Package 'GCCfactor' reference manual

Title:	GCC Estimation of the Multilevel Factor Model
Description:	Provides methods for model selection, estimation, bootstrap inference, and simulation for the multilevel factor model, based on the principal component estimation and generalised canonical correlation approach. Details can be found in "Generalised Canonical Correlation Estimation of the Multilevel Factor Model." Lin and Shin (2023) <doi:10.2139/ssrn.4295429>.
Authors:	Rui Lin [aut, cre], Yongcheol Shin [aut]
Maintainer:	Rui Lin <[email protected]>
License:	GPL (>= 3)
Version:	1.0.1
Built:	2024-11-23 03:01:45 UTC
Source:	https://github.com/cran/GCCfactor

Get an asymptotic confidence interval for the local component

Description

This function computes the asymptotic confidence intervals for the local loadings for the $j$ -th individual in block $i$ . See Lin and Shin (2023) for details.

Usage

AsymCI_local_loading(object, i, j, alpha = 0.05)
AsymCI_local_loading(object, i, j, alpha = 0.05)

Arguments

`object`	An S3 object of class 'multi_result' created by multilevel().
`i`	An integer indicating the $i$ -th block.
`j`	An integer indicating the $j$ -th individual in the $i$ -th block.
`alpha`	The significance level, a single numeric between 0 and 1. 0.05 by default.

Value

A matrix containing the upper and lower band.

References

Lin, R. and Shin, Y., 2022. Generalised Canonical Correlation Estimation of the Multilevel Factor Model. Available at SSRN 4295429.

Examples


panel <- UKhouse # load the data
est_multi <- multilevel(panel, ic = "BIC3", standarise = TRUE, r_max = 5,
                           depvar_header = "dlPrice", i_header = "Region",
                           j_header = "LPA_Type", t_header = "Date")
bs_local_loading_11 <- AsymCI_local_loading(est_multi, i = 1, j = 1)

panel <- UKhouse # load the data
est_multi <- multilevel(panel, ic = "BIC3", standarise = TRUE, r_max = 5,
                           depvar_header = "dlPrice", i_header = "Region",
                           j_header = "LPA_Type", t_header = "Date")
bs_local_loading_11 <- AsymCI_local_loading(est_multi, i = 1, j = 1)

Bartlett kernel function

Description

Evaluate the Bartlett kernel function: $Bartlett(x)=1-|x|$ if $|x|\leq 1$ and $Bartlett(x)=1-|x|$ otherwise.

Usage

Bartlett(x)
Bartlett(x)

Arguments

`x`	A single numeric.

Value

A single numeric between 0 and 1.

Examples


Bartlett(0.5)

Bartlett(0.5)

Get a bootstrap confidence interval for the global component

Description

This function employs a bootstrap procedure to obtain confidence intervals for the global component for the $j$ -th individual in block $i$ at time $t$ . See Lin and Shin (2023) for details.

Usage

BS_global_comp(object, i, j, t, BB = 599, alpha = 0.05)
BS_global_comp(object, i, j, t, BB = 599, alpha = 0.05)

Arguments

`object`	An S3 object of class 'multi_result' created by multilevel().
`i`	An integer indicating the $i$ -th block.
`j`	An integer indicating the $j$ -th individual in the $i$ -th block.
`t`	An integer specifying the time point at which the CI is constructed.
`BB`	An integer indicating the number of bootstrap repetition. 599 by default.
`alpha`	The significance level, a single numeric between 0 and 1. 0.05 by default.

Value

A matrix containing the upper and lower band.

References

Lin, R. and Shin, Y., 2022. Generalised Canonical Correlation Estimation of the Multilevel Factor Model. Available at SSRN 4295429.

Examples


panel <- UKhouse # load the data
est_multi <- multilevel(panel, ic = "BIC3", standarise = TRUE, r_max = 5,
                           depvar_header = "dlPrice", i_header = "Region",
                           j_header = "LPA_Type", t_header = "Date")
bs_gcomp_111 <- BS_global_comp(est_multi, i = 1, j = 1, t = 1)

panel <- UKhouse # load the data
est_multi <- multilevel(panel, ic = "BIC3", standarise = TRUE, r_max = 5,
                           depvar_header = "dlPrice", i_header = "Region",
                           j_header = "LPA_Type", t_header = "Date")
bs_gcomp_111 <- BS_global_comp(est_multi, i = 1, j = 1, t = 1)

Get bootstrap confidence intervals for the global factors

Description

This function employs a bootstrap procedure to obtain confidence intervals for the global factors at time $t$ .

