ftsa: ftsm – R documentation

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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, ...)

Arguments

`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.

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.

Value

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.
`coeff`	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.

Author(s)

Rob J Hyndman

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.

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_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)

ftsa

Functional Time Series Analysis

v6.0

GPL-3

Authors

Rob Hyndman [aut] (<https://orcid.org/0000-0002-2140-5352>), Han Lin Shang [aut, cre, cph] (<https://orcid.org/0000-0003-1769-6430>)

Initial release

2020-11-29