ftsmiterativeforecasts: Forecast functional time series

In ftsa: Functional Time Series Analysis

Forecast functional time series

Description

The coefficients from the fitted object are forecasted using either an ARIMA model (method = "arima"), an AR model (method = "ar"), an exponential smoothing method (method = "ets"), a linear exponential smoothing method allowing missing values (method = "ets.na"), or a random walk with drift model (method = "rwdrift"). The forecast coefficients are then multiplied by the principal components to obtain a forecast curve.

Usage

ftsmiterativeforecasts(object, components, iteration = 20)

Arguments

object	An object of class fts.
components	Number of principal components.
iteration	Number of iterative one-step-ahead forecasts.

Details

1. Obtain a smooth curve f_t(x) for each t using a nonparametric smoothing technique.

2. Decompose the smooth curves via a functional principal component analysis.

3. Fit a univariate time series model to each of the principal component scores.

4. Forecast the principal component scores using the fitted time series models.

5. Multiply the forecast principal component scores by fixed principal components to obtain forecasts of f_{n+h}(x).

6. The estimated variances of the error terms (smoothing error and model residual error) are used to compute prediction intervals for the forecasts.

Value

List with the following components:

mean	An object of class fts containing point forecasts.
lower	An object of class fts containing lower bound for prediction intervals.
upper	An object of class fts containing upper bound for prediction intervals.
fitted	An object of class fts of one-step-ahead forecasts for historical data.
error	An object of class fts of one-step-ahead errors for historical data.
coeff	List of objects of type forecast containing the coefficients and their forecasts.
coeff.error	One-step-ahead forecast errors for each of the coefficients.
var	List containing the various components of variance: model, error, mean, total and coeff.
model	Fitted ftsm model.
bootsamp	An array of dim = c(p, B, h) containing the bootstrapped point forecasts. p is the number of variables. B is the number of bootstrap samples. h is the forecast horizon.

Author(s)

Han Lin Shang

References

H. Booth and R. J. Hyndman and L. Tickle and P. D. Jong (2006) "Lee-Carter mortality forecasting: A multi-country comparison of variants and extensions", Demographic Research, 15, 289-310.

B. Erbas and R. J. Hyndman and D. M. Gertig (2007) "Forecasting age-specific breast cancer mortality using functional data model", Statistics in Medicine, 26(2), 458-470.

R. J. Hyndman and M. S. Ullah (2007) "Robust forecasting of mortality and fertility rates: A functional data approach", Computational Statistics and Data Analysis, 51(10), 4942-4956.

R. J. Hyndman and H. Booth (2008) "Stochastic population forecasts using functional data models for mortality, fertility and migration", International Journal of Forecasting, 24(3), 323-342.

R. J. Hyndman and H. L. Shang (2009) "Forecasting functional time series" (with discussion), Journal of the Korean Statistical Society, 38(3), 199-221.

See Also

ftsm, plot.ftsf, plot.fm, residuals.fm, summary.fm

Examples

# Iterative one-step-ahead forecasts via functional principal component analysis.	
ftsmiterativeforecasts(object = Australiasmoothfertility, components = 2, iteration = 5)

ftsa documentation built on May 29, 2024, 2:47 a.m.