Description Usage Arguments Details Value Note Author(s) References See Also Examples

Estimates the parameters of a nested reduced-rank autoregressive model for multiple time series.

1 |

`Ranks` |
Vector of integers: the ranks of the model.
Each value must be at least one and no more than |

`coefstart` |
Optional numerical vector of initial values for the coefficients. By default, the family function chooses these automatically. |

Full details are given in Ahn and Reinsel (1988).
Convergence may be very slow, so setting `maxits = 50`

, say, may help.
If convergence is not obtained, you might like to try inputting different
initial values.

Setting `trace = TRUE`

in `vglm`

is useful for monitoring
the progress at each iteration.

An object of class `"vglmff"`

(see `vglmff-class`

).
The object is used by modelling functions such as `vglm`

and `vgam`

.

This family function should be used within `vglm`

and not with `rrvglm`

because it does not fit into
the RR-VGLM framework exactly. Instead, the reduced-rank model
is formulated as a VGLM!

A methods function `Coef.rrar`

, say, has yet to be written.
It would return the quantities
`Ak1`

,
`C`

,
`D`

,
`omegahat`

,
`Phi`

,
etc. as slots, and then `show.Coef.rrar`

would also need to be
written.

T. W. Yee

Ahn, S. and Reinsel, G. C. (1988).
Nested reduced-rank autoregressive models for multiple
time series.
*Journal of the American Statistical Association*,
**83**, 849–856.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 | ```
## Not run:
year <- seq(1961 + 1/12, 1972 + 10/12, by = 1/12)
par(mar = c(4, 4, 2, 2) + 0.1, mfrow = c(2, 2))
for (ii in 1:4) {
plot(year, grain.us[, ii], main = names(grain.us)[ii], las = 1,
type = "l", xlab = "", ylab = "", col = "blue")
points(year, grain.us[, ii], pch = "*", col = "blue")
}
apply(grain.us, 2, mean) # mu vector
cgrain <- scale(grain.us, scale = FALSE) # Center the time series only
fit <- vglm(cgrain ~ 1, rrar(Ranks = c(4, 1)), trace = TRUE)
summary(fit)
print(fit@misc$Ak1, digits = 2)
print(fit@misc$Cmatrices, digits = 3)
print(fit@misc$Dmatrices, digits = 3)
print(fit@misc$omegahat, digits = 3)
print(fit@misc$Phimatrices, digits = 2)
par(mar = c(4, 4, 2, 2) + 0.1, mfrow = c(4, 1))
for (ii in 1:4) {
plot(year, fit@misc$Z[, ii], main = paste("Z", ii, sep = ""),
type = "l", xlab = "", ylab = "", las = 1, col = "blue")
points(year, fit@misc$Z[, ii], pch = "*", col = "blue")
}
## End(Not run)
``` |

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