calc_reg: Perform multivariate regression using different methods, and...

In algoquant/HighFreq: High Frequency Time Series Management

Perform multivariate regression using different methods, and return a vector of regression coefficients, their t-values, and the last residual z-score.

Description

Perform multivariate regression using different methods, and return a vector of regression coefficients, their t-values, and the last residual z-score.

Usage

calc_reg(respv, predm, controlv)

Arguments

respv	A single-column time series or a vector of response data.
predm	A time series or a matrix of predictor data.
controlv	A list of model parameters (see Details).

Details

The function calc_reg() performs multivariate regression using different methods, and returns a vector of regression coefficients, their t-values, and the last residual z-score.

The function calc_reg() accepts a list of regression model parameters through the argument controlv. The list of model parameters can be created using the function param_reg(). Below is a description of the model parameters.

If regmod = "least_squares" (the default) then it performs the standard least squares regression, the same as the function calc_lm(), and the function lm() from the R package stats. But it uses RcppArmadillo C++ code so it's several times faster than lm().

If regmod = "regular" then it performs shrinkage regression. It calculates the reduced inverse of the predictor matrix from its singular value decomposition. It performs regularization by selecting only the largest singular values equal in number to dimax.

If regmod = "quantile" then it performs quantile regression (not implemented yet).

The length of the return vector depends on the number of columns of the predictor matrix (including the intercept column, if it's been added in R). The number of regression coefficients is equal to the number of columns of the predictor matrix. The length of the return vector is equal to the number of regression coefficients, plus their t-values, plus the z-score. The number of t-values is equal to the number of coefficients.

For example, if the number of columns of the predictor matrix is equal to n, then calc_reg() returns a vector with 2n+1 elements: n regression coefficients, n corresponding t-values, and 1 z-score value.

Value

A single-row matrix with the regression coefficients, their t-values, and the last residual z-score.

Examples

## Not run: 
# Calculate historical returns
retp <- na.omit(rutils::etfenv$returns[, c("XLF", "VTI", "IEF")])
# Response equals XLF returns
respv <- retp[, 1]
# Predictor matrix equals VTI and IEF returns
predm <- retp[, -1]
# Perform multivariate regression using lm()
regmod <- lm(respv ~ predm)
regsum <- summary(regmod)
coeff <- regsum$coefficients
# Create a default list of regression parameters
controlv <- HighFreq::param_reg()
# Add unit intercept column to the predictor matrix
predm <- cbind(rep(1, NROW(predm)), predm)
# Perform multivariate regression using calc_reg()
regarma <- drop(HighFreq::calc_reg(respv=respv, predm=predm, controlv=controlv))
# Compare the outputs of both functions
all.equal(regarma[1:(2*NCOL(predm))], 
  c(coeff[, "Estimate"], coeff[, "t value"]), check.attributes=FALSE)
# Compare the speed of RcppArmadillo with R code
library(microbenchmark)
summary(microbenchmark(
  Rcpp=HighFreq::calc_reg(respv=respv, predm=predm, controlv=controlv),
  Rcode=lm(respv ~ predm),
  times=10))[, c(1, 4, 5)]  # end microbenchmark summary

## End(Not run)

algoquant/HighFreq documentation built on Feb. 9, 2024, 8:15 p.m.