feat(examples): add anomaly detection and covariates examples

Anomaly Detection Example:
- Uses quantile forecasts as prediction intervals
- Flags values outside 80%/90% CI as warnings/critical anomalies
- Includes visualization with deviation plot

Covariates (XReg) Example:
- Demonstrates forecast_with_covariates() API
- Shows dynamic numerical/categorical covariates
- Shows static categorical covariates
- Includes synthetic retail sales data with price, promotion, holiday

SKILL.md Updates:
- Added anomaly detection section with code example
- Expanded covariates section with covariate types table
- Added XReg modes explanation
- Updated 'When not to use' section to note anomaly detection workaround

scientific-skills/timesfm-forecasting/examples/covariates-forecasting/demo_covariates.py

@@ -0,0 +1,440 @@
+#!/usr/bin/env python3
+"""
+TimesFM Covariates (XReg) Example
+
+This example demonstrates TimesFM's exogenous variable support through the
+forecast_with_covariates() API. This requires `timesfm[xreg]` installation.
+
+Covariate Types Supported:
+- Dynamic Numerical: Time-varying numeric features (e.g., price, temperature)
+- Dynamic Categorical: Time-varying categorical features (e.g., holiday, day_of_week)
+- Static Numerical: Per-series numeric features (e.g., store_size)
+- Static Categorical: Per-series categorical features (e.g., store_type, region)
+
+Note: TimesFM 1.0 (used here) does NOT support forecast_with_covariates().
+This example uses TimesFM 2.5 which requires a different API. We'll demonstrate
+the concept with synthetic data and show the API signature.
+"""
+
+from __future__ import annotations
+
+import json
+from pathlib import Path
+
+import matplotlib.pyplot as plt
+import numpy as np
+import pandas as pd
+
+# Note: TimesFM 1.0 does not support forecast_with_covariates
+# This example demonstrates the API with TimesFM 2.5
+# Installation: pip install timesfm[xreg]
+
+EXAMPLE_DIR = Path(__file__).parent
+OUTPUT_DIR = EXAMPLE_DIR / "output"
+
+# Synthetic data configuration
+N_STORES = 3
+CONTEXT_LEN = 48  # 48 weeks of history
+HORIZON_LEN = 12  # 12 weeks forecast
+TOTAL_LEN = CONTEXT_LEN + HORIZON_LEN
+
+
+def generate_sales_data() -> dict:
+    """Generate synthetic retail sales data with covariates."""
+    rng = np.random.default_rng(42)
+
+    # Store configurations
+    stores = {
+        "store_A": {"type": "premium", "region": "urban", "base_sales": 1000},
+        "store_B": {"type": "standard", "region": "suburban", "base_sales": 750},
+        "store_C": {"type": "discount", "region": "rural", "base_sales": 500},
+    }
+
+    data = {"stores": {}, "covariates": {}}
+
+    for store_id, config in stores.items():
+        # Base sales with trend
+        weeks = np.arange(TOTAL_LEN)
+        trend = config["base_sales"] * (1 + 0.005 * weeks)
+
+        # Seasonality (yearly pattern)
+        seasonality = 100 * np.sin(2 * np.pi * weeks / 52)
+
+        # Noise
+        noise = rng.normal(0, 50, TOTAL_LEN)
+
+        # Price (affects sales negatively)
+        price = 10 + rng.uniform(-1, 1, TOTAL_LEN)
+        price_effect = -20 * (price - 10)
+
+        # Holidays (boost sales)
+        holidays = np.zeros(TOTAL_LEN)
+        holiday_weeks = [0, 11, 23, 35, 47, 51]  # Major holidays
+        for hw in holiday_weeks:
+            if hw < TOTAL_LEN:
+                holidays[hw] = 1
+
+        holiday_effect = 200 * holidays
+
+        # Promotion (boost sales)
+        promotion = rng.choice([0, 1], TOTAL_LEN, p=[0.8, 0.2])
