Timesfm Forecasting

TimesFM Forecasting

Overview

TimesFM (Time Series Foundation Model) is a pretrained decoder-only foundation model developed by Google Research for time-series forecasting. It works zero-shot 鈥?feed it any univariate time series and it returns point forecasts with calibrated quantile prediction intervals, no training required.

This skill wraps TimesFM for safe, agent-friendly local inference. It includes a mandatory preflight system checker that verifies RAM, GPU memory, and disk space before the model is ever loaded so the agent never crashes a user's machine.

Key numbers: TimesFM 2.5 uses 200M parameters (~800 MB on disk, ~1.5 GB in RAM on CPU, ~1 GB VRAM on GPU). The archived v1/v2 500M-parameter model needs ~32 GB RAM. Always run the system checker first.

When to Use This Skill

Use this skill when:

• Forecasting any univariate time series (sales, demand, sensor, vitals, price, weather)
• You need zero-shot forecasting without training a custom model
• You want probabilistic forecasts with calibrated prediction intervals (quantiles)
• You have time series of any length (the model handles 1鈥?6,384 context points)
• You need to batch-forecast hundreds or thousands of series efficiently
• You want a foundation model approach instead of hand-tuning ARIMA/ETS parameters

Do not use this skill when:

• You need classical statistical models with coefficient interpretation 鈫?use statsmodels
• You need time series classification or clustering 鈫?use aeon
• You need multivariate vector autoregression or Granger causality 鈫?use statsmodels
• Your data is tabular (not temporal) 鈫?use scikit-learn

Note on Anomaly Detection: TimesFM does not have built-in anomaly detection, but you can use the quantile forecasts as prediction intervals 鈥?values outside the 90% CI (q10鈥搎90) are statistically unusual. See the examples/anomaly-detection/ directory for a full example.

鈿狅笍 Mandatory Preflight: System Requirements Check

CRITICAL 鈥?ALWAYS run the system checker before loading the model for the first time.

python scripts/check_system.py

This script checks:

1. Available RAM 鈥?warns if below 4 GB, blocks if below 2 GB
2. GPU availability 鈥?detects CUDA/MPS devices and VRAM
3. Disk space 鈥?verifies room for the ~800 MB model download
4. Python version 鈥?requires 3.10+
5. Existing installation 鈥?checks if timesfm and torch are installed

Note: Model weights are NOT stored in this repository. TimesFM weights (800 MB) download on-demand from HuggingFace on first use and cache in `/.cache/huggingface/`. The preflight checker ensures sufficient resources before any download begins.

flowchart TD
    accTitle: Preflight System Check
    accDescr: Decision flowchart showing the system requirement checks that must pass before loading TimesFM.

    start["馃殌 Run check_system.py"] --> ram{"RAM 鈮?4 GB?"}
    ram -->|"Yes"| gpu{"GPU available?"}
    ram -->|"No (2-4 GB)"| warn_ram["鈿狅笍 Warning: tight RAM<br/>CPU-only, small batches"]
    ram -->|"No (< 2 GB)"| block["馃洃 BLOCKED<br/>Insufficient memory"]
    warn_ram --> disk
    gpu -->|"CUDA / MPS"| vram{"VRAM 鈮?2 GB?"}
    gpu -->|"CPU only"| cpu_ok["鉁?CPU mode<br/>Slower but works"]
    vram -->|"Yes"| gpu_ok["鉁?GPU mode<br/>Fast inference"]
    vram -->|"No"| cpu_ok
    gpu_ok --> disk{"Disk 鈮?2 GB free?"}
    cpu_ok --> disk
    disk -->|"Yes"| ready["鉁?READY<br/>Safe to load model"]
    disk -->|"No"| block_disk["馃洃 BLOCKED<br/>Need space for weights"]

    classDef ok fill:#dcfce7,stroke:#16a34a,stroke-width:2px,color:#14532d
    classDef warn fill:#fef9c3,stroke:#ca8a04,stroke-width:2px,color:#713f12
    classDef block fill:#fee2e2,stroke:#dc2626,stroke-width:2px,color:#7f1d1d
    classDef neutral fill:#f3f4f6,stroke:#6b7280,stroke-width:2px,color:#1f2937

    class ready,gpu_ok,cpu_ok ok
    class warn_ram warn
    class block,block_disk block
    class start,ram,gpu,vram,disk neutral

