Time Series — Diagnostics & Primary Modeling
Table of Contents
Open-source skill.
Scope Boundary
Use this skill when:
- The data are a univariate series indexed by calendar time and the first need is a classical ARIMA-style baseline.
- Trend, seasonality, stationarity, and short-horizon forecasting are the immediate priorities.
Do not use this skill when:
- The data are panel / longitudinal across subjects with few waves; use
vera-data-repeated-reviewing or vera-data-repeated-generating.
- The task is multivariate cross-series modeling, regime switching, or advanced forecasting from the start.
Workflow
Read each step file in workflow/ before executing that step.
| Step |
Responsibility |
Executor |
Document |
Input |
Output |
| Collect |
Collect Inputs |
Main Agent |
workflow/step01-collect-inputs.md |
User input |
Structured input summary |
| Diagnose |
Check Distribution |
Main Agent |
workflow/step02-check-distribution.md |
Prior step output |
PART 1 code block |
| Model |
Run Primary Test |
Main Agent |
workflow/step03-run-primary-test.md |
Prior step output |
PART 2-3 code blocks |
Decision Tree
1. STATIONARITY CHECK
├── Stationary (ADF p < .05 AND KPSS p ≥ .05) → fit ARIMA(p,0,q)
├── Non-stationary → difference, retest, fit ARIMA(p,d,q)
└── Seasonal pattern detected → recommend SARIMA
2. MODEL SELECTION
├── ACF/PACF inspection → candidate ARIMA(p,d,q) orders
├── Auto-ARIMA for automated selection (AIC minimization)
└── Ljung-Box residual diagnostics → confirm adequacy
Required Inputs
| Role |
What to collect |
| Time series (Y) |
Variable name, units, what it measures |
| Frequency |
Daily, weekly, monthly, quarterly, annual |
| Date/time index |
Column name or implicit ordering |
| Exogenous (optional) |
Any external predictors (for recommendation) |
Code Structure
PART 0: Setup & Data Loading
PART 1: Time Series Diagnostics → plot_01_ts_diagnostics.png
PART 2: Primary ARIMA Model → plot_02_forecast.png
PART 3: Recommendation Block → text listing additional analyses available
Reporting Standards
- p-values: "< .001" not "0.000"; exact to 3 decimals otherwise
- ADF test: report test statistic + p-value + number of lags used
- KPSS test: report test statistic + p-value + bandwidth
- Model notation: ARIMA(p,d,q) or ARIMA(p,d,q)(P,D,Q)[s]
- Information criteria: AIC and BIC
- Ljung-Box: Q statistic + lag + p-value. Use adaptive lag = min(⌊T/5⌋, 20) where T is series length — the fixed (5, 10, 15) scheme can underdetect misspecification in short series and overtest in long ones. Report the chosen lag explicitly.
- Forecast intervals: 80% and 95% prediction intervals
- Accuracy metrics: RMSE, MAE, MAPE on training data
- Decimal places: 2 for coefficients, 3 for p-values
- Non-significance: "not statistically significant at alpha = .05" — never "no effect"
Hypothesis Tests
| Test |
Null Hypothesis |
Stationary if |
| ADF (Augmented Dickey-Fuller) |
Unit root present (non-stationary) |
p < .05 (reject null) |
| KPSS |
Series is stationary |
p >= .05 (fail to reject null) |
Conflicting results → note ambiguity, proceed with differencing as conservative choice.
Example Dataset
R built-in AirPassengers: monthly airline passengers 1949-1960.
Python: sm.datasets.get_rdataset("AirPassengers") (with offline fallback to bundled examples/airpassengers.csv).
Method Status
| Status |
Methods |
| Implemented in this skill |
ADF/KPSS diagnostics, ACF/PACF-based ARIMA triage, baseline ARIMA/SARIMA fit, forecast intervals, residual checks |
Implemented downstream in vera-data-timeseries-generating |
ETS, GARCH, VAR, spectral analysis, regression with ARIMA errors, ML forecasting on lagged features |
| Out of scope in this open-source baseline |
Panel time series, spatial time series, and forecasting families not explicitly named above |
Minimal Smoke Test
- Smoke-test prompt: "Run
vera-data-timeseries-reviewing on AirPassengers, using the passenger count as the series and monthly frequency. Produce the standard baseline artifacts."
Cross-Skill Interface
Output:
├── code_r → .R script
├── code_python → .py script
├── figures/ → 2 PNGs (diagnostics + forecast)
└── recommendations → text block (additional analyses available)
Next step: Invoke vera-data-timeseries-generating from this skillset to run the full pipeline (additional tests, subgroup analysis, modeling, manuscript generation). See ../../CROSS-SKILL-INTERFACE.md for the shared handoff contract.
