| Title: | High-Dimensional Functional Time Series Analysis |
|---|---|
| Description: | Offers methods for visualizing, modelling, and forecasting high-dimensional functional time series, also known as functional panel data. Documentation about 'hdftsa' is provided via the paper by Cristian F. Jimenez-Varon, Ying Sun and Han Lin Shang (2024, <doi:10.1080/10618600.2024.2319166>). |
| Authors: | Han Lin Shang [aut, cre]
|
| Maintainer: | Han Lin Shang <[email protected]> |
| License: | GPL-3 |
| Version: | 1.0 |
| Built: | 2025-01-24 14:58:49 UTC |
| Source: | CRAN |
Offers methods for visualizing, modelling, and forecasting high-dimensional functional time series, also known as functional panel data. Documentation about 'hdftsa' is provided via the paper by Cristian F. Jimenez-Varon, Ying Sun and Han Lin Shang (2024, <doi:10.1080/10618600.2024.2319166>).
Han Lin Shang [aut, cre] (<https://orcid.org/0000-0003-1769-6430>)
Maintainer: Han Lin Shang <[email protected]>
C. F. Jimenez-Varon, Y. Sun and H. L. Shang (2024) Forecasting high-dimensional functional time series: Application to sub-national age-specific mortality, Journal of Computational and Graphical Statistics, 33(4), 1160-1174.
C. F. Jimenez-Varon, Y. Sun and H. L. Shang (2024) Forecasting density-valued functional panel data, Australian and New Zealand Journal of Statistics, under minor revision.
Decomposition by functional analysis of variance fitted by means.
FANOVA(data_pop1, data_pop2, year=1959:2020, age= 0:100, n_prefectures=51, n_populations=2)FANOVA(data_pop1, data_pop2, year=1959:2020, age= 0:100, n_prefectures=51, n_populations=2)
data_pop1 |
It's a p by n matrix |
data_pop2 |
It's 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. |
FGE_mean |
FGE_mean, a vector of dimension p |
FRE_mean |
FRE_mean, a matrix of dimension length(row_partition_index) by p. |
FCE_mean |
FCE_mean, a matrix of dimension length(column_partition_index) by p. |
Cristian Felipe Jimenez Varon, Ying Sun, Han Lin Shang
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
# 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 <- FANOVA(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) ##1. The funcional grand effect FGE = FANOVA_means$FGE_mean ##2. The funcional row effect FRE = FANOVA_means$FRE_mean ##3. The funcional column effect FCE = FANOVA_means$FCE_mean# The US mortality data 1959-2020 for two populations and three states # (New York, California, Illinois) # Compute the functional Anova decomposition fitted by means. FANOVA_means <- FANOVA(data_pop1 = t(all_hmd_male_data), data_pop2 = t(all_hmd_female_data), year = 1959:2020, age = 0:100, n_prefectures = 3, n_populations = 2) ##1. The funcional grand effect FGE = FANOVA_means$FGE_mean ##2. The funcional row effect FRE = FANOVA_means$FRE_mean ##3. The funcional column effect FCE = FANOVA_means$FCE_mean
Decomposition by one-way functional median polish.
One_way_median_polish(Y, n_prefectures=51, year=1959:2020, age=0:100)One_way_median_polish(Y, n_prefectures=51, year=1959:2020, age=0:100)
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. |
year |
Vector with the years considered in each population. |
n_prefectures |
Number of prefectures. |
age |
Vector with the ages considered in each year. |
grand_effect |
Grand_effect, a vector of dimension p. |
row_effect |
Row_effect, a matrix of dimension length(row_partition_index) by p. |
Cristian Felipe Jimenez Varon, Ying Sun, Han Lin Shang
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. \ Sun, Ying, and Marc G. Genton (2012) “Functional Median Polish", Journal of Agricultural, Biological, and Environmental Statistics 17(3), 354-376.