Hardware Requirements by Model Version

Recommendation: Always use TimesFM 2.5 unless you have a specific reason to use an older checkpoint. It is smaller, faster, and supports 8脳 longer context.

馃敡 Installation

Step 1: Verify System (always first)

python scripts/check_system.py

Step 2: Install TimesFM

# Using uv (recommended by this repo)
uv pip install timesfm[torch]

# Or using pip
pip install timesfm[torch]

# For JAX/Flax backend (faster on TPU/GPU)
uv pip install timesfm[flax]

Step 3: Install PyTorch for Your Hardware

# CUDA 12.1 (NVIDIA GPU)
pip install torch>=2.0.0 --index-url https://download.pytorch.org/whl/cu121

# CPU only
pip install torch>=2.0.0 --index-url https://download.pytorch.org/whl/cpu

# Apple Silicon (MPS)
pip install torch>=2.0.0  # MPS support is built-in

Step 4: Verify Installation

import timesfm
import numpy as np
print(f"TimesFM version: {timesfm.__version__}")
print("Installation OK")

馃幆 Quick Start

Minimal Example (5 Lines)

import torch, numpy as np, timesfm

torch.set_float32_matmul_precision("high")

model = timesfm.TimesFM_2p5_200M_torch.from_pretrained(
    "google/timesfm-2.5-200m-pytorch"
)
model.compile(timesfm.ForecastConfig(
    max_context=1024, max_horizon=256, normalize_inputs=True,
    use_continuous_quantile_head=True, force_flip_invariance=True,
    infer_is_positive=True, fix_quantile_crossing=True,
))

point, quantiles = model.forecast(horizon=24, inputs=[
    np.sin(np.linspace(0, 20, 200)),  # any 1-D array
])
# point.shape == (1, 24)        鈥?median forecast
# quantiles.shape == (1, 24, 10) 鈥?10th鈥?0th percentile bands

Forecast from CSV

import pandas as pd, numpy as np

df = pd.read_csv("monthly_sales.csv", parse_dates=["date"], index_col="date")

# Convert each column to a list of arrays
inputs = [df[col].dropna().values.astype(np.float32) for col in df.columns]

point, quantiles = model.forecast(horizon=12, inputs=inputs)

# Build a results DataFrame
for i, col in enumerate(df.columns):
    last_date = df[col].dropna().index[-1]
    future_dates = pd.date_range(last_date, periods=13, freq="MS")[1:]
    forecast_df = pd.DataFrame({
        "date": future_dates,
        "forecast": point[i],
        "lower_80": quantiles[i, :, 2],  # 20th percentile
        "upper_80": quantiles[i, :, 8],  # 80th percentile
    })
    print(f"\n--- {col} ---")
    print(forecast_df.to_string(index=False))

Forecast with Covariates (XReg)

TimesFM 2.5+ supports exogenous variables through forecast_with_covariates(). Requires timesfm[xreg].

# Requires: uv pip install timesfm[xreg]
point, quantiles = model.forecast_with_covariates(
    inputs=inputs,
    dynamic_numerical_covariates={"price": price_arrays},
    dynamic_categorical_covariates={"holiday": holiday_arrays},
    static_categorical_covariates={"region": region_labels},
    xreg_mode="xreg + timesfm",  # or "timesfm + xreg"
)

XReg Modes:

• "xreg + timesfm" (default): TimesFM forecasts first, then XReg adjusts residuals
• "timesfm + xreg": XReg fits first, then TimesFM forecasts residuals

See examples/covariates-forecasting/ for a complete example with synthetic retail data.

