Greymodels (version 2.0.1)

BackgroundValues: Improved background values

Description

A collection of grey forecasting models with improvements to the underlying background value z.

Usage

gm11(x0)
epgm11(x0)
tbgm11(x0)
igm11(x0)
gm114(x0)

Value

fitted and predicted values

Arguments

x0

Raw data

gm11

Basic grey model

epgm11

Extrapolation-based grey model

tbgm11

Data transformation-based grey model

igm11

Improved grey model

gm114

Grey model with single variable, one first-order variable, four background values

References

Chang C (2019). Extrapolation-based Grey Model for Small-Dataset Forecasting. Economic Computation and Economic Cybernetics Studies and Research, 53(1), 171-182. DOI:10.24818/18423264/53.1.19.11.

Li K, Zhang T (2019). A Novel Grey Forecasting Model and its Application in Forecasting the Energy Consumption in Shanghai. Energy Systems, pp. 1-16. DOI:10.1007/s12667-019-00344-0.

Ou S (2012). Forecasting Agricultural Output with an Improved Grey Forecasting Model based on the Genetic Algorithm. Computers and Electronics in Agriculture, 85, 33-39. DOI:10.1016/j.compag.2012.03.007.

Li S, Zhou M, Meng W, Zhou W (2019). A new Prediction Model for Forecasting the Automobiles Ownership in China. Journal of Control and Decision, 8(2), 155-164. DOI:10.1080/23307706.2019.1666310.

Examples

# GM(1,1) model

# x0 is the original data sequence
x0 <- c(2350,2465,2557,2577,2689,2739,2797,2885,2937,2996)

# Calculate AGO
  x1 <- cumsum(x0)

# Determine length of x0
  n <- length(x0)

# Generate background value sequence Z
  b <- numeric(n)

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

  b1 <- b[1:n-1]

# Create a matrix B
  B <- matrix(1,nrow=n-1,ncol=2)
  B[,1] <- t(t(b1[1:n-1]))

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

# Estimate parameters a and b by ordinary least squares method (OLS)
  xcap <- solve (t(B)%*% B)%*% t(B) %*% yn
  a <- xcap[1,1]
  b <- xcap[2,1]

# Calculate fitted values
  scale_with <- function(k)
  {
    (x0[1] - (b/a)) * exp(-a*k) * (1 - exp(a))
  }
  fitted <- scale_with(1:n)
  x0cap <- c(x0[1],fitted[1:n-1])
  x0cap

# A is the number of forecast values
  A <- 4

# Predicted values
  x0cap4 <- scale_with(1 : n+A-1)
  x0cap5 <- tail(x0cap4,A)
  x0cap5

# Fitted and predicted values
  x0cap2 <- c(x0cap,x0cap5)
  x0cap2