ftsm {ftsa} | R Documentation |
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$y)), method = c("classical", "M", "rapca"), mean = TRUE, level = FALSE, lambda = 3, weight = FALSE, beta = 0.1, ...)
y |
An object of class fts . |
order |
Number of principal components to fit. |
ngrid |
Number of grid points to use in calculations. Set to maximum of 500 and ncol(y$y) . |
method |
Method to use for principal components decomposition. Possibilities are “M”, “rapca” and “classical”. |
mean |
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. |
level |
If mean = TRUE , it will include an additional (intercept) term that depends on t but not on x. |
lambda |
Tuning parameter for robustness when method = "M" . |
weight |
When weight = TRUE , a set of geometrically decaying weights is applied to the decentralized data. |
beta |
When weight = TRUE , the speed of geometric decay is governed by a weight parameter. |
... |
Additional arguments controlling the fitting procedure. |
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.
Object of class “ftsm” with the following components:
x1 |
Time period of a fts object, which can be obtained from colnames(y$y) . |
y1 |
Variables of a fts object, which can be obtained from y$x . |
y |
Original functional time series or sliced functional time series. |
basis |
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. |
basis2 |
Matrix of principal components excluded from the selected model. |
coeffs |
Matrix of coefficients (one column for each coefficient series). The first column is all ones. |
coeff2 |
Matrix of coefficients associated with the principal components excluded from the selected model. |
fitted |
An object of class fts containing the fitted values. |
residuals |
An object of class fts containing the regression residuals (difference between observed and fitted). |
varprop |
Proportion of variation explained by each principal component. |
wt |
Weight associated with each time period. |
v |
Measure of variation for each time period. |
mean.se |
Measure of standar error associated with the mean. |
Rob J Hyndman
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.
forecast.ftsm
, plot.fm
, plot.ftsf
, residuals.fm
, summary.fm
ftsm(y = ElNino) ftsm(y = ElNino, weight = TRUE)