Vector Autoregression (VAR) with Rolling Window

Introduction

Vector Autoregression (VAR) is a statistical technique used to model the relationships between multiple time series. In this article, we will explore how to implement VAR with a rolling window using R and parallel computing.

Problem Statement

The original question posed by the OP describes two main issues:

1. The output matrices rolling.var.coef and var.resids have incorrect lengths, resulting in only a few coefficients being calculated for the first days.
2. The current approach requires calculating VAR with a fixed window size using separate functions.

Solution Overview

To address these issues, we will develop a new function that calculates VAR with a rolling window in parallel. This function, rollvar, will handle both coefficient and residual calculations efficiently.

Parallel Computations Using Linux/Mac

For parallel computations on Linux/mac systems, we can utilize the pbapply package, which provides built-in support for parallel processing.

## Load necessary packages
library(vars)
library(pbapply)

## Define data and parameters
data <- data.frame(Canada)
window <- 10

## Define function to calculate VAR with rolling window
caller <- function(j) {
  var.2c <- VAR(data[(1:window)+j,], p=1, type = "const")
  B <- Bcoef(var.2c)
  r <- resid(var.2c)
  list(B, r)
}

## Calculate VAR with rolling window in parallel
out <- pbapply::pblapply(0:(nrow(Canada)-window), caller, cl = makeCluster(detectCores() - 1, type = "FORK"))

## Stop cluster and retrieve results
stopCluster(cluster)

Parallel Computations Using Windows

For parallel computations on Windows systems, we can utilize the psOCK package to create a process-based cluster.

## Load necessary packages
library(vars)
library(pssock)

## Define data and parameters
data <- data.frame(Canada)
window <- 10

## Define function to calculate VAR with rolling window
caller <- function(j) {
  var.2c <- VAR(data[(1:window)+j,], p=1, type = "const")
  B <- Bcoef(var.2c)
  r <- resid(var.2c)
  list(B, r)
}

## Calculate number of cores and create cluster
no_cores <- detectCores() - 1
cluster <- makeCluster(no_cores)

## Export necessary data and functions to the global environment of the cluster workers
clusterExport(cluster, c("Canada", "data", "window", "caller"), envir = environment())
clusterEvalQ(cluster, library(vars))

## Moving window estimation using pblapply
out <- pblapply(0:(nrow(Canada)-window), caller, cl = cluster)

## Stop cluster and retrieve results
stopCluster(cluster)

Rollvar Function

The rollvar function is a wrapper around the caller function that takes care of calculating VAR with a rolling window in parallel.

rollvar <- function(data, window, nrow) {
  caller <- function(j) {
    var.2c <- VAR(data[(1:window)+j,], p=1, type = "const")
    B <- Bcoef(var.2c)
    r <- resid(var.2c)
    list(B, r)
  }
  
  out <- pbapply::pblapply(0:(nrow - window), caller, cl = makeCluster(detectCores() - 1, type = "FORK"))
  stopCluster(cluster)
  return(out)
}

Usage

To use the rollvar function, simply pass in your data and window size as arguments.

data <- data.frame(Canada)
window <- 10
nrow <- nrow(data)

out <- rollvar(data, window, nrow)

This will calculate VAR with a rolling window of size window on each row of the input data data, using multiple cores to speed up computation.

Conclusion

In this article, we have developed a solution for calculating Vector Autoregression (VAR) with a rolling window in parallel using R. The rollvar function is a convenient wrapper around the original code that handles both coefficient and residual calculations efficiently. With parallel computing, you can significantly speed up your computations on Linux/mac systems or Windows.

Last modified on 2024-09-21