Usage

BS_global_factor(object, t, BB = 599, alpha = 0.05)
BS_global_factor(object, t, BB = 599, alpha = 0.05)

Arguments

`object`	An S3 object of class 'multi_result' created by multilevel().
`t`	An integer specifying the time point at which the CI is constructed.
`BB`	An integer indicating the number of bootstrap repetition. 599 by default.
`alpha`	The significance level, a single numeric between 0 and 1. 0.05 by default.

Value

A matrix containing the upper and lower band.

Examples



panel <- UKhouse # load the data
est_multi <- multilevel(panel, ic = "BIC3", standarise = TRUE, r_max = 5,
                           depvar_header = "dlPrice", i_header = "Region",
                           j_header = "LPA_Type", t_header = "Date")
bs_global_mid <- BS_global_factor(est_multi, t = est_multi$T / 2)

panel <- UKhouse # load the data
est_multi <- multilevel(panel, ic = "BIC3", standarise = TRUE, r_max = 5,
                           depvar_header = "dlPrice", i_header = "Region",
                           j_header = "LPA_Type", t_header = "Date")
bs_global_mid <- BS_global_factor(est_multi, t = est_multi$T / 2)

Get a bootstrap confidence interval for the global factor loadings

Description

This function employs a bootstrap procedure to obtain confidence intervals for the global factor loadings for the $j$ -th individual in block $i$ . See Lin and Shin (2023) for details.

Usage

BS_global_loading(object, i, j, BB = 599, alpha = 0.05)
BS_global_loading(object, i, j, BB = 599, alpha = 0.05)

Arguments

`object`	An S3 object of class 'multi_result' created by [multilevel()].
`i`	An integer indicating the $i$ -th block.
`j`	An integer indicating the $j$ -th individual in the $i$ -th block.
`BB`	An integer indicating the number of bootstrap repetition. 599 by default.
`alpha`	The significance level, a single numeric between 0 and 1. 0.05 by default.

Value

A matrix containing the upper and lower band.

References

Lin, R. and Shin, Y., 2022. Generalised Canonical Correlation Estimation of the Multilevel Factor Model. Available at SSRN 4295429.

Examples



panel <- UKhouse # load the data
est_multi <- multilevel(panel, ic = "BIC3", standarise = TRUE, r_max = 5,
                           depvar_header = "dlPrice", i_header = "Region",
                           j_header = "LPA_Type", t_header = "Date")
bs_gamma_11 <- BS_global_loading(est_multi, i = 1, j = 1)

panel <- UKhouse # load the data
est_multi <- multilevel(panel, ic = "BIC3", standarise = TRUE, r_max = 5,
                           depvar_header = "dlPrice", i_header = "Region",
                           j_header = "LPA_Type", t_header = "Date")
bs_gamma_11 <- BS_global_loading(est_multi, i = 1, j = 1)

Get a bootstrap confidence interval for the global component

Description

This function employs a bootstrap procedure to obtain confidence intervals for the local component for the $j$ -th individual in block $i$ at time $t$ . See Lin and Shin (2023) for details.

Usage

BS_local_comp(object, i, j, t, BB = 599, alpha = 0.05)
BS_local_comp(object, i, j, t, BB = 599, alpha = 0.05)

Arguments

`object`	An S3 object of class 'multi_result' created by multilevel().
`i`	An integer indicating the $i$ -th block.
`j`	An integer indicating the $j$ -th individual in the $i$ -th block.
`t`	An integer specifying the time point at which the CI is constructed.
`BB`	An integer indicating the number of bootstrap repetition. 599 by default.
`alpha`	The significance level, a single numeric between 0 and 1. 0.05 by default.

Value

A matrix containing the upper and lower band.

References

Lin, R. and Shin, Y., 2022. Generalised Canonical Correlation Estimation of the Multilevel Factor Model. Available at SSRN 4295429.

