identify_echelon
Identifies the ECHELON VARMA form and Kronecker indices from time-series data, searching candidate row degrees by SC/HQ to reveal which AR/MA cross terms are free.
Instructions
N2 — the third form, the ECHELON VARMA of Lutkepohl and Poskitt (1996), and its Kronecker indices from the data.
The indices n_i are the row degrees of the system's unique echelon form:
series i gets its own AR(n_i)/MA(n_i), and their table says which cross
terms are free, the contemporaneous ones included. Unlike the VARMA(p, q),
the form is identified: no common factors, no MA driven to the wall by
spare parameters. The univariate orders do NOT give the indices (every
component's marginal is ARMA(N, N), N = the sum of the indices), so they
are searched on the stationary vector: a long VAR (its residuals stand
for the innovations), then least squares on each candidate's echelon form
with one round of Hannan and Kavalieris' correction, and a criterion. SC
(default) or HQ, which overfits. Every candidate with each index in
0..max_index while there are at most 256, Hannan and Kavalieris' two
steps beyond.
The ORDER of the series is part of the echelon form (A_0 is lower triangular): the indices are those of the files' order. Measured on simulated systems (drvarma docs/STUDY-echelon-search.md): the true indices in 80-97 % of the replications, more with more data; weak cross dynamics are missed (the search underfits), which check_residuals then shows.
On ROUTE U each univariate model's seasonal and fixed-frequency factors are its row's FACTOR (they multiply the whole row; drvarma's echelon stage 4) and the search runs on each row filtered by them; the univariate regular ARMA is replaced by the row's own AR(n_i)/MA(n_i).
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": "identify_echelon"
}
}Input Schema
| Name | Required | Description | Default |
|---|---|---|---|
| name | Yes | ||
| criterion | No | SC | |
| max_index | No |
Output Schema
| Name | Required | Description | Default |
|---|---|---|---|
| result | Yes |