Realized Kernel
Install and import#
npm install fintech-algorithmsimport { calculate } from "fintech-algorithms/volatility-and-covariance/realized-measures/realized-kernel";Signature#
calculate(data)Explain each weighted lag correction to realized variance. Supplied-parameter educational reference; no fitted performance claim.
Parameters#
| Name | Type | Notes |
|---|---|---|
data | TopicInput | See data-contract/CONTRACT.md. |
Returns#
TopicResult
Structured result with readiness, values, parameters, and diagnostics.
Warm-up#
The first depends on window or model order positions are null prefix until minimum history exists.
Errors#
- When required data is missing, non-finite, malformed, or out of range — raises ContractError / Error
Complexity: time O(nwH),
space Full diagnostic trace retained for teaching; see implementation for observation/window/matrix dimensions.
Worked example#
executed Captured by running this function on the input its own test provides. Real output of real code — but not asserted against a published figure.
Input#
{
"returns": [0.01, -0.02, 0.03, -0.01],
"parameters": {
"window": 4,
"annualization_factor": 1,
"bandwidth": 1
}
}Call#
calculate(data)Returns#
object with 8 fields: topic_id, title, parameters, series, latest, ready, ready_at, diagnostics
{
"topic_id": "D10-F02-A05",
"title": "Realized Kernel",
"parameters": {
"window": 4,
"annualization_factor": 1,
"bandwidth": 1
},
"series": [
null,
null,
null,
{
"realized_kernel": 0.0004000000000000002,
"volatility": 0.020000000000000004,
"bandwidth": 1,
"lags": [
{
"lag": 0,
"weight": 1,
"gamma": 0.0015,
"contribution": 0.0015
},
{
"lag": 1,
"weight": 0.5,
"gamma": -0.0010999999999999998,
"contribution": -0.0010999999999999998
}
],
"window_start": 0,
"window_end": 3
}
],
"latest": {
"realized_kernel": 0.0004000000000000002,
"volatility": 0.020000000000000004,
"bandwidth": 1,
"lags": [
{
"lag": 0,
"weight": 1,
"gamma": 0.0015,
"contribution": 0.0015
},
{
"lag": 1,
"weight": 0.5,
"gamma": -0.0010999999999999998,
"contribution": -0.0010999999999999998
}
],
"window_start": 0,
"window_end": 3
},
"ready": true,
"ready_at": 3,
"diagnostics": {
"causal": true,
"input_count": 4,
"annualization_factor": 1
}
}Diagrams#
Calculation flow#
Realized Kernel — calculation-flow
flowchart TD
N0["Lag zero = realized variance"]
N1["Compute signed lag products"]
N2["Apply Bartlett weights and factor two"]
N3["Sum the quadratic-form contributions"]
N0 --> N1 --> N2 --> N3
Realized Kernel — decision-boundary
flowchart TD
A["Supplied observations and parameters"] --> B{"Contract valid?"}
B -->|No| E["Reject with explicit error"]
B -->|Yes| C{"Required history available?"}
C -->|No| W["Withhold; never insert zero"]
C -->|Yes| D["Realized Kernel calculation"]
D --> F["Inspect diagnostics and stated limits"]
How it works#
This page states the contract — how to call it correctly. The article explains the concept: why it works, and where it breaks.
References#
- Scope of evidence