+        promo_effect = 150 * promotion
+
+        # Final sales
+        sales = (
+            trend + seasonality + noise + price_effect + holiday_effect + promo_effect
+        )
+        sales = np.maximum(sales, 50)  # Ensure positive
+
+        # Day of week effect (0=Mon, 6=Sun) - simplified to weekly
+        day_of_week = np.tile(np.arange(7), TOTAL_LEN // 7 + 1)[:TOTAL_LEN]
+
+        data["stores"][store_id] = {
+            "sales": sales.astype(np.float32),
+            "config": config,
+        }
+
+        # Covariates (same structure for all stores, different values)
+        if store_id == "store_A":
+            data["covariates"] = {
+                "price": {store_id: price.astype(np.float32) for store_id in stores},
+                "promotion": {
+                    store_id: promotion.astype(np.float32) for store_id in stores
+                },
+                "holiday": {
+                    store_id: holidays.astype(np.float32) for store_id in stores
+                },
+                "day_of_week": {
+                    store_id: day_of_week.astype(np.int32) for store_id in stores
+                },
+                "store_type": {store_id: config["type"] for store_id in stores},
+                "region": {store_id: config["region"] for store_id in stores},
+            }
+
+    return data
+
+
+def demonstrate_api() -> None:
+    """Show the forecast_with_covariates API structure."""
+
+    print("\n" + "=" * 70)
+    print("  TIMESFM COVARIATES API (TimesFM 2.5)")
+    print("=" * 70)
+
+    api_code = """
+# Installation
+pip install timesfm[xreg]
+
+# Import
+import timesfm
+
+# Load TimesFM 2.5 (supports covariates)
+hparams = timesfm.TimesFmHparams(
+    backend="cpu",  # or "gpu"
+    per_core_batch_size=32,
+    horizon_len=12,
+)
+checkpoint = timesfm.TimesFmCheckpoint(
+    huggingface_repo_id="google/timesfm-2.5-200m-pytorch"
+)
+model = timesfm.TimesFm(hparams=hparams, checkpoint=checkpoint)
+
+# Prepare inputs
+inputs = [sales_store_a, sales_store_b, sales_store_c]  # List of historical sales
+
+# Dynamic numerical covariates (context + horizon values per series)
+dynamic_numerical_covariates = {
+    "price": [
+        price_history_store_a,  # Shape: (context_len + horizon_len,)
+        price_history_store_b,
+        price_history_store_c,
+    ],
+    "promotion": [promo_a, promo_b, promo_c],
+}
+
+# Dynamic categorical covariates
+dynamic_categorical_covariates = {
+    "holiday": [holiday_a, holiday_b, holiday_c],  # 0 or 1 flags
+    "day_of_week": [dow_a, dow_b, dow_c],  # 0-6 integer values
+}
+
+# Static categorical covariates (one value per series)
+static_categorical_covariates = {
+    "store_type": ["premium", "standard", "discount"],
+    "region": ["urban", "suburban", "rural"],
+}
+
+# Forecast with covariates
+point_forecast, quantile_forecast = model.forecast_with_covariates(
+    inputs=inputs,
+    dynamic_numerical_covariates=dynamic_numerical_covariates,
+    dynamic_categorical_covariates=dynamic_categorical_covariates,
+    static_categorical_covariates=static_categorical_covariates,
+    xreg_mode="xreg + timesfm",  # or "timesfm + xreg"
+    ridge=0.0,                   # Ridge regularization
+    normalize_xreg_target_per_input=True,
+)
+
+# Output shapes
+# point_forecast: (num_series, horizon_len)
+# quantile_forecast: (num_series, horizon_len, 10)
+"""
+    print(api_code)
+
+
+def explain_xreg_modes() -> None:
+    """Explain the two XReg modes."""
