  q = 0:5,
  Npc = 1,
  n_lags = NULL,
  alpha = 0.05,
  iid = FALSE,
  starts = NULL,
  valid = NULL,
  valid_eval = NULL,
  h = 10,
  window = c("expanding", "fixed"),
  cv_score = c("rmse", "mae"),
  seed = NULL,
  verbose = FALSE
)

Arguments

x: A matrix of short-memory training curves (grid points by time) or an fts object. For plot(), a farfima_order object.
main: Plot title.
...: Other arguments passed to graphics::image(), or to graphics::barplot() for "bj".
method: "ic_full", "ic_auto", "bj" or "cv".
p, q: Candidate AR and MA orders. (0, 0) is excluded.
Npc: Number of principal components in the operator estimator.
n_lags: Number of residual autocovariance lags. Defaults to \(\lfloor \log T \rfloor\) for the criteria and 20 for "bj".
alpha: Significance level of the white-noise test ("bj").
iid: Whether the white-noise test assumes iid noise rather than weak white noise ("bj").
starts: Starting models, a data frame with columns p and q ("ic_auto"). Defaults to (2, 2), (1, 0) and (0, 1).
valid: Validation curves following x, also short-memory ("cv").
valid_eval: Optional curves to check the validation forecasts against, in place of valid ("cv").
h: Maximum forecast horizon ("cv").
window: "expanding" or "fixed" window ("cv").
cv_score: "rmse" or "mae" ("cv").
seed: Optional seed. The white-noise test of "bj" uses Monte Carlo integration, so its p-values change between runs without one.
verbose: Whether to show progress messages and a progress bar.

Value

An object of class farfima_order with the selected p and q and a table of the candidates. "ic_auto" also returns its search_path. plot() shows the criterion or CV score of each candidate with the selected model boxed, or the p-values for "bj".

Details

"ic_full" (functional IC) minimises the adaptive functional Hannan-Quinn information criterion over all candidates.
"ic_auto" (auto functional IC) uses the same adaptive functional Hannan-Quinn information criterion with a stepwise search from a few starting models. Its noise level comes from the largest model.
"bj" (functional Box-Jenkins) tries the candidates by increasing p + q and stops at the first whose residuals pass the functional portmanteau test.
"cv" (cross-validation) minimises the RMSPE, or MAPE, of the forecasts from the validation origins, averaged over horizons. A candidate whose fit fails at any origin is dropped.

References

Hannan, E. J. and Quinn, B. G. (1979). The determination of the order of an autoregression. Journal of the Royal Statistical Society: Series B.

Kokoszka, P., Rice, G. and Shang, H. L. (2017). Inference for the autocovariance of a functional time series under conditional heteroscedasticity. Journal of Multivariate Analysis.

Kuenzer, T. (2024). Estimation of functional ARMA models. Bernoulli.

Examples

x = sim_farfima(n = 300, d = 0, p = 1, q = 0, seed = 1)
o = select_order(x, method = "ic_full", p = 0:2, q = 0:2)
o
#> Selected (p, q) = (1, 0)
#>   functional IC (exhaustive search), 8 candidates
plot(o)