Description
Generate a retained initial value followed by Gaussian drift/noise increments on an explicit increasing seconds grid, then delegate cumulative sums and trailing moving averages with the core's 12-digit convention; no forecast or real-process claim.
Synthetic statistical data separates a specified generating model from the values observed in a finite draw. A model parameter, a sample summary, and the result of a fitted analysis answer different questions; retaining them separately makes numerical and statistical checks easier to interpret.
Generate a retained initial value followed by Gaussian drift/noise increments on an explicit increasing seconds grid, then delegate cumulative sums and trailing moving averages with the core's 12-digit convention; no forecast or real-process claim.
When to use this tool
Use this generator to create reproducible time series cases from the supplied model or bank. Inspect the returned evidence before using cases in a test or exercise.
How to use the tool and how it works
- Supply count, initialValue, driftPerStep, noiseStandardDeviationPerStep, startTimeSeconds, timeStepSeconds, windowSize in the field shapes below. Set seed when you need an explicit replay.
- Run the tool and correct any input error. For generated controls, distinguish a successful fixture containing an invalid case from failure to generate the fixture.
- Read timesSeconds, values, increments, smoothedTimesSeconds, smoothedValues. Use the conventions below and keep answer-bearing fields separate when presenting an exercise.
Starting at initialValue, successive values add driftPerStep plus Gaussian noise scaled by noiseStdPerStep. Times are startSecond plus index times stepSeconds. Delegated calculations return cumulative sums and a trailing moving average whose times align with window ends.1
Delegated operations used for this result: cumulative sum; moving average. Their calculation or parsing conventions apply to the corresponding result fields.2, 3
| Input field | Meaning and units | Accepted input |
|---|---|---|
| count | Requested count; the mechanics explain whether one draw expands into several returned records. | Required. Safe integer; minimum 1; maximum 2048. |
| initialValue | Initial Value | Required. Finite number. |
| driftPerStep | Drift Per Step | Required. Finite number. |
| noiseStandardDeviationPerStep | Noise Standard Deviation Per Step | Required. Finite number; minimum 0. |
| startTimeSeconds | Explicit first sample time in seconds. | Required. Finite number. |
| timeStepSeconds | Time Step Seconds | Required. Finite number; strictly above 0. |
| windowSize | Window Size | Required. Safe integer; minimum 1; maximum 2048. |
| seed | Optional numeric seed; takes precedence over context randomness. Without either, use the fixed tool.io default seed. | Optional. Safe integer. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| timesSeconds | Times Seconds | Required. Array of Finite number.; minimum items 1; maximum items 2048. |
| values | Values | Required. Array of Finite number.; minimum items 1; maximum items 2048. |
| increments | Increments | Required. Array of Finite number.; minimum items 0; maximum items 2047. |
| smoothedTimesSeconds | Smoothed Times Seconds | Required. Array of Finite number.; minimum items 1; maximum items 2048. |
| smoothedValues | Smoothed Values | Required. Array of Finite number.; minimum items 1; maximum items 2048. |
| randomness | Replay metadata: source is seed or context; seed is the normalized 32-bit seed or null for a context source. | Required. Object; no unknown keys. |
| randomness.seed | Optional numeric replay seed; normalization and precedence are explained below. | Required. Safe integer. or Null. |
| randomness.source | Source | Required. Text; one of "context", "seed". |
An explicit safe-integer seed takes precedence over injected context randomness and is normalized to an unsigned 32-bit integer. With no seed and no context source, replay uses the fixed tool.io default seed. A context source must return finite values from zero inclusive to one exclusive; its advancing state must be retained separately. randomness records the source and normalized seed, or null for context. These generators are not cryptographic random sources.
{
"input": {
"count": 6,
"initialValue": 10,
"driftPerStep": 0.2,
"noiseStandardDeviationPerStep": 0.1,
"startTimeSeconds": 0,
"timeStepSeconds": 60,
"windowSize": 3,
"seed": 42
},
"output": {
"timesSeconds": [
0,
60,
120,
180,
240,
300
],
"values": [
10,
10.104383777061585,
10.277081166573325,
10.292918448094964,
10.378830240999562,
10.52588686162792
],
"increments": [
0.10438377706158511,
0.17269738951173896,
0.015837281521640323,
0.08591179290459759,
0.14705662062835848
],
"smoothedTimesSeconds": [
120,
180,
240,
300
],
"smoothedValues": [
10.1271549812,
10.2247944639,
10.3162766186,
10.3992118502
],
"randomness": {
"seed": 42,
"source": "seed"
}
}
}Limitations and assumptions
- This is a synthetic discrete process, not a fitted forecast. The smoothing window cannot exceed count; timestamps must remain finite and distinguishable. Delegated aggregates retain their numeric rounding conventions.
- A replay requires the same complete input and implementation. Randomized construction does not guarantee uniform coverage of every feasible output; finite samples can repeat unless a distinct-selection rule is explicitly stated.
- The field tables state structural bounds; cross-field constraints and bounded search or output budgets also apply. Unknown keys are rejected where the object contract disallows them. Input errors are distinct from null fields and deliberate invalid controls in a successful output.
Alternative or Complementary methods
For a supplied example, inspect the returned construction or delegated check directly. To evaluate a consumer, also test cases chosen for its own boundaries; a generated finite corpus does not establish exhaustive coverage.
References
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