Anomaly Detection (via Quantile Intervals)

TimesFM does not have built-in anomaly detection, but the quantile forecasts naturally provide prediction intervals that can detect anomalies:

point, q = model.forecast(horizon=H, inputs=[values])

# 90% prediction interval
lower_90 = q[0, :, 1]  # 10th percentile
upper_90 = q[0, :, 9]  # 90th percentile

# Detect anomalies: values outside the 90% CI
actual = test_values  # your holdout data
anomalies = (actual < lower_90) | (actual > upper_90)

# Severity levels
is_warning = (actual < q[0, :, 2]) | (actual > q[0, :, 8])  # outside 80% CI
is_critical = anomalies  # outside 90% CI

See examples/anomaly-detection/ for a complete example with visualization.

# Requires: uv pip install timesfm[xreg]
point, quantiles = model.forecast_with_covariates(
    inputs=inputs,
    dynamic_numerical_covariates={"temperature": temp_arrays},
    dynamic_categorical_covariates={"day_of_week": dow_arrays},
    static_categorical_covariates={"region": region_labels},
    xreg_mode="xreg + timesfm",  # or "timesfm + xreg"
)

馃搳 Understanding the Output

Quantile Forecast Structure

TimesFM returns (point_forecast, quantile_forecast):

• point_forecast: shape (batch, horizon) 鈥?the median (0.5 quantile)
• quantile_forecast: shape (batch, horizon, 10) 鈥?ten slices:

Extracting Prediction Intervals

point, q = model.forecast(horizon=H, inputs=data)

# 80% prediction interval (most common)
lower_80 = q[:, :, 1]  # 10th percentile
upper_80 = q[:, :, 9]  # 90th percentile

# 60% prediction interval (tighter)
lower_60 = q[:, :, 2]  # 20th percentile
upper_60 = q[:, :, 8]  # 80th percentile

# Median (same as point forecast)
median = q[:, :, 5]

flowchart LR
    accTitle: Quantile Forecast Anatomy
    accDescr: Diagram showing how the 10-element quantile vector maps to prediction intervals.

    input["馃搱 Input Series<br/>1-D array"] --> model["馃 TimesFM<br/>compile + forecast"]
    model --> point["馃搷 Point Forecast<br/>(batch, horizon)"]
    model --> quant["馃搳 Quantile Forecast<br/>(batch, horizon, 10)"]
    quant --> pi80["80% PI<br/>q[:,:,1] 鈥?q[:,:,9]"]
    quant --> pi60["60% PI<br/>q[:,:,2] 鈥?q[:,:,8]"]
    quant --> median["Median<br/>q[:,:,5]"]

    classDef data fill:#dbeafe,stroke:#2563eb,stroke-width:2px,color:#1e3a5f
    classDef model fill:#f3e8ff,stroke:#9333ea,stroke-width:2px,color:#581c87
    classDef output fill:#dcfce7,stroke:#16a34a,stroke-width:2px,color:#14532d

    class input data
    class model model
    class point,quant,pi80,pi60,median output

馃敡 ForecastConfig Reference

All forecasting behavior is controlled by timesfm.ForecastConfig:

timesfm.ForecastConfig(
    max_context=1024,                    # Max context window (truncates longer series)
    max_horizon=256,                     # Max forecast horizon
    normalize_inputs=True,               # Normalize inputs (RECOMMENDED for stability)
    per_core_batch_size=32,              # Batch size per device (tune for memory)
    use_continuous_quantile_head=True,   # Better quantile accuracy for long horizons
    force_flip_invariance=True,          # Ensures f(-x) = -f(x) (mathematical consistency)
    infer_is_positive=True,              # Clamp forecasts 鈮?0 when all inputs > 0
    fix_quantile_crossing=True,          # Ensure q10 鈮?q20 鈮?... 鈮?q90
    return_backcast=False,               # Return backcast (for covariate workflows)
)

