Two_way_Residuals {ftsa}

Functional time series decomposition into deterministic (from functional median polish from Sun and Genton (2012)), and time-varying components (functional residuals).

Description

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

Usage

Two_way_Residuals(Y, n_prefectures, year, age, n_populations)

Arguments

Y

A matrix with dimension n by 2p. The functional data

year

Vector with the years considered in each population

n_prefectures

Number of prefectures

age

Vector with the ages considered in each year

n_populations

Number of populations

Value

residuals1

A matrix with dimension n by p

residuals2

A matrix with dimension n by p

rd

A two dimension logic vector that proves that the decomposition sum up to the data

R

A matrix with the same dimension as Y. This represent the time-varying component in the decomposition

Fixed_comp

A matrix with the same dimension as Y. This represent the deterministic component in the decomposition

Author(s)

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".

Sun, Ying, and Marc G. Genton (2012). "Functional Median Polish". Journal of Agricultural, Biological, and Environmental Statistics 17(3), 354-376.

See Also

Two_way_Residuals_means

Examples

# The US mortality data  1959-2020, for two populations
# and three states (New York, California, Illinois)
# Column binds the data from both populations
Y = cbind(all_hmd_male_data, all_hmd_female_data)
# Decompose FTS into deterministic (from functional median polish)
# and time-varying components (functional residuals).
FMP_residuals <- Two_way_Residuals(Y,n_prefectures=3,year=1959:2020,
                                   age=0:100,n_populations=2)
# The results
##1. The functional residuals from population 1
Residuals_pop_1=FMP_residuals$residuals1
##2. The functional residuals from population 2
Residuals_pop_2=FMP_residuals$residuals2
##3. A logic vector whose components indicate whether the sum of deterministic
##   and time-varying components recover the original FTS.
Construct_data=FMP_residuals$rd
##4. Time-varying components for all the populations. The functional residuals
All_pop_functional_residuals <- FMP_residuals$R
##5. The deterministic components from the functional median polish decomposition
deterministic_comp <- FMP_residuals$Fixed_comp