Time Series Process Data Analysis

Time-Series Diagnostics and Block Bootstrap for Process Data

Overview

Process data are almost always autocorrelated, which means ordinary i.i.d. inference (Wald CIs, t-tests, normal CIs) understates uncertainty. This skill provides:

• Sample ACF and PACF.
• A simple block-length heuristic (2 × first lag where |rho| < 2/sqrt(n)).
• Moving-block bootstrap (Kuensch 1989) for built-in statistics exposed by

the CLI: mean, median, standard deviation, minimum, and maximum.

The ACF/PACF are useful for picking residual-autocorrelation orders for regressions and for selecting a sensible block length.

Prerequisites

1. uv available.
2. On first use, the script writes LICENSE_NOTIFICATION.txt.

When to Use

• Computing a CI for the mean of a daily lab series.
• Diagnosing autocorrelation before using a separate regression workflow.
• Diagnosing the order of a residual AR(p) for ARIMA / DLM modelling.
• Picking a block length for downstream block-bootstrap procedures.

Don't use for

• Stationary white-noise data — use engineering-statistics.
• Forecasting future values — use a state-space model.
• Strongly non-stationary data — pre-process (detrend, deseasonalise) first.

Utility Scripts

• uv run scripts/ts.py acf --data series.csv --column y --max-lag 30 --output /tmp/acf.json
• uv run scripts/ts.py pacf --data series.csv --column y --max-lag 30 --output /tmp/pacf.json
• uv run scripts/ts.py block-len --data series.csv --column y --output /tmp/L.json
• uv run scripts/ts.py bootstrap --data series.csv --column y --block-length 8 --n-resamples 2000 --statistic mean --output /tmp/bs.json

Procedure

1. Compute ACF and PACF; eyeball the lag structure.
2. Pick a block length:

• Use the block-len helper as a starting point.
• For short series (< 200), constrain block length to ≤ n/4.
• For long series, consider Politis-White optimal block length

(not implemented; use statsmodels if needed).

1. Choose a supported statistic (mean, median, std, min, or max).
2. Run the bootstrap. Compare the bootstrap SE / CI against the i.i.d.

counterpart; the bootstrap should be wider for positively autocorrelated data.

1. Report both intervals for transparency.

Pitfalls

• Using ordinary bootstrap (i.i.d. resampling) on autocorrelated data; the

CI is too narrow.

• Using a tiny block length (e.g. 2-3) for very autocorrelated data; the

CI is still too narrow.

• Using a huge block length (≥ n/4); the bootstrap has very few effective

resamples and the CI is unreliable.

• Reporting block-bootstrap CIs without specifying the block length.
• Treating the PACF as if it were independent of ACF; they are connected

by the Durbin-Levinson recursion.

• Treating spikes outside ±2/sqrt(n) as automatically meaningful; the

multiple-testing rate is not controlled.

• Failing to detrend / deseasonalise before computing ACF; non-stationary

trends inflate the ACF.

Fallback Strategies

• If the series is too short for block bootstrap (<50), report the i.i.d.

CI with a warning that it likely understates uncertainty.

• If statsmodels is available, use it for ARIMA-style residual diagnostics

(not implemented here).

Verification

• Run the listed script with representative inputs and an --output file when a deterministic calculation is available.
• Confirm the JSON result contains ok: true, expected units, and no unhandled warnings.
• Check result magnitudes against the stated assumptions, references, and a hand calculation or known operating range before reporting them.

References

• references/methods_notes.md — block-bootstrap derivation, references.
• Kuensch, H. R. "The Jackknife and the Bootstrap for General Stationary

Observations," Annals of Statistics, 1989.

• Politis & Romano, Subsampling.

Anti-Patterns

• Quoting "p < 0.05" on a process-data regression without addressing

autocorrelation.

• Designing SPC limits assuming independence on data that is clearly

serially correlated.

• Using the bootstrap to "rescue" a model that is misspecified.

Source & license

This open-source skill is cataloged on AgentStack and links to its original source — we do not rehost the code.

• Author: jskherman
• Source: jskherman/engg-skills
• License: Apache-2.0

Install and usage instructions live in the source repository linked above.