ftsa (version 4.4)

ftsm: Fit functional time series model

Description

Fits a principal component model to a fts object. The function uses optimal orthonormal principal components obtained from a principal components decomposition.

Usage

ftsm(y, order = 6, ngrid = max(500, ncol(y$y)), method = c("classical", 
 "M", "rapca"), mean = TRUE, level = FALSE, lambda = 3, 
  weight = FALSE, beta = 0.1, ...)

Value

Object of class ftsm with the following components:x1Time period of a fts object, which can be obtained from colnames(y$y).y1Variables of a fts object, which can be obtained from y$x.yOriginal functional time series or sliced functional time series.basisMatrix of principal components evaluated at value of y$x (one column for each principal component). The first column is the fitted mean or median.basis2Matrix of principal components excluded from the selected model.coeffsMatrix of coefficients (one column for each coefficient series). The first column is all ones.coeff2Matrix of coefficients associated with the principal components excluded from the selected model.fittedAn object of class fts containing the fitted values.residualsAn object of class fts containing the regression residuals (difference between observed and fitted).varpropProportion of variation explained by each principal component.wtWeight associated with each time period.vMeasure of variation for each time period.mean.seMeasure of standar error associated with the mean.

Details

If method = "classical", then standard functional principal component decomposition is used, as described by Ramsay and Dalzell (1991). If method = "rapca", then the robust principal component algorithm of Hubert, Rousseeuw and Verboven (2002) is used. If method = "M", then the hybrid algorithm of Hyndman and Ullah (2005) is used.

References

J. O. Ramsay and C. J. Dalzell (1991) "Some tools for functional data analysis (with discussion)", Journal of the Royal Statistical Society: Series B, 53(3), 539-572. M. Hubert and P. J. Rousseeuw and S. Verboven (2002) "A fast robust method for principal components with applications to chemometrics", Chemometrics and Intelligent Laboratory Systems, 60(1-2), 101-111. 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

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

Examples

# ElNino is an object of class sliced functional time series, constructed 
# from a univariate time series. 
# By default, all observations are assigned with equal weighting. 	
ftsm(y = ElNino, order = 6, method = "classical", weight = FALSE)
# When weight = TRUE, geometrically decaying weights are used.
ftsm(y = ElNino, order = 6, method = "classical", weight = TRUE)