Nested Reduced-rank Autoregressive Models for Multiple Time Series

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

Usage

rrar(Ranks = 1, coefstart = NULL)

Arguments

Ranks

Vector of integers: the ranks of the model. Each value must be at least one and no more than M, where M is the number of response variables in the time series. The length of Ranks is the lag, which is often denoted by the symbol L in the literature.

coefstart

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

Details

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.

Value

An object of class "vglmff" (see vglmff-class). The object is used by modelling functions such as vglm and vgam.

References

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.

Author

T. W. Yee

Note

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.

Examples

if (FALSE) { # \dontrun{
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")
}
} # }