Two_way_Residuals_means {ftsa}

Functional time series decomposition into deterministic (functional analysis of variance fitted by means), and time-varying components (functional residuals).

Description

Decomposition of functional time series into deterministic (by functional analysis of variance fitted by means), and time-varying components (functional residuals)

Usage

Two_way_Residuals_means(data_pop1, data_pop2, year, age, n_prefectures, n_populations)

Arguments

data_pop1

A p by n matrix

data_pop2

A p by n matrix

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 proving that the decomposition sum up the data.

R

A matrix of dimension as n by 2p. This represents the time-varying component in the decomposition.

Fixed_comp

A matrix of dimension as n by 2p. This represents 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".

Ramsay, J. and B. Silverman (2006). Functional Data Analysis. Springer Series in Statistics. Chapter 13. New York: Springer.

See Also

Two_way_Residuals

Examples

# The US mortality data  1959-2020, for two populations
# and three states (New York, California, Illinois)
# Compute the functional Anova decomposition fitted by means.
FANOVA_means_residuals <- Two_way_Residuals_means(data_pop1=t(all_hmd_male_data),
                            data_pop2=t(all_hmd_female_data), year = 1959:2020,
                            age = 0:100, n_prefectures = 3, n_populations = 2)
                            
# The results
##1. The functional residuals from population 1
Residuals_pop_1=FANOVA_means_residuals$residuals1
##2. The functional residuals from population 2
Residuals_pop_2=FANOVA_means_residuals$residuals2
##3. A logic vector whose components indicate whether the sum of deterministic
##  and time-varying components recover the original FTS.
Construct_data=FANOVA_means_residuals$rd
##4. Time-varying components for all the populations. The functional residuals
All_pop_functional_residuals <- FANOVA_means_residuals$R
##5. The deterministic components from the functional ANOVA decomposition
deterministic_comp <- FANOVA_means_residuals$Fixed_comp