馃搵 Common Workflows

Workflow 1: Single Series Forecast

flowchart TD
    accTitle: Single Series Forecast Workflow
    accDescr: Step-by-step workflow for forecasting a single time series with system checking.

    check["1. Run check_system.py"] --> load["2. Load model<br/>from_pretrained()"]
    load --> compile["3. Compile with ForecastConfig"]
    compile --> prep["4. Prepare data<br/>pd.read_csv 鈫?np.array"]
    prep --> forecast["5. model.forecast()<br/>horizon=N"]
    forecast --> extract["6. Extract point + PI"]
    extract --> plot["7. Plot or export results"]

    classDef step fill:#f3f4f6,stroke:#6b7280,stroke-width:2px,color:#1f2937
    class check,load,compile,prep,forecast,extract,plot step

import torch, numpy as np, pandas as pd, timesfm

# 1. System check (run once)
# python scripts/check_system.py

# 2-3. Load and compile
torch.set_float32_matmul_precision("high")
model = timesfm.TimesFM_2p5_200M_torch.from_pretrained(
    "google/timesfm-2.5-200m-pytorch"
)
model.compile(timesfm.ForecastConfig(
    max_context=512, max_horizon=52, normalize_inputs=True,
    use_continuous_quantile_head=True, fix_quantile_crossing=True,
))

# 4. Prepare data
df = pd.read_csv("weekly_demand.csv", parse_dates=["week"])
values = df["demand"].values.astype(np.float32)

# 5. Forecast
point, quantiles = model.forecast(horizon=52, inputs=[values])

# 6. Extract prediction intervals
forecast_df = pd.DataFrame({
    "forecast": point[0],
    "lower_80": quantiles[0, :, 1],
    "upper_80": quantiles[0, :, 9],
})

# 7. Plot
import matplotlib.pyplot as plt
fig, ax = plt.subplots(figsize=(12, 5))
ax.plot(values[-104:], label="Historical")
x_fc = range(len(values[-104:]), len(values[-104:]) + 52)
ax.plot(x_fc, forecast_df["forecast"], label="Forecast", color="tab:orange")
ax.fill_between(x_fc, forecast_df["lower_80"], forecast_df["upper_80"],
                alpha=0.2, color="tab:orange", label="80% PI")
ax.legend()
ax.set_title("52-Week Demand Forecast")
plt.tight_layout()
plt.savefig("forecast.png", dpi=150)
print("Saved forecast.png")

Workflow 2: Batch Forecasting (Many Series)

import pandas as pd, numpy as np

# Load wide-format CSV (one column per series)
df = pd.read_csv("all_stores.csv", parse_dates=["date"], index_col="date")
inputs = [df[col].dropna().values.astype(np.float32) for col in df.columns]

# Forecast all series at once (batched internally)
point, quantiles = model.forecast(horizon=30, inputs=inputs)

# Collect results
results = {}
for i, col in enumerate(df.columns):
    results[col] = {
        "forecast": point[i].tolist(),
        "lower_80": quantiles[i, :, 1].tolist(),
        "upper_80": quantiles[i, :, 9].tolist(),
    }

# Export
import json
with open("batch_forecasts.json", "w") as f:
    json.dump(results, f, indent=2)
print(f"Forecasted {len(results)} series 鈫?batch_forecasts.json")

Workflow 3: Evaluate Forecast Accuracy

import numpy as np

# Hold out the last H points for evaluation
H = 24
train = values[:-H]
actual = values[-H:]

point, quantiles = model.forecast(horizon=H, inputs=[train])
pred = point[0]

# Metrics
mae = np.mean(np.abs(actual - pred))
rmse = np.sqrt(np.mean((actual - pred) ** 2))
mape = np.mean(np.abs((actual - pred) / actual)) * 100

