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Grey-Markov Prediction Model

Source: R/pred_markov.R
GM11_markov.Rd

Fits a GM(1,1) model and then uses a Markov chain on relative error states to correct both historical fitted values and future predictions.

Usage

GM11_markov(X, n_ahead = 3, breaks = c(-0.1, -0.05, -0.02, 0, 0.02, 0.05, 0.1))

Arguments

X

Numeric vector of original time series data.

n_ahead

Number of future periods to predict. Must be a positive integer.

breaks

Numeric vector of boundaries for classifying relative errors into states. -Inf and Inf are prepended/appended internally.

Value

A data frame with columns:

Period

Time period labels, such as T1, T2, ..., T+n.

Raw

Original values; future periods are NA.

GM11_fitted

GM(1,1) fitted or predicted values.

err_state

Relative error state for historical periods, and predicted state for future periods.

adj_eff

Adjustment effect, defined as the midpoint of the state interval.

Markov_adj

Markov-chain-adjusted fitted or predicted values.

Details

The function first fits a GM(1,1) model to the original series, classifies relative errors into states using breaks, builds a Markov chain on these error states, and finally adjusts the GM(1,1) fitted and predicted values.

Examples

X = c(174, 179, 183, 189, 207, 234, 220.5, 256, 270, 285)
GM11_markov(X, n_ahead = 3)
#> Level ratio test passed!
#>    Period   Raw GM11_fitted err_state adj_eff Markov_adj
#> 1      T1 174.0      174.00         5   0.010     174.00
#> 2      T2 179.0      172.81         6   0.035     174.55
#> 3      T3 183.0      183.94         4  -0.010     182.11
#> 4      T4 189.0      195.78         3  -0.035     189.16
#> 5      T5 207.0      208.38         4  -0.010     206.32
#> 6      T6 234.0      221.80         7   0.075     214.30
#> 7      T7 220.5      236.08         2  -0.075     219.61
#> 8      T8 256.0      251.28         5   0.010     253.82
#> 9      T9 270.0      267.46         5   0.010     270.16
#> 10    T10 285.0      284.68         5   0.010     287.56
#> 11    T+1    NA      303.01         5   0.010     306.07
#> 12    T+2    NA      322.52         5   0.010     325.78
#> 13    T+3    NA      343.29         5   0.010     346.76