Examples


panel <- UKhouse # load the data
est_multi <- multilevel(panel, ic = "BIC3", standarise = TRUE, r_max = 5,
                           depvar_header = "dlPrice", i_header = "Region",
                           j_header = "LPA_Type", t_header = "Date")
bs_fcomp_111 <- BS_local_comp(est_multi, i = 1, j = 1, t = 1)

panel <- UKhouse # load the data
est_multi <- multilevel(panel, ic = "BIC3", standarise = TRUE, r_max = 5,
                           depvar_header = "dlPrice", i_header = "Region",
                           j_header = "LPA_Type", t_header = "Date")
bs_fcomp_111 <- BS_local_comp(est_multi, i = 1, j = 1, t = 1)

Get a bootstrap confidence interval for the local factors

Description

This function employs a bootstrap procedure to obtain confidence intervals for the local factors in block $i$ at time $t$ . See Lin and Shin (2023) for details.

Usage

BS_local_factor(object, i, t, BB = 599, alpha = 0.05)
BS_local_factor(object, i, t, BB = 599, alpha = 0.05)

Arguments

`object`	An S3 object of class 'multi_result' created by multilevel().
`i`	An integer indicating the $i$ -th block.
`t`	An integer specifying the time point at which the CI is constructed.
`BB`	An integer indicating the number of bootstrap repetition. 599 by default.
`alpha`	The significance level, a single numeric between 0 and 1. 0.05 by default.

Value

A matrix containing the upper and lower band.

References

Lin, R. and Shin, Y., 2022. Generalised Canonical Correlation Estimation of the Multilevel Factor Model. Available at SSRN 4295429.

Examples


panel <- UKhouse # load the data
est_multi <- multilevel(panel, ic = "BIC3", standarise = TRUE, r_max = 5,
                           depvar_header = "dlPrice", i_header = "Region",
                           j_header = "LPA_Type", t_header = "Date")
bs_local_factor_11 <- BS_local_factor(est_multi, i = 1, t = 1)

panel <- UKhouse # load the data
est_multi <- multilevel(panel, ic = "BIC3", standarise = TRUE, r_max = 5,
                           depvar_header = "dlPrice", i_header = "Region",
                           j_header = "LPA_Type", t_header = "Date")
bs_local_factor_11 <- BS_local_factor(est_multi, i = 1, t = 1)

Check validity of the data and headers

Description

This is an internal function which checks the validity of the data and provide a list of matrices of length $R$ for estimation.

Usage

check_data(
  data,
  depvar_header = NULL,
  i_header = NULL,
  j_header = NULL,
  t_header = NULL
)
check_data(
  data,
  depvar_header = NULL,
  i_header = NULL,
  j_header = NULL,
  t_header = NULL
)

Arguments

`data`	Either a data.frame or a list of data matrices of length $R$ . See Details.
`depvar_header`	A character string specifying the header of the dependent variable. See Details.
`i_header`	A character string specifying the header of the block identifier. See Details.
`j_header`	A character string specifying the header of the individual identifier. See Details.
`t_header`	A character string specifying the header of the time identifier. See Details.

Details

See Details of GCC().

Value

A list of data matrices of length $R$ .

Examples

panel <- UKhouse # load the data
Y_list <- check_data(panel,
  depvar_header = "dlPrice", i_header = "Region",
  j_header = "LPA_Type", t_header = "Date"
)
panel <- UKhouse # load the data
Y_list <- check_data(panel,
  depvar_header = "dlPrice", i_header = "Region",
  j_header = "LPA_Type", t_header = "Date"
)

Dependent wild bootstrap for resampling time series

Description

Select an optimal bandwidth parameter and apply the dependent wild bootstrap with Bartlett kernel to obtain the resampled time series.

Usage

dwBS(y)
dwBS(y)

Arguments

`y`	A $T\times 1$ vector of time series to be resampled.

Value

A $T\times 1$ matrix of resampled time series.

References

Shao, X., 2010. The dependent wild bootstrap. Journal of the American Statistical Association, 105(489), pp.218-235.

Examples

panel <- UKhouse # load the data
est_multi <- multilevel(panel, ic = "BIC3", standarise = TRUE, r_max = 5,
                           depvar_header = "dlPrice", i_header = "Region",
                           j_header = "LPA_Type", t_header = "Date")
G_star <- dwBS(est_multi$G)
panel <- UKhouse # load the data
est_multi <- multilevel(panel, ic = "BIC3", standarise = TRUE, r_max = 5,
                           depvar_header = "dlPrice", i_header = "Region",
                           j_header = "LPA_Type", t_header = "Date")
G_star <- dwBS(est_multi$G)

Generalised canonical correlation estimation for the global factors

Description

This function is one of the main functions the package, employing the generalized canonical correlation estimation for both the global factors $\boldsymbol{G}$ and, when not explicitly provided, for the number of global factors $r_{0}$ . Typically, this function is intended for internal purposes. However, users one can opt for GCC() instead of multilevel(), if the users only need to estimate the number of global factors.