# Prediction interval coverage
lower = quantiles[0, :, 1]
upper = quantiles[0, :, 9]
coverage = np.mean((actual >= lower) & (actual <= upper)) * 100

print(f"MAE:  {mae:.2f}")
print(f"RMSE: {rmse:.2f}")
print(f"MAPE: {mape:.1f}%")
print(f"80% PI Coverage: {coverage:.1f}% (target: 80%)")

鈿欙笍 Performance Tuning

GPU Acceleration

import torch

# Check GPU availability
if torch.cuda.is_available():
    print(f"GPU: {torch.cuda.get_device_name(0)}")
    print(f"VRAM: {torch.cuda.get_device_properties(0).total_mem / 1e9:.1f} GB")
elif hasattr(torch.backends, "mps") and torch.backends.mps.is_available():
    print("Apple Silicon MPS available")
else:
    print("CPU only 鈥?inference will be slower but still works")

# Always set this for Ampere+ GPUs (A100, RTX 3090, etc.)
torch.set_float32_matmul_precision("high")

Batch Size Tuning

# Start conservative, increase until OOM
# GPU with 8 GB VRAM:  per_core_batch_size=64
# GPU with 16 GB VRAM: per_core_batch_size=128
# GPU with 24 GB VRAM: per_core_batch_size=256
# CPU with 8 GB RAM:   per_core_batch_size=8
# CPU with 16 GB RAM:  per_core_batch_size=32
# CPU with 32 GB RAM:  per_core_batch_size=64

model.compile(timesfm.ForecastConfig(
    max_context=1024,
    max_horizon=256,
    per_core_batch_size=32,  # <-- tune this
    normalize_inputs=True,
    use_continuous_quantile_head=True,
    fix_quantile_crossing=True,
))

Memory-Constrained Environments

import gc, torch

# Force garbage collection before loading
gc.collect()
if torch.cuda.is_available():
    torch.cuda.empty_cache()

# Load model
model = timesfm.TimesFM_2p5_200M_torch.from_pretrained(
    "google/timesfm-2.5-200m-pytorch"
)

# Use small batch size on low-memory machines
model.compile(timesfm.ForecastConfig(
    max_context=512,        # Reduce context if needed
    max_horizon=128,        # Reduce horizon if needed
    per_core_batch_size=4,  # Small batches
    normalize_inputs=True,
    use_continuous_quantile_head=True,
    fix_quantile_crossing=True,
))

# Process series in chunks to avoid OOM
CHUNK = 50
all_results = []
for i in range(0, len(inputs), CHUNK):
    chunk = inputs[i:i+CHUNK]
    p, q = model.forecast(horizon=H, inputs=chunk)
    all_results.append((p, q))
    gc.collect()  # Clean up between chunks

馃敆 Integration with Other Skills

With statsmodels

Use statsmodels for classical models (ARIMA, SARIMAX) as a comparison baseline:

# TimesFM forecast
tfm_point, tfm_q = model.forecast(horizon=H, inputs=[values])

# statsmodels ARIMA forecast
from statsmodels.tsa.arima.model import ARIMA
arima = ARIMA(values, order=(1,1,1)).fit()
arima_forecast = arima.forecast(steps=H)

# Compare
print(f"TimesFM MAE: {np.mean(np.abs(actual - tfm_point[0])):.2f}")
print(f"ARIMA MAE:   {np.mean(np.abs(actual - arima_forecast)):.2f}")

With matplotlib / scientific-visualization

Plot forecasts with prediction intervals as publication-quality figures.

With exploratory-data-analysis

Run EDA on the time series before forecasting to understand trends, seasonality, and stationarity.

