ExtendedForms {Greymodels}

Extended forms of grey models

Description

A collection of extended grey forecasting models.

Usage

dgm11(x0)
dgm21(x0)
odgm21(x0)
ndgm11(x0)
vssgm11(x0)
gom11(x0)
gomia11(x0)
ungom11(x0)
exgm11(x0)
egm11(k,x0,k_A,x0_A)

Arguments

x0

Raw data

k

Data index of raw data

x0_A

Raw data (testing set)

k_A

Data index (testing set)

dgm11

Discrete grey model with single variable, first order differential equation

dgm21

Discrete grey model with single variable, second order differential equation model

odgm21

Optimized discrete grey model with single variable, second order differential equation

ndgm11

Non-homogeneous discrete grey model

vssgm11

Variable speed and adaptive structure-based grey model

gom11

Grey opposite-direction model based on inverse accumulation and traditional interpolation method

gomia11

Grey opposite-direction model based on inverse accumulation

ungom11

Unbiased grey opposite-direction model based on inverse accumulation

exgm11

Exponential grey model

egm11

Extended grey model

Value

fitted and predicted values

References

Xie N, Liu S (2009). Discrete Grey Forecasting Model and its Application. Applied Mathematical Modelling, 33(2), 1173-1186. DOI:10.1016/j.apm.2008.01.011.

Shao Y, Su H (2012). On Approximating Grey Model DGM (2, 1). 2012 AASRI Conference on Computational Intelligence and Bioinformatics, 1, 8-13. DOI:10.1016/j.aasri.2012.06.003.

Xie N, Liu S, Yang Y, Yuan C (2013). On Novel Grey Forecasting Model based on Non-homogeneous Index Sequence. Applied Mathematical Modelling, 37, 5059-5068. DOI:10.1016/j.apm.2012.10.037.

Li S, Miao Y, Li G, Ikram M (2020). A Novel Varistructure Grey Forecasting Model with Speed Adaptation and its Application. Mathematical and Computers in Simulation, 172, 45-70. DOI:10.1016/j.matcom.2019.12.020.

Che X, Luo Y, He Z (2013). Grey New Information GOM (1, 1) Model based Opposite-Direction Accumulated Generating and its Application. Applied Mechanics and Materials, 364, 207-210. DOI:10.4028/www.scientific.net/AMM.364.207.

Power Load Forecasting based on GOM (1, 1) Model under the Condition of Missing Data. 2016 IEEEPES Asia-Pacific Power and Energy Engineering Conference (APPEEC), pp. 2461-2464. DOI:10.1109/appeec.2016.7779929.

Luo Y, Liao D (2012). Grey New Information Unbiased GOM (1, 1) Model based on Opposite-Direction Accumulated Generating and its Application. Advanced Materials Research, 507, 265-268. DOI:10.4028/www.scientific.net/AMR.507.265.

Bilgil H (2020). New Grey Forecasting Model with its Application and Computer Code. AIMS Mathematics, 6(2), 1497-1514. DOI: 10.3934/math.2021091.

An Extended Grey Forecasting Model for Omnidirectional Forecasting considering Data Gap Difference. Applied Mathematical Modeling, 35, 5051-5058. DOI:10.1016/j.apm.2011.04.006.

Examples

  # EXGM (1, 1): Exponential grey model

  # Input data x0
  x0 <- c(2028,2066,2080,2112,2170,2275,2356,2428)

  # Calculate accumulated generating operation (AGO)
  x1 <- cumsum(x0)

  # n is the length of sequence x0
  n <- length(x0)

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

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

  # Create matrix B2
  mat1 <- matrix(c(b1),ncol=1)
  mat2 <- matrix(1,nrow=n-1,ncol=1)
  f <- numeric(n)
  for (i in 1:n){
    f[i] <- ( exp(1) - 1) * exp(-i)
  }
  f1 <- f[2:n]

  mat3 <- matrix(c(f1),ncol=1)
  B2 <- cbind(mat1, mat2, mat3)

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

  scale_with <- function(k)
  {
    ( x1[1] - (b/a) - ( ( c/(a-1) )*exp(-1) ) ) * exp(a*(1-k)) + (b/a) + ( c/(a-1) )*exp(-k)
  }
  forecast1 <- scale_with(1:n)
  x1cap <- c(forecast1)
  x0cap1 <- numeric(n)
  for (i in 1:n){
    x0cap1[i] <- x1cap[i+1] - x1cap[i]
  }
  x0cap <- c(x0[1],x0cap1[1:n-1])
  # Fitted values
  x0cap

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

  x1cap4 <- scale_with(1 : n+A )
  t4 <- length(x1cap4)
  x0cap4 <- numeric(t4-1)
  for (i in 1:t4-1) {
    x0cap4[i] <- x1cap4[i+1] - x1cap4[i]
  }
  x0cap4 <- c(x0[1],x0cap4[1:t4-1])
  x0cap5 <- tail(x0cap4,A)
  # Predicted values
  x0cap5

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