+
+    print("\n" + "=" * 70)
+    print("  XREG MODES EXPLAINED")
+    print("=" * 70)
+
+    print("""
+┌─────────────────────────────────────────────────────────────────────┐
+│  Mode 1: "xreg + timesfm" (DEFAULT)                                │
+├─────────────────────────────────────────────────────────────────────┤
+│  1. TimesFM makes baseline forecast (ignoring covariates)          │
+│  2. Calculate residuals: actual - baseline                         │
+│  3. Fit linear regression: residuals ~ covariates                  │
+│  4. Final forecast = TimesFM baseline + XReg adjustment            │
+│                                                                     │
+│  Best for: Covariates capture residual patterns                    │
+│           (e.g., promotions affecting baseline sales)              │
+└─────────────────────────────────────────────────────────────────────┘
+
+┌─────────────────────────────────────────────────────────────────────┐
+│  Mode 2: "timesfm + xreg"                                          │
+├─────────────────────────────────────────────────────────────────────┤
+│  1. Fit linear regression: target ~ covariates                     │
+│  2. Calculate residuals: actual - regression_prediction            │
+│  3. TimesFM forecasts residuals                                     │
+│  4. Final forecast = XReg prediction + TimesFM residual forecast   │
+│                                                                     │
+│  Best for: Covariates explain main signal                          │
+│           (e.g., temperature driving ice cream sales)              │
+└─────────────────────────────────────────────────────────────────────┘
+""")
+
+
+def create_visualization(data: dict) -> None:
+    """Create visualization of sales data with covariates."""
+
+    OUTPUT_DIR.mkdir(exist_ok=True)
+
+    fig, axes = plt.subplots(3, 2, figsize=(16, 12))
+
+    weeks = np.arange(TOTAL_LEN)
+    context_weeks = weeks[:CONTEXT_LEN]
+    horizon_weeks = weeks[CONTEXT_LEN:]
+
+    # Plot 1: Sales by store
+    ax = axes[0, 0]
+    for store_id, store_data in data["stores"].items():
+        ax.plot(
+            context_weeks,
+            store_data["sales"][:CONTEXT_LEN],
+            label=f"{store_id} ({store_data['config']['type']})",
+            linewidth=2,
+        )
+    ax.axvline(x=CONTEXT_LEN, color="red", linestyle="--", label="Forecast Start")
+    ax.set_xlabel("Week")
+    ax.set_ylabel("Sales")
+    ax.set_title("Historical Sales by Store")
+    ax.legend()
+    ax.grid(True, alpha=0.3)
+
+    # Plot 2: Price covariate
+    ax = axes[0, 1]
+    for store_id in data["stores"]:
+        ax.plot(weeks, data["covariates"]["price"][store_id], label=store_id, alpha=0.7)
+    ax.axvline(x=CONTEXT_LEN, color="red", linestyle="--")
+    ax.set_xlabel("Week")
+    ax.set_ylabel("Price ($)")
+    ax.set_title("Dynamic Numerical Covariate: Price")
+    ax.legend()
+    ax.grid(True, alpha=0.3)
+
+    # Plot 3: Holiday covariate
+    ax = axes[1, 0]
+    holidays = data["covariates"]["holiday"]["store_A"]
+    ax.bar(weeks, holidays, alpha=0.7, color="orange")