馃摎 Available Scripts

scripts/check_system.py

Mandatory preflight checker. Run before first model load.

python scripts/check_system.py

Output example:

=== TimesFM System Requirements Check ===

[RAM]       Total: 32.0 GB | Available: 24.3 GB  鉁?PASS
[GPU]       NVIDIA RTX 4090 | VRAM: 24.0 GB      鉁?PASS
[Disk]      Free: 142.5 GB                        鉁?PASS
[Python]    3.12.1                                 鉁?PASS
[timesfm]   Installed (2.5.0)                      鉁?PASS
[torch]     Installed (2.4.1+cu121)                鉁?PASS

VERDICT: 鉁?System is ready for TimesFM 2.5 (GPU mode)
Recommended: per_core_batch_size=128

scripts/forecast_csv.py

End-to-end CSV forecasting with automatic system check.

python scripts/forecast_csv.py input.csv \
    --horizon 24 \
    --date-col date \
    --value-cols sales,revenue \
    --output forecasts.csv

馃摉 Reference Documentation

Detailed guides in references/:

Common Pitfalls

1. Not running system check 鈫?model load crashes on low-RAM machines. Always run check_system.py first.
2. Forgetting model.compile() 鈫?RuntimeError: Model is not compiled. Must call compile() before forecast().
3. Not setting normalize_inputs=True 鈫?unstable forecasts for series with large values.
4. Using v1/v2 on machines with < 32 GB RAM 鈫?use TimesFM 2.5 (200M params) instead.
5. Not setting fix_quantile_crossing=True 鈫?quantiles may not be monotonic (q10 > q50).
6. Huge per_core_batch_size on small GPU 鈫?CUDA OOM. Start small, increase.
7. Passing 2-D arrays 鈫?TimesFM expects a list of 1-D arrays, not a 2-D matrix.
8. Forgetting torch.set_float32_matmul_precision("high") 鈫?slower inference on Ampere+ GPUs.
9. Not handling NaN in output 鈫?edge cases with very short series. Always check np.isnan(point).any().
10. Using infer_is_positive=True for series that can be negative 鈫?clamps forecasts at zero. Set False for temperature, returns, etc.

Model Versions

timeline
    accTitle: TimesFM Version History
    accDescr: Timeline of TimesFM model releases showing parameter counts and key improvements.

    section 2024
        TimesFM 1.0 : 200M params, 2K context, JAX only
        TimesFM 2.0 : 500M params, 2K context, PyTorch + JAX
    section 2025
        TimesFM 2.5 : 200M params, 16K context, quantile head, no frequency indicator

Hugging Face checkpoints:

• google/timesfm-2.5-200m-pytorch (recommended)
• google/timesfm-2.5-200m-flax
• google/timesfm-2.0-500m-pytorch (archived)
• google/timesfm-1.0-200m-pytorch (archived)

Resources

• Paper: A Decoder-Only Foundation Model for Time-Series Forecasting (ICML 2024)
• Repository: https://github.com/google-research/timesfm
• Hugging Face: https://huggingface.co/collections/google/timesfm-release-66e4be5fdb56e960c1e482a6
• Google Blog: https://research.google/blog/a-decoder-only-foundation-model-for-time-series-forecasting/
• BigQuery Integration: https://cloud.google.com/bigquery/docs/timesfm-model

Examples

Three fully-working reference examples live in examples/. Use them as ground truth for correct API usage and expected output shape.

Running the Examples

# Global temperature (no TimesFM 2.5 needed)
cd examples/global-temperature && python run_forecast.py && python visualize_forecast.py

# Anomaly detection (uses TimesFM 1.0)
cd examples/anomaly-detection && python detect_anomalies.py

# Covariates (API demo -- requires TimesFM 2.5 + timesfm[xreg] for real inference)
cd examples/covariates-forecasting && python demo_covariates.py

Expected Outputs

Quality Checklist

Run this checklist after every TimesFM task before declaring success:

