IntervalMultivariable {Greymodels}

Multivariate interval sequences

Description

A collection of multivariate grey forecasting models based on interval number sequences.

Usage

igndgm12(LB,UB)
mdbgm12(x01L,x01U,x02L,x02U,x01La,x01Ua,x02La,x02Ua)

Arguments

LB, UB

Lower and upper bound of interval sequence

x01L, x01U

Lower and upper bound of first interval sequence (training set)

x02L, x02U

Lower and upper bound of second interval sequence (training set)

x01La, x01Ua

Lower and upper bound of first interval sequence (testing set)

x02La, x02Ua

Lower and upper bound of second interval sequence (testing set)

igndgm12

Interval grey number sequence based on non-homogeneous discrete grey model

mdbgm12

Multivariate grey model based on dynamic background algorithm

Value

fitted and predicted values

References

Xie N, Liu S (2015). Interval Grey Number Sequence Prediction by using Nonhomogeneous Exponential Discrete Grey Forecasting Model. Journal of Systems Engineering and Electronics, 26(1), 96-102. DOI:10.1109/JSEE.2015.00013.

Zeng X, Yan S, He F, Shi Y (2019). Multivariable Grey Model based on Dynamic Background Algorithm for Forecasting the Interval Sequence. Applied Mathematical Modelling, 80(23). DOI:10.1016/j.apm.2019.11.032.

Examples

  #MDBGM (1, 2) model: Multivariate grey model based on dynamic background algorithm.

  # Input data
  #x01 Lower and upper bound of sequence 1
  #x02 Lower and upper bound of sequence 2

  # x01L is the lower bound of sequence 1
  x01L <- c(2721,3136,3634,3374,3835,3595,3812,4488)

  # x01U is the upper bound of sequence 1
  x01U <- c(3975,4349,4556,5103,5097,5124,5631,6072)

  # x02L is the lower bound of sequence
  x02L <- c(24581,30070,36656,36075,42173,42074,45537,55949)

  # x02U is the upper bound of sequence 2
  x02U <- c(41731,49700,55567,61684,68295,68342,73989,78194)

  x01 <- cbind(x01L,x01U)
  x02 <- cbind(x02L,x02U)

  # AGO
  x11L <- cumsum(x01L)
  x11U <- cumsum(x01U)

  x11 <- cbind(x11L,x11U)

  x12L <- cumsum(x02L)
  x12U <- cumsum(x02U)

  x12 <- cbind(x12L,x12U)

  # Length of sequence
  n <- length(x01L)

  # Background values
  b <- numeric(n)
  for (i in 1:n){
    b[i] <- (0.5*x11L[i + 1] + 0.5*x11L[i])
    b1 <- b[1:n-1]
  }
  z1L <- matrix(c(b1),ncol=1)

  n <- length(x01L)
  d <- numeric(n)
  for (i in 1:n){
    d[i] <- (0.5*x11U[i + 1] + 0.5*x11U[i])
    d1 <- d[1:n-1]
  }
  z1U <- matrix(c(d1),ncol=1)

  # Create matrix Y
  YL <- matrix(c(x01L[2:n]),ncol=1)
  YU <- matrix(c(x01U[2:n]),ncol=1)

  # Create matrix X
  mat1 <- matrix(c(x12L[2:n]),ncol=1)
  mat2 <- matrix(c(x12U[2:n]),ncol=1)
  mat3 <- matrix(c(x11L[1:n-1]),ncol=1)
  mat4 <- matrix(c(x11U[1:n-1]),ncol=1)
  mat5 <- matrix(2:n,nrow=n-1,ncol=1)
  mat6 <- matrix(1,nrow=n-1,ncol=1)

  X <- cbind(mat1,mat2,mat3,mat4,mat5,mat6)

  # Parameters estimation by OLS - Lower
  A1 <- solve (t(X) %*% X) %*% t(X) %*% YL
  miu11 <- A1[1,1]
  miu12 <- A1[2,1]
  gamma11 <- A1[3,1]
  gamma12 <- A1[4,1]
  g1 <- A1[5,1]
  h1 <- A1[6,1]

  # Parameters estimation by OLS - Upper
  A2 <- solve (t(X) %*% X) %*% t(X) %*% YU
  miu21 <- A2[1,1]
  miu22 <- A2[2,1]
  gamma21 <- A2[3,1]
  gamma22 <- A2[4,1]
  g2 <- A2[5,1]
  h2 <- A2[6,1]

  # Fitted values - Lower
  scale_with <- function(k)
  {
    (miu11*x12L[k]) + (miu12*x12U[k]) + (gamma11*x11L[k-1]) + (gamma12*x11U[k-1]) + (g1*k) + h1
  }
  forecast_L <- scale_with(2:n)
  x0cap1L <- c(x01L[1],forecast_L)

  # Fitted values - Upper
  scale_with <- function(k)
  {
    (miu21*x12L[k]) + (miu22*x12U[k]) + (gamma21*x11L[k-1]) + (gamma22*x11U[k-1]) + (g2*k) + h2
  }
  forecast_U <- scale_with(2:n)
  x0cap1U <- c(x01U[1],forecast_U)

  # Matrix of fitted values (lower and upper)
  x0cap <- matrix(c(cbind(x0cap1L,x0cap1U)),ncol=2)
  x0cap