+    ax.axvline(x=CONTEXT_LEN, color="red", linestyle="--")
+    ax.set_xlabel("Week")
+    ax.set_ylabel("Holiday Flag")
+    ax.set_title("Dynamic Categorical Covariate: Holiday")
+    ax.grid(True, alpha=0.3)
+
+    # Plot 4: Promotion covariate
+    ax = axes[1, 1]
+    promotions = data["covariates"]["promotion"]["store_A"]
+    ax.bar(weeks, promotions, alpha=0.7, color="green")
+    ax.axvline(x=CONTEXT_LEN, color="red", linestyle="--")
+    ax.set_xlabel("Week")
+    ax.set_ylabel("Promotion Flag")
+    ax.set_title("Dynamic Categorical Covariate: Promotion")
+    ax.grid(True, alpha=0.3)
+
+    # Plot 5: Store type (static)
+    ax = axes[2, 0]
+    store_types = [data["covariates"]["store_type"][s] for s in data["stores"]]
+    store_ids = list(data["stores"].keys())
+    colors = {"premium": "gold", "standard": "silver", "discount": "brown"}
+    ax.bar(store_ids, [1, 1, 1], color=[colors[t] for t in store_types])
+    ax.set_ylabel("Store Type")
+    ax.set_title("Static Categorical Covariate: Store Type")
+    ax.set_yticks([])
+    for i, (sid, t) in enumerate(zip(store_ids, store_types)):
+        ax.text(i, 0.5, t, ha="center", va="center", fontweight="bold")
+
+    # Plot 6: Data structure summary
+    ax = axes[2, 1]
+    ax.axis("off")
+
+    summary_text = """
+    COVARIATE DATA STRUCTURE
+    ─────────────────────────
+    
+    Dynamic Numerical Covariates:
+    • price: np.ndarray[context_len + horizon_len] per series
+    • promotion: np.ndarray[context_len + horizon_len] per series
+    
+    Dynamic Categorical Covariates:
+    • holiday: np.ndarray[context_len + horizon_len] per series
+    • day_of_week: np.ndarray[context_len + horizon_len] per series
+    
+    Static Categorical Covariates:
+    • store_type: ["premium", "standard", "discount"]
+    • region: ["urban", "suburban", "rural"]
+    
+    Note: Future covariate values must be known!
+    (Price, promotion schedule, holidays are planned in advance)
+    """
+    ax.text(
+        0.1,
+        0.5,
+        summary_text,
+        transform=ax.transAxes,
+        fontfamily="monospace",
+        fontsize=10,
+        verticalalignment="center",
+    )
+
+    plt.tight_layout()
+
+    output_path = OUTPUT_DIR / "covariates_data.png"
+    plt.savefig(output_path, dpi=150, bbox_inches="tight")
+    print(f"\n📊 Saved visualization: {output_path}")
+    plt.close()
+
+
+def main() -> None:
+    print("=" * 70)
+    print("  TIMESFM COVARIATES (XREG) EXAMPLE")
+    print("=" * 70)
+
+    # Generate synthetic data
+    print("\n📊 Generating synthetic retail sales data...")
+    data = generate_sales_data()
+
+    print(f"   Stores: {list(data['stores'].keys())}")
+    print(f"   Context length: {CONTEXT_LEN} weeks")
+    print(f"   Horizon length: {HORIZON_LEN} weeks")
+    print(f"   Covariates: {list(data['covariates'].keys())}")
+
+    # Show API
+    demonstrate_api()
+
+    # Explain modes
+    explain_xreg_modes()
+
+    # Create visualization
+    print("\n📊 Creating data visualization...")
+    create_visualization(data)
+
+    # Save data
+    print("\n💾 Saving synthetic data...")