• Output shape correct -- point_fc shape is (n_series, horizon), quant_fc is (n_series, horizon, 10)
• Quantile indices -- index 0 = mean, 1 = q10, 2 = q20 ... 9 = q90. NOT 0 = q0, 1 = q10.
• Frequency flag -- TimesFM 1.0/2.0: pass freq=[0] for monthly data. TimesFM 2.5: no freq flag.
• Series length -- context must be >= 32 data points (model minimum). Warn if shorter.
• No NaN -- np.isnan(point_fc).any() should be False. Check input series for gaps first.
• Visualization axes -- if multiple panels share data, use sharex=True. All time axes must cover the same span.
• Binary outputs in Git LFS -- PNG and GIF files must be tracked via .gitattributes (repo root already configured).
• No large datasets committed -- any real dataset > 1 MB should be downloaded to tempfile.mkdtemp() and annotated in code.
• matplotlib.use('Agg') -- must appear before any pyplot import when running headless.
• infer_is_positive -- set False for temperature anomalies, financial returns, or any series that can be negative.

Common Mistakes

These bugs have appeared in this skill's examples. Learn from them:

1. Quantile index off-by-one -- The most common mistake. quant_fc[..., 0] is the mean, not q0. q10 = index 1, q90 = index 9. Always define named constants: IDX_Q10, IDX_Q20, IDX_Q80, IDX_Q90 = 1, 2, 8, 9.

2. Variable shadowing in comprehensions -- If you build per-series covariate dicts inside a loop, do NOT use the loop variable as the comprehension variable. Accumulate into separate dict[str, ndarray] outside the loop, then assign.

   # WRONG -- outer `store_id` gets shadowed:
   covariates = {store_id: arr[store_id] for store_id in stores}  # inside outer loop over store_id
   # CORRECT -- use a different name or accumulate beforehand:
   prices_by_store: dict[str, np.ndarray] = {}
   for store_id, config in stores.items():
       prices_by_store[store_id] = compute_price(config)
   

3. Wrong CSV column name -- The global-temperature CSV uses anomaly_c, not anomaly. Always print(df.columns) before accessing.

4. tight_layout() warning with sharex=True -- Harmless; suppress with plt.tight_layout(rect=[0, 0, 1, 0.97]) or ignore.

5. TimesFM 2.5 required for forecast_with_covariates() -- TimesFM 1.0 does NOT have this method. Install pip install timesfm[xreg] and use checkpoint google/timesfm-2.5-200m-pytorch.

6. Future covariates must span the full horizon -- Dynamic covariates (price, promotions, holidays) must have values for BOTH the context AND the forecast horizon. You cannot pass context-only arrays.

7. Anomaly thresholds must be defined once -- Define CRITICAL_Z = 3.0, WARNING_Z = 2.0 as module-level constants. Never hardcode 3 or 2 inline.

8. Context anomaly detection uses residuals, not raw values -- Always detrend first (np.polyfit linear, or seasonal decomposition), then Z-score the residuals. Raw-value Z-scores are misleading on trending data.

Validation & Verification

Use the example outputs as regression baselines. If you change forecasting logic, verify:

# Anomaly detection regression check:
python -c "
import json
d = json.load(open('examples/anomaly-detection/output/anomaly_detection.json'))
ctx = d['context_summary']
assert ctx['critical'] >= 1, 'Sep 2023 must be CRITICAL'
assert any(r['date'] == '2023-09' and r['severity'] == 'CRITICAL'
           for r in d['context_detections']), 'Sep 2023 not found'
print('Anomaly detection regression: PASS')"

# Covariates regression check:
python -c "
import pandas as pd
df = pd.read_csv('examples/covariates-forecasting/output/sales_with_covariates.csv')
assert len(df) == 108, f'Expected 108 rows, got {len(df)}'
prices = df.groupby('store_id')['price'].mean()
assert prices['store_A'] > prices['store_B'] > prices['store_C'], 'Store price ordering wrong'
print('Covariates regression: PASS')"