Conditional sum of squares for an ARIMA(p, d, q) model

e_t = (w_t - mu) - sum_i phi_i (w_{t-i} - mu) - sum_j theta_j e_{t-j} on w = (1-B)^d y with zero presample innovations; CSS = sum e_t^2 and logLik = -(m/2)(1 + log(2 pi) + log(CSS/m)).

Usage

Arimacss(y, phi = numeric(0), theta = numeric(0), d = 0, mu = 0)

Arguments

y

Observed series.

phi

Autoregressive coefficients.

theta

Moving-average coefficients (Box-Jenkins +theta sign).

d

Order of differencing.

mu

Mean of the differenced series.

Value

List with css, sigma2, loglik, aic, resid, diff, m, p, q, d, n.

References

Box and Jenkins (1970), Time Series Analysis: Forecasting and Control, Chapters 4 and 7; standard published form.

Examples

V <- c(1, 2, 3, 4, 5, 6, 7, 8)
Arimacss(V)
#> $css
#> [1] 204
#> 
#> $sigma2
#> [1] 25.5
#> 
#> $loglik
#> [1] -24.30622
#> 
#> $aic
#> [1] 50.61244
#> 
#> $resid
#> [1] 1 2 3 4 5 6 7 8
#> 
#> $diff
#> [1] 1 2 3 4 5 6 7 8
#> 
#> $m
#> [1] 8
#> 
#> $p
#> [1] 0
#> 
#> $q
#> [1] 0
#> 
#> $d
#> [1] 0
#> 
#> $n
#> [1] 8
#> 
#> $method
#> [1] "ARIMA conditional sum of squares (Box-Jenkins 1970)"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"