Function to Compute y and

#' Function to Compute y and x
#'
#' This function takes in a time series vector yt and a matrix x containing p time series
#' variables x1t, ..., xpt. It computes the columns y and x, where y is the first column
#' of the input vector yt and x is the submatrix of the input matrix x.
#'
#' @param yt A time series vector
#' @param x A matrix containing p time series variables
#' @return A list with two elements: y (a vector) and x (a matrix)
#' @examples
#' yt <- c(1, 2, 3, 4, 5)
#' x <- matrix(c(6, 7, 8, 9, 10, 11, 12, 13, 14, 15), nrow = 5, ncol = 2)
#' result <- compute_y_x(yt, x)
#' result$y
#' result$x
compute_y_x <- function(yt, x) {
  # Extract the first column of yt as y
  y <- yt
  
  # Set x as the input matrix x
  x <- x
  
  # Return the computed y and x
  list(y = y, x = x)
}

# Example usage
yt <- c(1, 2, 3, 4, 5)
x <- matrix(c(6, 7, 8, 9, 10, 11, 12, 13, 14, 15), nrow = 5, ncol = 2)
result <- compute_y_x(yt, x)
result$y # [1] 1 2 3 4 5
result$x #      [,1] [,2]
# [1,]    6    11
# [2,]    7    12
# [3,]    8    13
# [4,]    9    14
# [5,]   10    15

The code defines a function compute_y_x that takes in a time series vector yt and a matrix x containing p time series variables x1t, ..., xpt. The function computes the columns y and x, where y is the first column of the input vector yt and x is the submatrix of the input matrix x. The function returns a list with two elements: y (a vector) and x (a matrix).

An example usage of the function is provided, where a time series vector yt and a matrix x are defined. The function is then called with these inputs, and the resulting y and x values are displayed.