Usage

GCC(
  data,
  standarise = TRUE,
  r_max = 10,
  r0 = NULL,
  ri = NULL,
  depvar_header = NULL,
  i_header = NULL,
  j_header = NULL,
  t_header = NULL
)
GCC(
  data,
  standarise = TRUE,
  r_max = 10,
  r0 = NULL,
  ri = NULL,
  depvar_header = NULL,
  i_header = NULL,
  j_header = NULL,
  t_header = NULL
)

Arguments

`data`	Either a data.frame or a list of data matrices of length $R$ . See Details.
`standarise`	A logical indicating whether the data is standardised before estimation or not. See Details.
`r_max`	An integer indicating the maximum number of factors allowed. See Details.
`r0`	An integer of the number of global factors. See Details.
`ri`	An array of length $R$ containing the number of local factors in each block. See Details.
`depvar_header`	A character string specifying the header of the dependent variable. See Details.
`i_header`	A character string specifying the header of the block identifier. See Details.
`j_header`	A character string specifying the header of the individual identifier. See Details.
`t_header`	A character string specifying the header of the time identifier. See Details.

Details

The user-supplied data.frame should contain at least four columns, namely the dependent variable ( $y_{ijt}$ ), block identifier ( $i$ ), individual identifier ( $j$ ), and time ( $t$ ). The user needs to supply their corresponding headers in the data.frame to the function using the parameters "depvar_header", "i_header", "j_header", and "t_header", respectively. If the data is supplied as a list, these arguments will not be used.

If either r0 = NULL or ri = NULL, both of them will be estimated. In such case, "r_max" must be supplied. If "r0" and "ri" are supplied then "r_max" is not needed and will be ignored.

If standarise = TRUE, each time series will be standardised so it has zero mean and unit variance. It is recommended to standardise the data before estimation.

See Lin and Shin (2023) for more details.

Value

A list containing the estimated number of global factors $\hat{r}_{0}$ , the global factors $\widehat{\boldsymbol{G}}$ , and the other elements that are used in multilevel().

References

Lin, R. and Shin, Y., 2022. Generalised Canonical Correlation Estimation of the Multilevel Factor Model. Available at SSRN 4295429.

Examples


panel <- UKhouse # load the data
Y_list <- panel2list(panel, depvar_header = "dlPrice", i_header = "Region",
                                       j_header = "LPA_Type", t_header = "Date")
est_GCC <- GCC(Y_list, r_max = 10)
r0_hat <- est_GCC$r0 # number of global factors
G_hat <- est_GCC$G # global factors
panel <- UKhouse # load the data
Y_list <- panel2list(panel, depvar_header = "dlPrice", i_header = "Region",
                                       j_header = "LPA_Type", t_header = "Date")
est_GCC <- GCC(Y_list, r_max = 10)
r0_hat <- est_GCC$r0 # number of global factors
G_hat <- est_GCC$G # global factors

Get an optimal bandwidth using Bartlett kernel

Description

Automatic bandwidth selection of Andrews (1991) using Bartlett kernel.

Usage

get_bw(y)
get_bw(y)

Arguments

`y`	A $T\times 1$ vector of time series

Value

A numeric.

References

Andrews, D.W., 1991. Heteroskedasticity and autocorrelation consistent covariance matrix estimation. Econometrica: Journal of the Econometric Society, pp.817-858.

Examples

panel <- UKhouse # load the data
est_multi <- multilevel(panel, ic = "BIC3", standarise = TRUE, r_max = 5,
                           depvar_header = "dlPrice", i_header = "Region",
                           j_header = "LPA_Type", t_header = "Date")
lT_G <- get_bw(est_multi$G)
panel <- UKhouse # load the data
est_multi <- multilevel(panel, ic = "BIC3", standarise = TRUE, r_max = 5,
                           depvar_header = "dlPrice", i_header = "Region",
                           j_header = "LPA_Type", t_header = "Date")
lT_G <- get_bw(est_multi$G)

Selection criteria for the approximate factor model

Description

This function performs model selection for the (2D) approximate factor model and returns the estimated number of factors.

