ARIMA(p, d, q) by Hannan-Rissanen (Geron Ch 13, morie.fn hmarim)

Pure AR models (q = 0) are plain OLS on lags; otherwise a long autoregression of order k supplies the innovations and the ARMA coefficients come from OLS on lags plus fitted innovations. forecast is a closure taking a horizon h.

Usage

morie_geron_arima(y, p = 1, d = 0, q = 0, include_mean = TRUE)

Arguments

y

Univariate series.

p, q

AR and MA orders.

d

Differencing order.

include_mean

Fit an intercept.

Value

List with ar, ma, intercept, residuals, sigma2, aic, fitted, differenced, forecast, order.

Examples

V <- c(1, 2, 3, 4, 5, 6, 7, 8)
morie_geron_arima(V)
#> $ar
#> [1] 1
#> 
#> $ma
#> numeric(0)
#> 
#> $intercept
#> [1] 1
#> 
#> $residuals
#> [1] -1.776357e-15 -1.776357e-15 -2.664535e-15 -2.664535e-15 -3.552714e-15
#> [6] -3.552714e-15 -3.552714e-15
#> 
#> $sigma2
#> [1] 1.167514e-29
#> 
#> $aic
#> [1] -460.3406
#> 
#> $fitted
#> [1] 2 3 4 5 6 7 8
#> 
#> $differenced
#> [1] 1 2 3 4 5 6 7 8
#> 
#> $forecast
#> function (h = 1) 
#> {
#>     H <- as.integer(h)
#>     .morie_gr_need(H >= 1L, "forecast: h must be >= 1")
#>     hist <- z
#>     errs <- resid
#>     out <- numeric(0)
#>     for (i in seq_len(H)) {
#>         val <- intercept
#>         if (length(ar)) 
#>             for (a in seq_along(ar)) val <- val + ar[a] * hist[length(hist) - 
#>                 a + 1L]
#>         if (length(ma)) {
#>             for (b in seq_along(ma)) {
#>                 val <- val + ma[b] * (if (length(errs) > b - 
#>                   1L) 
#>                   errs[length(errs) - b + 1L]
#>                 else 0)
#>             }
#>         }
#>         hist <- c(hist, val)
#>         errs <- c(errs, 0)
#>         out <- c(out, val)
#>     }
#>     f <- out
#>     if (length(anchors)) 
#>         for (a in rev(anchors)) f <- a + cumsum(f)
#>     f
#> }
#> <bytecode: 0x562173c2b370>
#> <environment: 0x56215faaf668>
#> 
#> $order
#> [1] 1 0 0
#> 
#> $estimate
#> [1] 1.167514e-29
#> 
#> $n
#> [1] 7
#> 
#> $method
#> [1] "ARIMA(1,0,0) by OLS"
#>