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variance_decomposition

Decompose forecast-error variance by series and horizon to show how much each innovation contributes to unpredictability, with optional Monte-Carlo bands.

Instructions

N6 — Forecast-error variance decomposition of the last estimated model.

For each series and horizon, the share of its forecast-error variance that comes from each series' innovation: how much of what is not predictable in one series is really the other's surprise. Same Cholesky order as impulse_response, and the same caveat: with correlated innovations the shares of the first series in the order are inflated by construction. With bands (default): 95% Monte-Carlo bands at the last horizon. On a VEC: the decomposition of the LEVELS' forecast errors (drvec), with the bootstrap's bands when irf_bands has run.

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": "variance_decomposition"
  }
}

Input Schema

Name	Required	Description	Default
`name`	Yes
`bands`	No
`ndraws`	No
`horizon`	No

Output Schema

Name	Required	Description	Default
`result`	Yes

Schema Changelog

Changes observed during successful MCP inspections.

First observedv0.2.0Oct 30, 2026

TDQS

A4/5.0

Behavior4/5

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

With no annotations, the description carries the burden and does disclose meaningful behavior: the Cholesky-ordering caveat that first-series shares are inflated by construction, the default Monte-Carlo bands, and the VEC levels/bootstrapped-bands special case. It doesn't state failure behavior when no model has been estimated, but the analytical caveats it does expose are genuinely valuable.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness4/5

Is the description appropriately sized, front-loaded, and free of redundancy?

Purpose is front-loaded and the paragraph breaks separate the core definition, the caveat, the bands behavior, and the VEC branch. Slightly verbose in places but essentially every sentence adds usable information.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness4/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

For a complex statistical procedure with an output schema present, the description covers what is computed, the ordering caveat, band defaults, and the VEC variant — enough for an agent to call it deliberately. The main omission is explaining how `horizon` and `ndraws` change the result, which prevents a 5.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters2/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema coverage is 0%, so the description must compensate, but it only clarifies one of four params: `bands` (default, 95% MC bands at last horizon). `horizon`, `ndraws`, and `name` are never explained in meaning or effect, leaving the agent to guess their semantics from bare titles.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose5/5

Does the description clearly state what the tool does and how it differs from similar tools?

States a specific verb+resource: 'Forecast-error variance decomposition of the last estimated model,' and elaborates what each output cell means ('the share of its forecast-error variance that comes from each series' innovation'). It also distinguishes itself from the graphical sibling and from impulse_response via the shared Cholesky order, so an agent can place it precisely among the ~45 siblings.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines4/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

Implies the prerequisite clearly ('of the last estimated model') and names the related sibling whose ordering and caveats it inherits (impulse_response). It also specifies the VEC branch. It never explicitly says when to use this instead of impulse_response or plot_variance_decomposition, so it stops short of full routing guidance.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.