Usage

infocrit(Y, method, r_max = 10)
infocrit(Y, method, r_max = 10)

Arguments

`Y`	A $T \times N$ data matrix. T = number of time series observations, N = cross-sectional dimension.
`method`	A character string indicating which criteria to use.
`r_max`	An integer indicating the maximum number of factors allowed. 10 by default.

Details

"method" can be one of the following: "ICp2" and "BIC3" by Bai and Ng (2002), "ER" by Ahn and Horenstein (2013), "ED" by Onatski (2010).

Value

The estimated number of factors.

References

Bai, J. and Ng, S., 2002. Determining the number of factors in approximate factor models. Econometrica, 70(1), pp.191-221.

Ahn, S.C. and Horenstein, A.R., 2013. Eigenvalue ratio test for the number of factors. Econometrica, 81(3), pp.1203-1227.

Onatski, A., 2010. Determining the number of factors from empirical distribution of eigenvalues. The Review of Economics and Statistics, 92(4), pp.1004-1016.

Examples

# simulate data

T <- 100
N <- 50
r <- 2
F <- matrix(stats::rnorm(T * r, 0, 1), nrow = T)
Lambda <- matrix(stats::rnorm(N * r, 0, 1), nrow = N)
err <- matrix(stats::rnorm(T * N, 0, 1), nrow = T)
Y <- F %*% t(Lambda) + err

# estimation

r_hat <- infocrit(Y, "BIC3", r_max = 10)
# simulate data

T <- 100
N <- 50
r <- 2
F <- matrix(stats::rnorm(T * r, 0, 1), nrow = T)
Lambda <- matrix(stats::rnorm(N * r, 0, 1), nrow = N)
err <- matrix(stats::rnorm(T * N, 0, 1), nrow = T)
Y <- F %*% t(Lambda) + err

# estimation

r_hat <- infocrit(Y, "BIC3", r_max = 10)

Full estimation of the multilevel factor model

Description

This is one of the main functions of this package which performs full estimation of the multilevel factor model.

Usage

multilevel(
  data,
  ic = "BIC3",
  standarise = TRUE,
  r_max = 10,
  r0 = NULL,
  ri = NULL,
  depvar_header = NULL,
  i_header = NULL,
  j_header = NULL,
  t_header = NULL
)
multilevel(
  data,
  ic = "BIC3",
  standarise = TRUE,
  r_max = 10,
  r0 = NULL,
  ri = NULL,
  depvar_header = NULL,
  i_header = NULL,
  j_header = NULL,
  t_header = NULL
)

Arguments

`data`	Either a data.frame or a list of data matrices of length $R$ . See Details.
`ic`	A character string of selection criteria to use for estimation of the numbers of local factors. See Details.
`standarise`	A logical indicating whether the data is standardised before estimation or not. See Details.
`r_max`	An integer indicating the maximum number of factors allowed. See Details.
`r0`	An integer of the number of global factors. See Details.
`ri`	An array of length $R$ containing the number of local factors in each block. See Details.
`depvar_header`	A character string specifying the header of the dependent variable. See Details.
`i_header`	A character string specifying the header of the block identifier. See Details.
`j_header`	A character string specifying the header of the individual identifier. See Details.
`t_header`	A character string specifying the header of the time identifier. See Details.

Details

If either r0 = NULL or ri = NULL, then both of them will be estimated. In such case, "r_max" must be supplied. If "r0" and "ri" are supplied then "r_max" is not needed and will be ignored.

If standarise = TRUE, each time series will be standardised so it has zero mean and unit variance. It is recommended to standardise the data before estimation.

See Lin and Shin (2023) for more details.

Value

The return value is an S3 object of class "multi_result". It contains a list of the following items:

G = A matrix of the estimated global factors.
Gamma = A list of length $R$ containing matrices of the estimated global loading matrices for each block.
F = A list of length $R$ containing matrices of the estimated local factors for each block.
Lambda = A list of length $R$ containing matrices of the estimated global loading matrices for each block.
N = The total number of cross-sections in the panel.
Ni = An array of length $R$ containing the number of cross-sections in each block.
r0 = The number of global factors. Unchanged if pre-specified.
ri = An array of length $R$ containing the number of local factors for each block. Unchanged if pre-specified.
d = An array of length $R$ containing the maximum total number of factors allowed for each block. The elements are identically equal to r_max if either r0 or ri is supplied as NULL.
Resid = A list of length $R$ containing the residual matrices for each block.
delta2 = An array of the mock and the $r_{\max} + 1$ largest squared singular values.
ic = Selection criteria used for estimating the numbers of local factors.
block_names = A array of block names.

