This function computes the theoretical Autocorrelation (ACF) of an ARMA process.
theo_acf(ar, ma = NULL, lagmax = 20)A vector containing the AR coefficients.
A vector containing the MA coefficients.
An integer indicating the maximum lag up to which to compute the theoretical ACF.
# Compute the theoretical ACF for an ARMA(1,0) (i.e. a first-order autoregressive model: AR(1))
theo_acf(ar = -0.25, ma = NULL)
#> , , Theoretical
#>
#> Theoretical
#> 0 1.000000e+00
#> 1 -2.500000e-01
#> 2 6.250000e-02
#> 3 -1.562500e-02
#> 4 3.906250e-03
#> 5 -9.765625e-04
#> 6 2.441406e-04
#> 7 -6.103516e-05
#> 8 1.525879e-05
#> 9 -3.814697e-06
#> 10 9.536743e-07
#> 11 -2.384186e-07
#> 12 5.960464e-08
#> 13 -1.490116e-08
#> 14 3.725290e-09
#> 15 -9.313226e-10
#> 16 2.328306e-10
#> 17 -5.820766e-11
#> 18 1.455192e-11
#> 19 -3.637979e-12
#> 20 9.094947e-13
#>
#> attr(,"type")
#> [1] "Autocorrelation"
#> attr(,"n")
#> [1] 20
#> attr(,"class")
#> [1] "simtsACF" "array"
# Computes the theoretical ACF for an ARMA(2, 1)
theo_acf(ar = c(.50, -0.25), ma = 0.20, lagmax = 10)
#> , , Theoretical
#>
#> Theoretical
#> 0 1.0000000000
#> 1 0.5050000000
#> 2 0.0025000000
#> 3 -0.1250000000
#> 4 -0.0631250000
#> 5 -0.0003125000
#> 6 0.0156250000
#> 7 0.0078906250
#> 8 0.0000390625
#> 9 -0.0019531250
#> 10 -0.0009863281
#>
#> attr(,"type")
#> [1] "Autocorrelation"
#> attr(,"n")
#> [1] 10
#> attr(,"class")
#> [1] "simtsACF" "array"