Fits a principal component model to a fts object. The
function uses optimal orthonormal principal components obtained from a
principal components decomposition.
ftsm(y, order = 6, ngrid = max(500, ncol(y$y)), method = c("classical",
"M", "rapca"), mean = TRUE, level = FALSE, lambda = 3,
weight = FALSE, beta = 0.1, ...)An object of class fts.
Number of principal components to fit.
Number of grid points to use in calculations. Set to maximum of 500 and ncol(y$y).
Method to use for principal components decomposition. Possibilities are “M”, “rapca” and “classical”.
If mean = TRUE, it will estimate mean term in the model before computing basis terms.
If mean = FALSE, the mean term is assumed to be zero.
If mean = TRUE, it will include an additional (intercept) term that depends on \(t\) but not on \(x\).
Tuning parameter for robustness when method = "M".
When weight = TRUE, a set of geometrically decaying weights is applied to the decentralized data.
When weight = TRUE, the speed of geometric decay is governed by a weight parameter.
Additional arguments controlling the fitting procedure.
Object of class “ftsm” with the following components:
Time period of a fts object, which can be obtained from colnames(y$y).
Variables of a fts object, which can be obtained from y$x.
Original functional time series or sliced functional time series.
Matrix of principal components evaluated at value of y$x (one column for each principal component).
The first column is the fitted mean or median.
Matrix of principal components excluded from the selected model.
Matrix of coefficients (one column for each coefficient series). The first column is all ones.
Matrix of coefficients associated with the principal components excluded from the selected model.
An object of class fts containing the fitted values.
An object of class fts containing the regression residuals (difference between observed and fitted).
Proportion of variation explained by each principal component.
Weight associated with each time period.
Measure of variation for each time period.
Measure of standar error associated with the mean.
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.
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.
ftsmweightselect, forecast.ftsm, plot.fm, plot.ftsf, residuals.fm, summary.fm
# NOT RUN {
# 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_ERSST_region_1and2, order = 6, method = "classical", weight = FALSE)
# When weight = TRUE, geometrically decaying weights are used.
ftsm(y = ElNino_ERSST_region_1and2, order = 6, method = "classical", weight = TRUE)
# }
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