ParametersEstimation {Greymodels}

Parameters estimation

Description

A collection of grey forecasting models based on parameters estimation.

Usage

sogm21(x0)
ngm11k(x0)
ngm11kc(x0)
ongm11kc(x0)

Arguments

x0

Raw data

sogm21

Structured optimized grey model with single variable and second order differential equation

ngm11k

Nonlinear grey model

ngm11kc

Nonlinear grey model

ongm11kc

Optimized nonlinear grey model

Value

fitted and predicted values

References

Xu N, Dang Y (2015). An Optimized Grey GM (2, 1) Model and Forecasting of Highway Subgrade Settlement. Mathematical Problems in Engineering, 2015(1), 1-6. DOI:10.1155/2015/606707.

Chen P, Yu H (2014). Foundation Settlement Prediction based on a Novel NGM Model. Mathematical Problems in Engineering 2014, 242809. DOI:10.1155/2014/242809.

Examples

  # ONGM (1, 1, k, c) model: Nonlinear grey model

  # Input data x0
  x0 <- c(23.36,43.19,58.73,70.87,83.71,92.91,99.73,105.08,109.73,112.19,113.45)

  # AGO
  x1 <- cumsum(x0)

  tm <- length(x0)

  # Create matrix y
  y <- matrix(c(x0),ncol=1)
  y <- t(t(x0[2:tm]))

  b <- numeric(tm)
  for (i in 1:tm){
    b[i] <- -0.5*(x1[i+1] + x1[i])
  }
  b1 <- b[1:tm-1]

  # Create matrix B2
  mat1 <- matrix(c(b1),ncol=1)
  mat2 <-matrix(2:tm, nrow=tm-1,ncol=1)
  mat3 <- matrix(1,nrow=tm-1,ncol=1)

  B2 <- cbind(mat1, mat2, mat3)

  # Parameters estimation by OLS
  rcap <- (solve (t(B2) %*% B2)) %*% t(B2) %*% y
  a <- rcap[1,1]
  b <- rcap[2,1]
  c <- rcap[3,1]

  m <- log ((2+a)/(2-a))
  n <- (m*b)/a
  p <- (m*c)/a - (n/a) + (n/2) + (n/m)

  scale_with <- function(k)
  {
    (1-exp(a))*(x1[1]-(n/m)+(n/(m^2))-(p/m))*exp(-m*(k-1))+(n/m)
  }
  forecast1 <- scale_with(2:tm)

  x0cap <- c(x0[1],forecast1)
  # Fitted values
  x0cap

  A <- 4

  x0cap4 <- scale_with(1 : tm+A )

  x0cap5 <- tail(x0cap4,A)
  # Predicted values
  x0cap5

  # Fitted & Predicted values
  x0cap2 <- c(x0cap,x0cap5)
  x0cap2