ftsa (version 4.4)

forecast.ftsm: 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

## S3 method for class 'ftsm':
forecast(object, h = 10, method = c("ets", "arima", "ar", "ets.na", 
 "rwdrift", "rw", "struct", "arfima"), level = 80, jumpchoice = c("fit", 
  "actual"), pimethod = c("parametric", "nonparametric"), B = 100, 
   usedata = nrow(object$coeff), adjust = TRUE, model = NULL,
    damped = NULL, stationary = FALSE, ...)

Value

List with the following components:meanAn object of class fts containing point forecasts.lowerAn object of class fts containing lower bound for prediction intervals.upperAn object of class fts containing upper bound for prediction intervals.fittedAn object of class fts of one-step-ahead forecasts for historical data.errorAn object of class fts of one-step-ahead errors for historical data.coeffList of objects of type forecast containing the coefficients and their forecasts.coeff.errorOne-step-ahead forecast errors for each of the coefficients.varList containing the various components of variance: model, error, mean, total and coeff.modelFitted ftsm model.bootsampAn array of $dimension = c(p, B, h)$ containing the bootstrapped point forecasts. $p$ is the number of variables. $B$ is the number of bootstrap samples. $h$ is the forecast horizon.

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.

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.

H. L. Shang (2012) "Functional time series approach for forecasting very short-term electricity demand", Journal of Applied Statistics, in press.

See Also

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

Examples

# ElNino is an object of class sliced functional time series.
# Via functional principal component decomposition, the dynamic was captured 
# by a few principal components and principal component scores. 
# By using an exponential smoothing method, 
# the principal component scores are forecasted.
# The forecasted curves are constructed by forecasted principal components 
# times fixed principal components plus the mean function.	
forecast(object = ftsm(ElNino), h = 10, method = "ets")              
forecast(object = ftsm(ElNino, weight = TRUE))