Convert between parameterizations for the AR(p) model

These functions convert between the AR(p) coefficients phi, the partial autorcorrelation coefficients pacf and the autocorrelation function acf. The phi-parameterization is the same as used for arima-models in R; see ?arima and the parameter-vector a in Details.

inla.ar.pacf2phi(pac)

inla.ar.phi2pacf(phi)

inla.ar.phi2acf(phi, lag.max = length(phi))

inla.ar.pacf2acf(pac, lag.max = length(pac))

Arguments

pac

The partial autorcorrelation coefficients

phi

The AR(p) parameters phi

lag.max

The maximum lag to compute the ACF for

Value

  • inla.ar.pacf2phi returns phi for given pacf.

  • inla.ar.phi2pacf returns pac for given phi.

  • inla.ar.phi2acf returns acf for given phi.

  • inla.ar.pacf2acf returns acf for given pacf.

Author

Havard Rue hrue@r-inla.org

Examples


pac <- runif(5)
phi <- inla.ar.pacf2phi(pac)
pac2 <- inla.ar.phi2pacf(phi)
print(paste("Error:", max(abs(pac2 - pac))))
#> [1] "Error: 1.11022302462516e-16"
print("Correlation matrix (from pac)")
#> [1] "Correlation matrix (from pac)"
print(toeplitz(inla.ar.pacf2acf(pac)))
#>            [,1]       [,2]       [,3]       [,4]       [,5]       [,6]
#> [1,] 1.00000000 0.08075014 0.83541328 0.25992219 0.64233806 0.38701695
#> [2,] 0.08075014 1.00000000 0.08075014 0.83541328 0.25992219 0.64233806
#> [3,] 0.83541328 0.08075014 1.00000000 0.08075014 0.83541328 0.25992219
#> [4,] 0.25992219 0.83541328 0.08075014 1.00000000 0.08075014 0.83541328
#> [5,] 0.64233806 0.25992219 0.83541328 0.08075014 1.00000000 0.08075014
#> [6,] 0.38701695 0.64233806 0.25992219 0.83541328 0.08075014 1.00000000
print("Correlation matrix (from phi)")
#> [1] "Correlation matrix (from phi)"
print(toeplitz(inla.ar.phi2acf(phi)))
#>            [,1]       [,2]       [,3]       [,4]       [,5]       [,6]
#> [1,] 1.00000000 0.08075014 0.83541328 0.25992219 0.64233806 0.38701695
#> [2,] 0.08075014 1.00000000 0.08075014 0.83541328 0.25992219 0.64233806
#> [3,] 0.83541328 0.08075014 1.00000000 0.08075014 0.83541328 0.25992219
#> [4,] 0.25992219 0.83541328 0.08075014 1.00000000 0.08075014 0.83541328
#> [5,] 0.64233806 0.25992219 0.83541328 0.08075014 1.00000000 0.08075014
#> [6,] 0.38701695 0.64233806 0.25992219 0.83541328 0.08075014 1.00000000