ARIMAX: exogenous regression with ARMA errors

(1-B)^d y = X beta + n with phi(B) n = theta(B) e. Stage one is OLS of the differenced response on the differenced covariates; stage two is the Hannan-Rissanen two-stage regression on the residual series.

Usage

Arimaxhr(y, X, p = 1, q = 1, d = 0, m = NULL)

Arguments

y

Observed response.

X

Exogenous regressors, differenced internally.

p, q

ARMA orders for the disturbance.

d

Order of differencing.

m

Stage-one long-autoregression order, or NULL.

Value

List with beta, phi, theta, intercept, sigma2, noise, resid, p, q, d, r, nobs.

References

Box and Jenkins (1976), Chapters 10-11 (transfer-function models); disturbance estimation by Hannan and Rissanen (1982), Biometrika 69(1), 81-94. Standard published form; neither source is in the local corpus and neither was read.

Examples

V <- c(1, 2, 3, 4, 5, 6, 7, 8)
Arimaxhr(V, V)
#> $beta
#> [1] 1
#> 
#> $phi
#> [1] 0
#> 
#> $theta
#> [1] 0
#> 
#> $intercept
#> [1] 6.097555e-16
#> 
#> $sigma2
#> [1] 7.888609e-31
#> 
#> $noise
#> [1] -2.220446e-16  0.000000e+00  4.440892e-16  8.881784e-16  8.881784e-16
#> [6]  8.881784e-16  1.776357e-15  1.776357e-15
#> 
#> $resid
#> [1] -4.440892e-16 -4.440892e-16  4.440892e-16  4.440892e-16
#> 
#> $p
#> [1] 1
#> 
#> $q
#> [1] 1
#> 
#> $d
#> [1] 0
#> 
#> $r
#> [1] 1
#> 
#> $nobs
#> [1] 4
#> 
#> $method
#> [1] "ARIMAX by OLS plus Hannan-Rissanen errors (Box-Jenkins 1976)"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"