Forecast from a FARFIMA fit

Point forecasts and conformal prediction bands up to h steps beyond the data. With a test sample, forecasts are also made from every test origin and evaluated.

Usage

# S3 method for class 'farfima'
predict(
  object,
  test = NULL,
  h = attr(object, "settings")$h,
  band = attr(object, "settings")$band,
  test_eval = NULL,
  verbose = TRUE,
  ...
)

Arguments

object: A fit from farfima().
test: Optional test sample, following the validation sample.
h: Maximum forecast horizon, at most the h of the fit.
band: Conformal prediction bands to return, from those calibrated in farfima().
test_eval: Optional curves to check the test forecasts against, in place of test. The forecasts are still made from test.
verbose: Whether to show progress messages and a progress bar.
...: Not used.

Value

An object of class farfima_forecast, a list with

point_forecast: the forecast curves beyond the data (grid by h);
bands: the conformal prediction bands, with the lower and upper matrices (grid by h) for each band and level (such as "80%");
evaluation, with a test sample: the tables point (RMSPE, the root mean squared prediction error, and MAPE, the mean absolute prediction error), interval (ECP, CPD and MIS of the bands) and wis (weighted interval score).

Details

The conformal prediction bands are those chosen in farfima():

"SR": scaled residual band, the forecast plus and minus a multiplier of the point-wise scale function;
"NS": non-conformity score band, with the width set by a quantile of the standardised non-conformity scores;
"AC": adaptive conformal band, an NS band whose quantile level is updated over the test sample;
"PID": conformal PID control band, whose multiplier is updated by a proportional term, an integral term and an optional scorecaster;
"AcMCP": autocorrelated multistep conformal band, an asymmetric PID band shifted by a forecast of the standardised residual curve.

The AC, PID and AcMCP bands are updated from the error rates of earlier bands, once their targets are observed.

In the test evaluation, the memory parameter and the orders stay fixed, and the operators and the mean are re-estimated at each origin. An origin whose fit fails is skipped with a warning. The forecast beyond the data starts after the last test curve, or after the last validation curve when there is no test sample.

References

Gibbs, I. and Candes, E. J. (2021). Adaptive conformal inference under distribution shift. Advances in Neural Information Processing Systems.

Angelopoulos, A. N., Candes, E. J. and Tibshirani, R. J. (2023). Conformal PID control for time series prediction. Advances in Neural Information Processing Systems.

Wang, X. and Hyndman, R. J. (2024). Online conformal inference for multi-step time series forecasting. arXiv:2410.13115.

Wang, X. and Girolimetto, D. (2026). conformalForecast: an R package for sequential conformal prediction in time series. arXiv:2610.21648.

Bracher, J., Ray, E. L., Gneiting, T. and Reich, N. G. (2021). Evaluating epidemic forecasts in an interval format. PLOS Computational Biology.

Examples

sim = sim_farfima(n = 200, d = 0.3, p = 1, q = 0, no_grid = 51, seed = 1)
blocks = split_curves(sim)
fit = farfima(blocks$train, blocks$valid, d = 0.3, order = c(1, 0), h = 5, trim = 30)
#> Calibrating the SR, NS, AC bands on 40 validation origins (36 at h = 5)
fc = predict(fit, test = blocks$test)
#> Evaluating on 40 test origins
fc
#> Forecasts from FARFIMA(p = 1, d = 0.3, q = 0)
#>   Horizons:  h = 1..5 after curve 200 (expanding window)
#>   Bands:     SR (scaled residual), NS (non-conformity score), AC (adaptive conformal)
#>   Levels:    80%, 95%
#> 
#> Test evaluation over 40 test curves, averaged over horizons:
#>   RMSPE = 0.8063, MAPE = 0.6193
#>  band level    ECP     CPD   MIS
#>    SR   80% 0.7798 0.04782 2.851
#>    NS   80% 0.7762 0.04989 2.853
#>    AC   80% 0.7463 0.05368 2.816
#>    SR   95% 0.9043 0.04809 4.009
#>    NS   95% 0.9040 0.04851 4.013
#>    AC   95% 0.9232 0.02679 3.753
#>   WIS: SR = 0.2780, NS = 0.2781, AC = 0.2740