One_way_Residuals, Two_way_median_polish, Two_way_Residuals
# 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 # Compute the functional median polish decomposition. FMP <- One_way_median_polish(Y,n_prefectures=3,year=1959:2020,age=0:100) # The results ##1. The funcional grand effect FGE <- FMP$grand_effect ##2. The funcional row effect FRE <- FMP$row_effect# 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 # Compute the functional median polish decomposition. FMP <- One_way_median_polish(Y,n_prefectures=3,year=1959:2020,age=0:100) # The results ##1. The funcional grand effect FGE <- FMP$grand_effect ##2. The funcional row effect FRE <- FMP$row_effect
Decomposition of functional time series into deterministic (from functional median polish), and functional residuals
One_way_Residuals(Y, n_prefectures = 51, year = 1959:2020, age = 0:100)One_way_Residuals(Y, n_prefectures = 51, year = 1959:2020, age = 0:100)
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. |
A matrix of dimension n by p.
Cristian Felipe Jimenez Varon, Ying Sun, Han Lin Shang
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.
# 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)# 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)
Decomposition by two-way functional median polish
Two_way_median_polish(Y, year=1959:2020, age=0:100, n_prefectures=51, n_populations=2)Two_way_median_polish(Y, year=1959:2020, age=0:100, n_prefectures=51, n_populations=2)
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. |
grand_effect |
grand_effect, a vector of dimension p |
row_effect |
row_effect, a matrix of dimension length(row_partition_index) by p. |
col_effect |
col_effect, a matrix of dimension length(column_partition_index) by p |
Cristian Felipe Jimenez Varon, Ying Sun, Han Lin Shang
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.
# The US mortality data 1959-2020 for two populations and three states # (New York, California, Illinois) # Compute the functional median polish decomposition. FMP = Two_way_median_polish(cbind(all_hmd_male_data, all_hmd_female_data), n_prefectures = 3, year = 1959:2020, age = 0:100, n_populations = 2) ##1. The functional grand effect FGE = FMP$grand_effect ##2. The functional row effect FRE = FMP$row_effect ##3. The functional column effect FCE = FMP$col_effect# The US mortality data 1959-2020 for two populations and three states # (New York, California, Illinois) # Compute the functional median polish decomposition. FMP = Two_way_median_polish(cbind(all_hmd_male_data, all_hmd_female_data), n_prefectures = 3, year = 1959:2020, age = 0:100, n_populations = 2) ##1. The functional grand effect FGE = FMP$grand_effect ##2. The functional row effect FRE = FMP$row_effect ##3. The functional column effect FCE = FMP$col_effect
Decomposition of functional time series into deterministic (from functional median polish), and time-varying components (functional residuals)
Two_way_Residuals(Y, n_prefectures, year, age, n_populations)Two_way_Residuals(Y, n_prefectures, year, age, n_populations)
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 |
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 |
Cristian Felipe Jimenez Varon, Ying Sun, Han Lin Shang
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.
# 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$Fixed_comp# The US mortality data 1959-2020, for two populations # and three states (New York, California, Illinois) # Column binds the data from both populations Y = cbind(all_hmd_male_data, all_hmd_female_data) # Decompose FTS into deterministic (from functional median polish) # and time-varying components (functional residuals). FMP_residuals <- Two_way_Residuals(Y,n_prefectures=3,year=1959:2020, age=0:100,n_populations=2) # The results ##1. The functional residuals from population 1 Residuals_pop_1=FMP_residuals$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
Decomposition of functional time series into deterministic (by functional analysis of variance fitted by means), and time-varying components (functional residuals)
Two_way_Residuals_means(data_pop1, data_pop2, year, age, n_prefectures, n_populations)Two_way_Residuals_means(data_pop1, data_pop2, year, age, n_prefectures, n_populations)
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. |
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. |
Cristian Felipe Jimenez Varon, Ying Sun, Han Lin Shang
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.
# 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$Fixed_comp# The US mortality data 1959-2020, for two populations # and three states (New York, California, Illinois) # Compute the functional Anova decomposition fitted by means. FANOVA_means_residuals <- Two_way_Residuals_means(data_pop1=t(all_hmd_male_data), data_pop2=t(all_hmd_female_data), year = 1959:2020, age = 0:100, n_prefectures = 3, n_populations = 2) # The results ##1. The functional residuals from population 1 Residuals_pop_1=FANOVA_means_residuals$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