+
+    # Convert to DataFrame for CSV export
+    records = []
+    for store_id, store_data in data["stores"].items():
+        for i, week in enumerate(range(TOTAL_LEN)):
+            records.append(
+                {
+                    "store_id": store_id,
+                    "week": week,
+                    "sales": store_data["sales"][i],
+                    "price": data["covariates"]["price"][store_id][i],
+                    "promotion": data["covariates"]["promotion"][store_id][i],
+                    "holiday": int(data["covariates"]["holiday"][store_id][i]),
+                    "day_of_week": int(data["covariates"]["day_of_week"][store_id][i]),
+                    "store_type": data["covariates"]["store_type"][store_id],
+                    "region": data["covariates"]["region"][store_id],
+                }
+            )
+
+    df = pd.DataFrame(records)
+    csv_path = OUTPUT_DIR / "sales_with_covariates.csv"
+    df.to_csv(csv_path, index=False)
+    print(f"   Saved: {csv_path}")
+
+    # Save metadata
+    metadata = {
+        "description": "Synthetic retail sales data with covariates for TimesFM XReg demo",
+        "stores": {sid: sdata["config"] for sid, sdata in data["stores"].items()},
+        "dimensions": {
+            "context_length": CONTEXT_LEN,
+            "horizon_length": HORIZON_LEN,
+            "total_length": TOTAL_LEN,
+        },
+        "covariates": {
+            "dynamic_numerical": ["price", "promotion"],
+            "dynamic_categorical": ["holiday", "day_of_week"],
+            "static_categorical": ["store_type", "region"],
+        },
+        "xreg_modes": {
+            "xreg + timesfm": "Fit regression on residuals after TimesFM forecast",
+            "timesfm + xreg": "TimesFM forecasts residuals after regression fit",
+        },
+    }
+
+    meta_path = OUTPUT_DIR / "covariates_metadata.json"
+    with open(meta_path, "w") as f:
+        json.dump(metadata, f, indent=2)
+    print(f"   Saved: {meta_path}")
+
+    # Summary
+    print("\n" + "=" * 70)
+    print("  ✅ COVARIATES EXAMPLE COMPLETE")
+    print("=" * 70)
+
+    print("""
+💡 Key Points:
+
+1. INSTALLATION: Requires timesfm[xreg] extra
+   pip install timesfm[xreg]
+
+2. COVARIATE TYPES:
+   • Dynamic: Changes over time (price, promotion, holiday)
+   • Static: Fixed per series (store type, region)
+
+3. DATA REQUIREMENTS:
+   • Dynamic covariates need values for context + horizon
+   • Future values must be known (e.g., planned prices, scheduled holidays)
+
+4. XREG MODES:
+   • "xreg + timesfm" (default): Regression on residuals
+   • "timesfm + xreg": TimesFM on residuals after regression
+
+5. LIMITATIONS:
+   • String categorical values work but slower (use int encoding)
+   • Requires TimesFM 2.5+ (v1.0 does not support XReg)
+
+📁 Output Files:
+   • output/covariates_data.png - Data visualization
+   • output/sales_with_covariates.csv - Sample data
+   • output/covariates_metadata.json - Metadata
+""")
+
+
+if __name__ == "__main__":
+    main()

scientific-skills/timesfm-forecasting/examples/covariates-forecasting/output/covariates_metadata.json

@@ -0,0 +1,43 @@
+{
+  "description": "Synthetic retail sales data with covariates for TimesFM XReg demo",
+  "stores": {
+    "store_A": {
+      "type": "premium",
+      "region": "urban",
+      "base_sales": 1000
+    },
+    "store_B": {
+      "type": "standard",
+      "region": "suburban",
+      "base_sales": 750
+    },
+    "store_C": {
+      "type": "discount",
+      "region": "rural",
+      "base_sales": 500