1---2name: vera-data-timeseries-reviewing3description: Runs time series diagnostics and primary ARIMA modeling for temporal data. Produces time plot, ACF/PACF, seasonal decomposition, stationarity tests (ADF + KPSS), and one fully interpreted ARIMA model with forecast and prediction intervals. Identifies trend, seasonality, and non-stationarity; fits ARIMA/SARIMA as baseline. Advanced methods (Prophet, state-space, VAR) delegated to vera-data-timeseries-generating. Outputs .R and .py scripts with 2 publication-quality plots. Triggered when user has temporal/time series data and says "time series," "temporal data," "forecast," "ARIMA," "seasonal," "trend," "autocorrelation," "monthly data," "daily data," "quarterly," "stationarity," or names a time-indexed variable like sales over time, temperature, stock price, monthly passengers. Does not handle panel/longitudinal data (redirect to vera-data-repeated-reviewing, or vera-data-repeated-generating for growth-curve / mixed-model extensions), cross-sectional data, or spatial time series.4---56# Time Series — Diagnostics & Primary Modeling78## Table of Contents910- [Scope Boundary](#scope-boundary)11- [Workflow](#workflow)12- [Decision Tree](#decision-tree)13- [Required Inputs](#required-inputs)14- [Code Structure](#code-structure)15- [Reporting Standards](#reporting-standards)16- [Hypothesis Tests](#hypothesis-tests)17- [Example Dataset](#example-dataset)18- [Method Status](#method-status)19- [Minimal Smoke Test](#minimal-smoke-test)20- [Cross-Skill Interface](#cross-skill-interface)212223Open-source skill.2425## Scope Boundary2627Use this skill when:28- The data are a univariate series indexed by calendar time and the first need is a classical ARIMA-style baseline.29- Trend, seasonality, stationarity, and short-horizon forecasting are the immediate priorities.3031Do not use this skill when:32- The data are panel / longitudinal across subjects with few waves; use `vera-data-repeated-reviewing` or `vera-data-repeated-generating`.33- The task is multivariate cross-series modeling, regime switching, or advanced forecasting from the start.3435## Workflow3637Read each step file in `workflow/` before executing that step.3839| Step | Responsibility | Executor | Document | Input | Output |40|---|---|---|---|---|---|41| Collect | Collect Inputs | Main Agent | `workflow/step01-collect-inputs.md` | User input | Structured input summary |42| Diagnose | Check Distribution | Main Agent | `workflow/step02-check-distribution.md` | Prior step output | PART 1 code block |43| Model | Run Primary Test | Main Agent | `workflow/step03-run-primary-test.md` | Prior step output | PART 2-3 code blocks |4445## Decision Tree4647```481. STATIONARITY CHECK49 ├── Stationary (ADF p < .05 AND KPSS p ≥ .05) → fit ARIMA(p,0,q)50 ├── Non-stationary → difference, retest, fit ARIMA(p,d,q)51 └── Seasonal pattern detected → recommend SARIMA52532. MODEL SELECTION54 ├── ACF/PACF inspection → candidate ARIMA(p,d,q) orders55 ├── Auto-ARIMA for automated selection (AIC minimization)56 └── Ljung-Box residual diagnostics → confirm adequacy57```5859## Required Inputs6061| Role | What to collect |62|---|---|63| **Time series (Y)** | Variable name, units, what it measures |64| **Frequency** | Daily, weekly, monthly, quarterly, annual |65| **Date/time index** | Column name or implicit ordering |66| **Exogenous (optional)** | Any external predictors (for recommendation) |6768## Code Structure6970```71PART 0: Setup & Data Loading72PART 1: Time Series Diagnostics → plot_01_ts_diagnostics.png73PART 2: Primary ARIMA Model → plot_02_forecast.png74PART 3: Recommendation Block → text listing additional analyses available75```7677## Reporting Standards78791. p-values: "< .001" not "0.000"; exact to 3 decimals otherwise802. ADF test: report test statistic + p-value + number of lags used813. KPSS test: report test statistic + p-value + bandwidth824. Model notation: ARIMA(p,d,q) or ARIMA(p,d,q)(P,D,Q)[s]835. Information criteria: AIC and BIC846. Ljung-Box: Q statistic + lag + p-value. Use **adaptive lag** = min(⌊T/5⌋, 20) where T is series length — the fixed (5, 10, 15) scheme can underdetect misspecification in short series and overtest in long ones. Report the chosen lag explicitly.857. Forecast intervals: 80% and 95% prediction intervals868. Accuracy metrics: RMSE, MAE, MAPE on training data879. Decimal places: 2 for coefficients, 3 for p-values8810. Non-significance: "not statistically significant at alpha = .05" — never "no effect"8990## Hypothesis Tests9192| Test | Null Hypothesis | Stationary if |93|---|---|---|94| ADF (Augmented Dickey-Fuller) | Unit root present (non-stationary) | p < .05 (reject null) |95| KPSS | Series is stationary | p >= .05 (fail to reject null) |9697Conflicting results → note ambiguity, proceed with differencing as conservative choice.9899## Example Dataset100101R built-in `AirPassengers`: monthly airline passengers 1949-1960.102Python: `sm.datasets.get_rdataset("AirPassengers")` (with offline fallback to bundled `examples/airpassengers.csv`).103104## Method Status105106| Status | Methods |107|---|---|108| Implemented in this skill | ADF/KPSS diagnostics, ACF/PACF-based ARIMA triage, baseline ARIMA/SARIMA fit, forecast intervals, residual checks |109| Implemented downstream in `vera-data-timeseries-generating` | ETS, GARCH, VAR, spectral analysis, regression with ARIMA errors, ML forecasting on lagged features |110| Out of scope in this open-source baseline | Panel time series, spatial time series, and forecasting families not explicitly named above |111112## Minimal Smoke Test113114- Smoke-test prompt: "Run `vera-data-timeseries-reviewing` on `AirPassengers`, using the passenger count as the series and monthly frequency. Produce the standard baseline artifacts."115116## Cross-Skill Interface117118```119Output:120├── code_r → .R script121├── code_python → .py script122├── figures/ → 2 PNGs (diagnostics + forecast)123└── recommendations → text block (additional analyses available)124```125126Next step: Invoke `vera-data-timeseries-generating` from this skillset to run the full pipeline (additional tests, subgroup analysis, modeling, manuscript generation). See `../../CROSS-SKILL-INTERFACE.md` for the shared handoff contract.
VeraSuperHub