factorModel: Factor Model Decomposition

In dppalomar/covFactorModel: Covariance Matrix Estimation via Factor Models

Description

Decomposes data matrix into factors and residual idiosyncratic component.

Usage

factorModel(X, type = c("Stat-PCA", "Macro", "Barra"), econ_fact, K = 1,
  orthonormal = c("factor", "beta"), max_iter = 10, tol = 0.001,
  Psi_struct = c("diag", "block_diag", "scaled_identity", "full"),
  stock_sector_info = NA, rtn_Sigma = FALSE)

Arguments

X	xts object of dimension T x N, with T number of observations and N number of assets
type	string object indicating the type of factor model to be used: "Macro" - macroeconomic factor model, requires user to pass econ_fact "Barra" - BARRA Industry factor model, requires user to pass stock_sector_info or colnames of X to be contained in the in-built database data(stock_sector_database) "Stat-PCA" - statistical factor model by PCA, requires user to pass number of factors K (default)
econ_fact	xts object of dimension T x K, required and used when type = "Macro"
K	number of factors when build a statistical factor model, used when type = "Stat-PCA" (default: 1)
orthonormal	string object indicating position of normalization in the statistical factor model, used when type = "Stat-PCA" "factor" - covariance matrix of factors is identity (default) "beta" - columns of beta are orthonormal
max_iter	positive integer indicating maximum number of iterations when build statistical factor model, used when type = "Stat-PCA" (default: 10)
tol	double object indicating relative tolerance to determine convergence when estimate statistical factor model, used when type = "Stat-PCA" (default: 0.001)
Psi_struct	string indicating type of structure imposed on the covariance matrix of the residuals, Psi, used when rtn_Sigma = TRUE "diag" - Psi is a diagonal matrix (default) "block_diag" - Psi is a block diagonal matrix, user required topass stock_sector_info to determine the structure of the blocks "scaled_identity" - Psi is a scale identity matrix "full" - Psi is a full matrix
stock_sector_info	positive integer vector of length N, used when type = "Barra" or Psi_struct = "block_diag"
rtn_Sigma	logical variable indicating whether to calculate and return the covariance matrix

Details

Decomposes data matrix into factors and residual idiosyncratic component. The user can choose different types of factor models, namely, macroeconomic, BARRA, or statistical. For macroeconomic factor model, set type = "Macro" and pass argument econ_fact; for BARRA Industry factor model, set type = "Barra" and pass argument stock_sector_info (or make column names of X be in the in-built database data(stock_sector_database)); for statistical factors model, set type = "Stat-PCA" and pass argument K, max_iter, tol and Psi_struct, and possibly stock_sector_info if a block diagonal structure for Psi is required. This function can also estimate covariance matrix when set rtn_Sigma = TRUE. User can choose different type of residual covariance matrix, namely, scaled identity, diagonal, block diagonal or full.

Value

A list with following components:

alpha	vector of length N, the constant part
beta	matrix of dimension N x K, the loading matrix
factors	xts object of dimension T x K, the factor data matrix
residual	xts object of dimension T x N, the residual data matrix
Sigma	matrix of dimension N x N, the covariance matrix, only returned when rtn_Sigma = TRUE

Author(s)

ZHOU Rui & Daniel P. Palomar

Examples

# generate synthetic data
set.seed(234)
N <- 3  # number of stocks
T <- 5  # number of samples
mu <- rep(0, N)
Sigma <- diag(N)/1000

# generate asset returns TxN data matrix
X <- xts(mvrnorm(T, mu, Sigma), order.by = as.Date('2017-04-15') + 1:T) 
colnames(X) <- c("A", "B", "C")

# generate K=2 macroeconomic factors
econ_fact <- xts(mvrnorm(T, c(0, 0), diag(2)/1000), order.by = index(X))
colnames(econ_fact) <- c("factor1", "factor2")

# build a macroeconomic factor model
macro_econ_model <- factorModel(X, type = "Macro", econ_fact = econ_fact)

# build a BARRA industry factor model 
# (assuming assets A and C belong to sector 1 and asset B to sector 2)
stock_sector_info <- c(1, 2, 1)
barra_model <- factorModel(X, type = "Barra", stock_sector_info = stock_sector_info)

# build a statistical factor model
# set factor dimension as K=2
stat_model <- factorModel(X, K = 2)

dppalomar/covFactorModel documentation built on May 17, 2019, 2:14 a.m.