fts object. The
function uses optimal orthonormal principal components obtained from a
principal components decomposition.
ftsm(y, order = 6, ngrid = max(500, ncol(y$y)), method = c("classical", "M", "rapca"), mean = TRUE, level = FALSE, lambda = 3, weight = FALSE, beta = 0.1, ...)fts.ncol(y$y).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.mean = TRUE, it will include an additional (intercept) term that depends on $t$ but not on $x$.method = "M".weight = TRUE, a set of geometrically decaying weights is applied to the decentralized data.weight = TRUE, the speed of geometric decay is governed by a weight parameter.fts object, which can be obtained from colnames(y$y).fts object, which can be obtained from y$x.y$x (one column for each principal component).
The first column is the fitted mean or median.fts containing the fitted values.fts containing the regression residuals (difference between observed and fitted).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.
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
# 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)
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