Illustrative code to compute the covariance of the second order autoregression (AR2) model.

Computes the auto-covariance for given coefficients.

Usage

ar2cov(a1, a2, k = 30, useC = FALSE)

Arguments

a1

the first auto-regression coefficient.

a2

the second auto-regression coefficient.

k

maximum lag for evaluating the auto-correlation.

useC

just a test (to use C code).

Value

the autocorrelation as a vector or matrix, whenever a1 or a2 are scalar or vector.

Details

Let the second order auto-regression model defined as x_t + a_1 x_{t-1} + a_2 x_{t-2} = w_t where w_t ~ N(0, 1).

See also

ar2precision

Examples

ar2cov(c(-1.7, -1.8), 0.963, k = 5)
#>           [,1]      [,2]       [,3]        [,4]       [,5]
#> [1,] 0.8660214 0.5092364 0.03172323 -0.43646514 -0.7725402
#> [2,] 0.9169638 0.6875349 0.35452664 -0.02394815 -0.3845158
plot(ar2cov(-1.7, 0.963), type = "o")