estimate
Fit a joint VARMA candidate with specified cross orders, optional linked pairs, and full/diagonal covariance, then report parameters, LR tests, innovation correlations, and optimizer diagnostics.
Instructions
N3/N4 — Estimate a candidate: cross orders p, q; full or diagonal covariance.
Each series keeps its univariate model on the diagonal (its ARMA factors are
re-estimated jointly, its deterministic terms stay as in its file). Reports
the parameters, the LR test against the univariates (in sample: necessary,
not sufficient), the innovation correlations, the residual portmanteau and
how the optimiser stopped. reason is recorded in the guion: say why this
candidate.
links restricts the cross dynamics to the pairs the evidence points at:
"A<-B, C<-A" (B enters the equation of A, AR and MA, every lag up to p and
q; names as in identify_cross). Empty (default): every pair. identify_cross
proposes it as option (d) when only some pairs showed anything.
start: where the cross terms start — "zero" (the default for the
VARMA) or "preliminary", Jenkins and Alavi's preliminary estimates (the
cross MA from the univariate residuals' cross covariances, the cross AR
from Yule-Walker). Usually the same optimum in fewer iterations; on an
ill-defined estimation (the MA wall) a second path worth comparing. The
echelon form starts at Lutkepohl and Poskitt's least-squares estimates
("echelon", its default).
cross: how the cross MA enters — "additive" (default: a cross polynomial
beside the univariate operators) or "residual", Jenkins and Alavi's form
(3.22): a model for the univariate residuals, multiplied by each series'
univariate MA. The same when the univariate models have no MA factors;
when they have (an airline), the two are different candidates — on m6 the
residual form converged inside where the additive one stopped on the MA
wall. identify_matrices' method 2 proposes it.
zeros: coefficients held at zero, by their printed names — Tiao and
Box's simplification (simplify proposes them): cross ones "AR3[A<-B],
MA1[B<-A]" on either route; a series' own "phi_A[B^4], theta_A[B^1]" on
route V, and on route U in the echelon form (with indices), whose own
AR(n_i)/MA(n_i) is sima's; otherwise route U's diagonal is the univariate
model, art's. A fit already made with the same arguments is reused, not
refitted.
indices: the ECHELON FORM with these Kronecker indices, one per series
in the files' order, e.g. "1, 2, 1" (identify_echelon proposes them).
Series i gets a free AR(n_i)/MA(n_i) of its own, the cross terms follow
Lutkepohl and Poskitt's (1996) table, and the contemporaneous AR0[i<-j]
terms make A_0 lower triangular: the order of the series is part of the
model. p and q are then max(n_i); leave them at 0. links and zeros
restrict it further. On route U the free AR(n_i)/MA(n_i) replaces the
univariate model's regular ARMA, and its seasonal and fixed-frequency
factors multiply the whole row (the row FACTOR), checked by an LR test
against the same rows with the factor's restriction dropped.
Tool call template
Replace each placeholder with a value matching the input schema. Only required parameters are included; add optional parameters as needed.
{
"id": 1,
"jsonrpc": "2.0",
"method": "tools/call",
"params": {
"arguments": {
"name": "<name>"
},
"name": "estimate"
}
}Input Schema
| Name | Required | Description | Default |
|---|---|---|---|
| p | No | ||
| q | No | ||
| name | Yes | ||
| cross | No | additive | |
| links | No | ||
| start | No | ||
| zeros | No | ||
| reason | No | ||
| diagcov | No | ||
| indices | No |
Output Schema
| Name | Required | Description | Default |
|---|---|---|---|
| result | Yes |