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stats_hurst-exponent

Read-onlyIdempotent

Calculate the Hurst exponent to classify a time series as mean-reverting, random walk, or trending. Provide a series to get exponent, classification, and confidence.

Instructions

Hurst exponent via rescaled range (R/S) analysis.

Use when determining if a time series is mean-reverting (H<0.5), random walk (H=0.5), or trending (H>0.5). Provide a price or return series. Returns: Hurst exponent via R/S analysis, classification, and confidence.

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
seriesYesTime series data
max_windowNoMaximum R/S window size (defaults to len/2)
min_windowNoMinimum R/S window size
Behavior4/5

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

Annotations declare readOnlyHint and idempotentHint, indicating a safe, deterministic operation. The description adds that it returns 'Hurst exponent, classification, and confidence,' which enriches understanding of the output without contradicting annotations.

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

Conciseness5/5

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

Three concise sentences, front-loaded with the tool's purpose, followed by usage guidance and return value. No redundant or irrelevant 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?

Covers the essential aspects: purpose, interpretation, input hint, and output. Lacks an output schema, but the description compensates by listing return components. Could be enhanced by noting the tool is safe and read-only, but annotations already provide that.

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

Parameters4/5

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

Schema description coverage is 100%, so baseline is 3. The description adds value by specifying 'Provide a price or return series,' which gives more concrete guidance than the schema's 'Time series data.'

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?

Description explicitly states the tool calculates the Hurst exponent via R/S analysis and explains the interpretation of H values for mean-reversion, random walk, or trending. It clearly distinguishes itself from sibling statistical tools by focusing on this specific analysis.

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?

Provides clear guidance on when to use: 'Use when determining if a time series is mean-reverting..., random walk..., or trending...' It does not explicitly state alternatives or when not to use, but the context is sufficient for selection among siblings.

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

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