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https://github.com/dppalomar/covFactorModel

Covariance Matrix Estimation via Factor Models
https://github.com/dppalomar/covFactorModel

covariance-matrix factor-model financial-data pca

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Covariance Matrix Estimation via Factor Models

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README 

        
---

output:

  html_document:

    variant: markdown_github

    keep_md: true

  md_document:

    variant: markdown_github

---



```{r, echo = FALSE}

knitr::opts_chunk$set(

  collapse = TRUE,

  comment = "#>"

)

```



# covFactorModel

Estimation of covariance matrix via factor models with application

    to financial data. Factor models decompose the asset returns into an 

    exposure term to some factors and a residual idiosyncratic component. The 

    resulting covariance matrix contains a low-rank term corresponding to the 

    factors and another full-rank term corresponding to the residual component. 

    

This package provides a function to separate the data into the factor 

    component and residual component, as well as to estimate the corresponding 

    covariance matrix. Different kind of factor models are considered, namely, 

    macroeconomic factor models and statistical factor models. The estimation

    of the covariance matrix accepts different kinds of structure on the 

    residual term: diagonal structure (implying that residual component is 

    uncorrelated) and block diagonal structure (allowing correlation within 

    sectors). The package includes a built-in database containing stock symbols

    and their sectors.

    

The package is based on the book:

    R. S. Tsay, _Analysis of Financial Time Series._ John Wiley & Sons, 2005.



## Installation

```{r, eval = FALSE}

# Installation from CRAN (not available yet)

#install.packages("covFactorModel")



# Installation from GitHub

# install.packages("devtools")

devtools::install_github("dppalomar/covFactorModel")



# Getting help

library(covFactorModel)

help(package = "covFactorModel")

package?covFactorModel

?factorModel

?covFactorModel

?getSectorInfo

```



## Vignette

For more detailed information, please check the vignette: [GitHub-html-vignette](https://rawgit.com/dppalomar/covFactorModel/master/vignettes/covFactorModel-vignette.html) and [GitHub-pdf-vignette](https://rawgit.com/dppalomar/covFactorModel/master/vignettes/covFactorModel-vignette.pdf).



## Usage of `factorModel()`

The function `factorModel()` builds a factor model for the data, i.e., it decomposes the asset returns into a factor component and a residual component. The user can choose different types of factor models, namely, macroeconomic, BARRA, or statistical. We start by generating some synthetic data:

```{r, message = FALSE, warning = FALSE}

library(covFactorModel)

library(xts)

library(MASS)



# 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")

```



We first build a _macroeconomic factor model_, which fits the data to the given macroeconomic factors:

```{r}

macro_econ_model <- factorModel(X, type = "Macro", econ_fact = econ_fact)



# sanity check

X_ <- with(macro_econ_model, 

           matrix(alpha, T, N, byrow = TRUE) + factors %*% t(beta) + residual)

norm(X - X_, "F")

```



Next, we build a _BARRA industry factor model_ (assuming assets A and C belong to sector 1 and asset B to sector 2):

```{r}

stock_sector_info <- c(1, 2, 1)

barra_model <- factorModel(X, type = "Barra", stock_sector_info = stock_sector_info)



# sanity check

X_ <- with(barra_model, 

           matrix(alpha, T, N, byrow = TRUE) + factors %*% t(beta) + residual)

norm(X - X_, "F")

```



Finally, we build a _statistical factor model_, which is based on principal component analysis (PCA):

```{r}

# set factor dimension as K=2

stat_model <- factorModel(X, K = 2)



# sanity check

X_ <- with(stat_model, 

           matrix(alpha, T, N, byrow = TRUE) + factors %*% t(beta) + residual)

norm(X - X_, "F")

```



## Usage of `covFactorModel()`

The function `covFactorModel()` estimates the covariance matrix of the data based on factor models. The user can choose not only the type of factor model (i.e., macroeconomic, BARRA, or statistical) but also the structure of the residual covariance matrix (i.e., scaled identity, diagonal, block diagonal, and full).

We start by preparing some synthetic data:

```{r}

library(covFactorModel)

library(xts)

library(MASS)



# generate synthetic data

set.seed(234)

K <- 1   # number of factors

N <- 400  # number of stocks

mu <- rep(0, N)

beta <- mvrnorm(N, rep(1, K), diag(K)/10)

Sigma <- beta %*% t(beta) + diag(N)

print(eigen(Sigma)$values[1:10])

```



Then, we simply use function `covFactorModel()` (by default it uses a _statistical factor model_ and a diagonal structure for the residual covariance matrix). We show the average error w.r.t number of observations:

```{r, warning = FALSE}

# estimate error by loop

err_scm_vs_T <- err_statPCA_diag_vs_T <- c()

index_T <- N*seq(5)

for (T in index_T) {

  X <- xts(mvrnorm(T, mu, Sigma), order.by = as.Date('1995-03-15') + 1:T)

  # use statistical factor model

  cov_statPCA_diag <- covFactorModel(X, K = K, max_iter = 10)

  err_statPCA_diag_vs_T <- c(err_statPCA_diag_vs_T, norm(Sigma - cov_statPCA_diag, "F")^2)

  # use sample covariance matrix

  err_scm_vs_T <- c(err_scm_vs_T, norm(Sigma - cov(X), "F")^2)

}

res <- rbind(err_scm_vs_T, err_statPCA_diag_vs_T)

rownames(res) <- c("SCM", "stat + diag")

colnames(res) <- paste0("T/N=", index_T/N)

print(res)

```



## Usage of `getSectorInfo()`

The function `getSectorInfo()` provides sector information for a given set of stock symbols. The usage is rather simple:

```{r}

library(covFactorModel)



mystocks <- c("AAPL",  "ABBV", "AET", "AMD", "APD", "AA","CF", "A", "ADI", "IBM")

getSectorInfo(mystocks)

```



The built-in sector database can be overidden by providing a stock-sector pairing:

```{r}

my_stock_sector_database <- cbind(mystocks, c(rep("sector1", 3),

                                              rep("sector2", 4),

                                              rep("sector3", 3)))

getSectorInfo(mystocks, my_stock_sector_database)

```



## Links

Package: [GitHub](https://github.com/dppalomar/covFactorModel).



README file: [GitHub-readme](https://rawgit.com/dppalomar/covFactorModel/master/README.html).



Vignette: [GitHub-html-vignette](https://rawgit.com/dppalomar/covFactorModel/master/vignettes/covFactorModel-vignette.html) and [GitHub-pdf-vignette](https://rawgit.com/dppalomar/covFactorModel/master/vignettes/covFactorModel-vignette.pdf).