References

Lin, R. and Shin, Y., 2022. Generalised Canonical Correlation Estimation of the Multilevel Factor Model. Available at SSRN 4295429.

Examples


panel <- UKhouse # load the data

# use data.frame
est_multi <- multilevel(panel, ic = "BIC3", standarise = TRUE, r_max = 5,
                           depvar_header = "dlPrice", i_header = "Region",
                           j_header = "LPA_Type", t_header = "Date")
# or one can use a list of data matrices
Y_list <- panel2list(panel, depvar_header = "dlPrice", i_header = "Region",
                                       j_header = "LPA_Type", t_header = "Date")
est_multi <- multilevel(Y_list, ic = "BIC3", standarise = TRUE, r_max = 5)
panel <- UKhouse # load the data

# use data.frame
est_multi <- multilevel(panel, ic = "BIC3", standarise = TRUE, r_max = 5,
                           depvar_header = "dlPrice", i_header = "Region",
                           j_header = "LPA_Type", t_header = "Date")
# or one can use a list of data matrices
Y_list <- panel2list(panel, depvar_header = "dlPrice", i_header = "Region",
                                       j_header = "LPA_Type", t_header = "Date")
est_multi <- multilevel(Y_list, ic = "BIC3", standarise = TRUE, r_max = 5)

data.frame to list of data matrices

Description

This function converts the data.frame to a list of data matrices and finds the dimensions of the multilevel panel.

Usage

panel2list(
  panel,
  depvar_header = NULL,
  i_header = NULL,
  j_header = NULL,
  t_header = NULL
)
panel2list(
  panel,
  depvar_header = NULL,
  i_header = NULL,
  j_header = NULL,
  t_header = NULL
)

Arguments

`panel`	The user-supplied data frame for the multilevel panel data. See Details.
`depvar_header`	A character string specifying the header of the dependent variable. See Details.
`i_header`	A character string specifying the header of the block identifier. See Details.
`j_header`	A character string specifying the header of the individual identifier. See Details.
`t_header`	A character string specifying the header of the time identifier. See Details.

Details

See the details of GCC().

Value

A list containing the data matrices of the $R$ blocks. Each of them has dimension $T\times N_{i}$ .

Examples


panel <- UKhouse # load the data

# panel$Region identifies different blocks i=1,...,R.
# panel$LPA_Type identifies different individuals j=1,...,N_i.

Y_list<- panel2list(panel, depvar_header = "dlPrice", i_header = "Region",
                                       j_header = "LPA_Type", t_header = "Date")

panel <- UKhouse # load the data

# panel$Region identifies different blocks i=1,...,R.
# panel$LPA_Type identifies different individuals j=1,...,N_i.

Y_list<- panel2list(panel, depvar_header = "dlPrice", i_header = "Region",
                                       j_header = "LPA_Type", t_header = "Date")

Principal component (PC) estimation of the approximate factor model

Description

Perform PC estimation of the (2D) approximate factor model:

$y_{it}=\boldsymbol{\lambda}_{i}^{\prime}\boldsymbol{F}_{t}+e_{it},$

or in matrix notation:

$\boldsymbol{Y}=\boldsymbol{F}\boldsymbol{\Lambda}^{\prime}+\boldsymbol{e}.$

The factors $\boldsymbol{F}$ is estimated as $\sqrt{T}$ times the $r$ eigenvectors of the matrix $\boldsymbol{Y}\boldsymbol{Y}^{\prime}$ corresponding to the $r$ largest eigenvalues in descending order, and the loading matrix is estimated by $\boldsymbol{\Lambda}=T^{-1}\boldsymbol{Y}^{\prime}\boldsymbol{F}$ . See e.g. Bai and Ng (2002).

Usage

PC(Y, r)
PC(Y, r)

Arguments

`Y`	A $T \times N$ data matrix. T = number of time series observations, N = cross-sectional dimension.
`r`	= the number of factors.

Value

A list containing the factors and factor loadings:

factor = a $T \times r$ matrix of the estimated factors.
loading = a $N \times r$ matrix of the estimated factor loadings.

References

Bai, J. and Ng, S., 2002. Determining the number of factors in approximate factor models. Econometrica, 70(1), pp.191-221.