+    }
+  },
+  "dimensions": {
+    "context_length": 48,
+    "horizon_length": 12,
+    "total_length": 60
+  },
+  "covariates": {
+    "dynamic_numerical": [
+      "price",
+      "promotion"
+    ],
+    "dynamic_categorical": [
+      "holiday",
+      "day_of_week"
+    ],
+    "static_categorical": [
+      "store_type",
+      "region"
+    ]
+  },
+  "xreg_modes": {
+    "xreg + timesfm": "Fit regression on residuals after TimesFM forecast",
+    "timesfm + xreg": "TimesFM forecasts residuals after regression fit"
+  }
+}

scientific-skills/timesfm-forecasting/examples/covariates-forecasting/output/sales_with_covariates.csv

@@ -0,0 +1,181 @@
+store_id,week,sales,price,promotion,holiday,day_of_week,store_type,region
+store_A,0,1212.6265,10.130472,0.0,1,0,premium,urban
+store_A,1,954.4545,10.529998,0.0,0,1,premium,urban
+store_A,2,1066.0654,10.269437,0.0,0,2,premium,urban
+store_A,3,1095.3456,10.107159,0.0,0,3,premium,urban
+store_A,4,966.55225,10.118414,0.0,0,4,premium,urban
+store_A,5,1024.5396,9.607901,0.0,0,5,premium,urban
+store_A,6,1121.4716,9.061636,0.0,0,6,premium,urban
+store_A,7,1096.5702,9.873435,0.0,0,0,premium,urban
+store_A,8,1132.875,9.42917,0.0,0,1,premium,urban
+store_A,9,1244.5522,9.817058,1.0,0,2,premium,urban
+store_A,10,1173.3354,10.706806,0.0,0,3,premium,urban
+store_A,11,1401.6262,9.467879,0.0,1,4,premium,urban
+store_A,12,1180.2404,9.116606,0.0,0,5,premium,urban
+store_A,13,1230.1067,9.562768,0.0,0,6,premium,urban
+store_A,14,1350.9026,9.587188,1.0,0,0,premium,urban
+store_A,15,1122.653,10.323833,0.0,0,1,premium,urban
+store_A,16,1189.6578,10.114064,0.0,0,2,premium,urban
+store_A,17,1114.2455,10.567797,0.0,0,3,premium,urban
+store_A,18,1209.6483,10.328627,0.0,0,4,premium,urban
+store_A,19,1171.0994,9.812774,0.0,0,5,premium,urban
+store_A,20,1294.5083,10.62804,1.0,0,6,premium,urban
+store_A,21,1141.081,9.333946,0.0,0,0,premium,urban
+store_A,22,1236.6909,9.045424,0.0,0,1,premium,urban
+store_A,23,1359.1321,9.180096,0.0,1,2,premium,urban
+store_A,24,1113.6208,10.444718,0.0,0,3,premium,urban
+store_A,25,1120.9719,9.923755,0.0,0,4,premium,urban
+store_A,26,1170.1646,9.322543,0.0,0,5,premium,urban
+store_A,27,1141.1768,10.0020895,0.0,0,6,premium,urban
+store_A,28,1300.6125,9.304625,1.0,0,0,premium,urban
+store_A,29,1273.2278,10.392641,1.0,0,1,premium,urban
+store_A,30,1212.7638,9.892313,0.0,0,2,premium,urban
+store_A,31,1082.632,9.762042,0.0,0,3,premium,urban
+store_A,32,1076.0151,9.6030245,0.0,0,4,premium,urban
+store_A,33,1044.249,10.260565,0.0,0,5,premium,urban
+store_A,34,1124.0281,9.723625,0.0,0,6,premium,urban
+store_A,35,1359.397,9.1753,0.0,1,0,premium,urban
+store_A,36,1096.0808,9.2360115,0.0,0,1,premium,urban
+store_A,37,1027.4221,10.923796,0.0,0,2,premium,urban
+store_A,38,1033.1619,10.817162,0.0,0,3,premium,urban
+store_A,39,1269.5414,10.399414,1.0,0,4,premium,urban
+store_A,40,1147.2571,9.53174,0.0,0,5,premium,urban
+store_A,41,1116.2965,10.938353,0.0,0,6,premium,urban
+store_A,42,1072.0729,10.557502,0.0,0,0,premium,urban
+store_A,43,1129.3868,10.433781,0.0,0,1,premium,urban
+store_A,44,1295.5614,9.898723,1.0,0,2,premium,urban
+store_A,45,1320.1937,9.544483,1.0,0,3,premium,urban
+store_A,46,1223.4036,9.192781,0.0,0,4,premium,urban
+store_A,47,1523.2692,10.805204,1.0,1,5,premium,urban
+store_A,48,1229.2423,9.911552,0.0,0,6,premium,urban
+store_A,49,1224.824,9.404727,0.0,0,0,premium,urban
+store_A,50,1248.2861,9.611914,0.0,0,1,premium,urban
+store_A,51,1621.3419,10.158439,1.0,1,2,premium,urban
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