ftsa (version 6.4)

One_way_Residuals: Functional time series decomposition into deterministic (from functional median polish of Sun and Genton (2012)), and functional residual components.

Description

Decomposition of functional time series into deterministic (from functional median polish), and functional residuals

Usage

One_way_Residuals(Y, n_prefectures = 51, year = 1959:2020, age = 0:100)

Value

A matrix of dimension n by p.

Arguments

Y

The multivariate functional data, which are a matrix with dimension n by 2p, where n is the sample size and p is the dimensionality.

n_prefectures

Number of prefectures.

year

Vector with the years considered in each population.

age

Vector with the ages considered in each year.

Author

Cristian Felipe Jimenez Varon, Ying Sun, Han Lin Shang

References

C. F. Jimenez Varon, Y. Sun and H. L. Shang (2023) ``Forecasting high-dimensional functional time series: Application to sub-national age-specific mortality", arXiv. \ Y. Sun and M. G. Genton (2012) ``Functional median polish", Journal of Agricultural, Biological, and Environmental Statistics, 17(3), 354-376.

See Also

One_way_median_polish

Examples

# The US mortality data  1959-2020, for one populations (female) 
# and 3 states (New York, California, Illinois)
# first define the parameters and the row  partitions.
# Define some parameters.
year = 1959:2020
age = 0:100
n_prefectures = 3

#Load the US data. Make sure it is a matrix. 
Y <- all_hmd_female_data
# The results
# Compute the functional residuals. 
FMP_residuals <- One_way_Residuals(Y, n_prefectures=3, year=1959:2020, age=0:100)