Examples


# simulate data

T <- 100
N <- 50
r <- 2
F <- matrix(stats::rnorm(T * r, 0, 1), nrow = T)
Lambda <- matrix(stats::rnorm(N * r, 0, 1), nrow = N)
err <- matrix(stats::rnorm(T * N, 0, 1), nrow = T)
Y <- F %*% t(Lambda) + err

# estimation

est_PC <- PC(Y, r)
# simulate data

T <- 100
N <- 50
r <- 2
F <- matrix(stats::rnorm(T * r, 0, 1), nrow = T)
Lambda <- matrix(stats::rnorm(N * r, 0, 1), nrow = N)
err <- matrix(stats::rnorm(T * N, 0, 1), nrow = T)
Y <- F %*% t(Lambda) + err

# estimation

est_PC <- PC(Y, r)

Print the relative importance ratios

Description

Print the relative importance ratios

Usage

## S3 method for class 'multi_result'
summary(object, ...)
## S3 method for class 'multi_result'
summary(object, ...)

Arguments

`object`	An S3 object of class 'multi_result' created by multilevel().
`...`	Additional arguments.

Value

A matrix containing the summary of the model.

Examples


panel <- UKhouse # load the data
est_multi <- multilevel(panel, ic = "BIC3", standarise = TRUE, r_max = 5,
                           depvar_header = "dlPrice", i_header = "Region",
                           j_header = "LPA_Type", t_header = "Date")
summary(est_multi)

panel <- UKhouse # load the data
est_multi <- multilevel(panel, ic = "BIC3", standarise = TRUE, r_max = 5,
                           depvar_header = "dlPrice", i_header = "Region",
                           j_header = "LPA_Type", t_header = "Date")
summary(est_multi)

England and Wales House Price Growth Data Categorised by Regions

Description

A data.frame containing the quarterly (mean) house prices of four different types of properties, (detached, semi-detached, terraced and flats/maisonettes) for 331 local planning authorities (LPA) over the period 1996Q1 to 2021Q2. See also Lin and Shin (2023).

Usage

UKhouse
UKhouse

Format

## 'UKhouse'

Details

Each LPA belongs to one of the ten regions: North East (NE), North West (NW), Yorkshire and the Humber (YH), East Midlands (EM), West Midlands(WM), East of England (EE), London (LD), South East (SE), South West (SW) and Wales (WA). The real house price growth of the $j$ -th LPA-type pair in region $i$ by deflating the nominal house price by CPI and log-differencing it as

$\pi_{ijt}=100\times \log\left(\frac{PRICE_{ijt}}{CPI_{t}}\right)-100 \times \log\left(\frac{PRICE_{ij,t-1}}{CPI_{t-1}}\right).$

By removing the series with missing observations, it ends up with a balanced panel with $R = 10$ , $N =\sum_{i=1}^{R} N_{i} = 1300$ and $T = 102$ .

Columns in the dataset:

"Date" Time variable.
"Region" Name of region which the LPA belongs to.
"LPA" Name of the LPA.
"Type" Name of the house type.
"LPA_Type" Name of the LPA-type pair.

Source

Office for National Statistics (ONS), ONS website, statistical bulletin, House price statistics for small areas in England and Wales: year ending June 2021

References

Lin, R. and Shin, Y., 2022. Generalised Canonical Correlation Estimation of the Multilevel Factor Model. Available at SSRN 4295429.

Package 'GCCfactor'

Help Index

Get an asymptotic confidence interval for the local component

Description

Usage

Arguments

Value

References

Examples

Bartlett kernel function

Description

Usage

Arguments

Value

Examples

Get a bootstrap confidence interval for the global component

Description

Usage

Arguments

Value

References

Examples

Get bootstrap confidence intervals for the global factors

Description

Usage

Arguments

Value

Examples

Get a bootstrap confidence interval for the global factor loadings

Description

Usage

Arguments

Value

References

Examples

Get a bootstrap confidence interval for the global component

Description

Usage

Arguments

Value

References

Examples

Get a bootstrap confidence interval for the local factors

Description

Usage

Arguments

Value

References

Examples

Check validity of the data and headers

Description

Usage

Arguments

Details

Value

Examples

Dependent wild bootstrap for resampling time series

Description

Usage

Arguments

Value

References

Examples

Generalised canonical correlation estimation for the global factors

Description

Usage

Arguments

Details

Value

References

Examples

Get an optimal bandwidth using Bartlett kernel

Description

Usage

Arguments

Value

References

Examples

Selection criteria for the approximate factor model

Description