Time Series Anomaly Detection

Time Series Anomaly Detection Framework

Comprehensive time series anomaly detection framework leverages Facebook Prophet's time-sereis trend prediction (counterfactural) in the target window and compare it with the actual data. An anomaly index that measures how much deviate the actual number is from the expected trend (counterfactural) for each of the categories or groups within that period. The anomaly index ranking can be used to identify outerstanding groups/categories that manifest unexpected surge and slump with quantitative index ranged -100 to 100.

Core Components

TimeSeriesAnomalyDetector

Main class for anomaly detection with configurable parameters.

Constructor Parameters

• min_training_days (int): Minimum days of the available training data required per category (default: 180). Groups have less than this number of days data would be skipped
• confidence_interval (float): Prophet confidence interval width (default: 0.68 = ±1 std) as the starting point to measure the unexpected deviation
• changepoint_prior_scale (float): Flexibility of trend changes (default: 0.05) However, if dataset is not in a big size, use 0.1
• seasonality_prior_scale (float): Strength of seasonality (default: 10.0)

Anomaly Index Calculation (This is CRITICAL and is the key to identify unsual pattern)

• Within confidence interval: Index = 0
• Above upper bound: Index = (actual - upper) / std
• Below lower bound: Index = (actual - lower) / std
• Scaled Index: 100 × tanh(raw_index) → maps to [-100, 100] so after this transformation
  • Index=1 → ~76 points
  • index=2 → ~96 points
  • index=3 → ~99.5 points (approaches ±100)

Usage

from anomaly_detection import TimeSeriesAnomalyDetector

# Initialize detector
detector = TimeSeriesAnomalyDetector(
    min_training_days=180, # depends on the dataset span (usually 50%+ of the dataset time span could be good threshold)
    confidence_interval=0.68 # 1 std for a good intepretability visually and statistically
)

# Run anomaly detection
results = detector.detect_anomalies(
    df=transaction_df,
    date_col='<temporal column>',
    category_col='<grouping column>',  
    value_col='<metric to analyze for anomalies>',
    cutoff_date='<training and prediction split date, format YYYY-MM-DD>',
    prediction_end='end of prediction window',
    agg_func='sum',    # Aggregation: 'sum', 'mean', 'count', or None (e.g if data is not transactional data and value_col value is ready for the modeling)
)

# Access results
anomaly_summary = results['anomaly_summary']  # All categories with anomaly indices

# Get top 10 postive anomaly groups
top_surge = results['anomaly_summary'].head(10)['<grouping column>'].tolist()

# Get top 10 negative anomaly groups (descendingly)
top_slump = results['anomaly_summary'].tail(10)['<grouping column>'].tolist()

Input Format

Required DataFrame columns:

• Date column (e.g., Order Date, Transaction Date, Purchase Date) - temporal dimension
• Category column (e.g., Category, Region) - grouping dimension | Granularity that the method will be applied in loops
• Value column (e.g., Price, Spend,Revenue, Quantity) - metric to detect anomalies in (This is very important as this, directly or indirectly, is the y of the modeling)
• Optional: Additional columns (e.g., User ID)

Parameters:

• cutoff_date: Divides training data (before) from prediction period (after)
• prediction_end: End of anomaly detection window
• agg_func: How to aggregate values per category per day
  • 'sum': Sum all values of the target column for each category-date (e.g user-level purchase data)
  • 'mean': Average values
  • 'count': Count records
  • None: No aggregation (e.g non transactional data)

Output

detect_anomalies() returns a dictionary with 3 keys:

{
    'anomaly_summary': pd.DataFrame,         # Summary metrics per category
    'predictions': Dict[str, pd.DataFrame],  # Prophet forecasts per category  
    'models': Dict[str, Prophet]             # Trained models per category
}

Output anomaly_summary Preview

Sorted by Anomaly_Index descending

predictions Dictionary

Key = category name, Value = DataFrame with columns:

• ds: Date
• yhat: Prophet prediction
• yhat_lower: Lower confidence bound
• yhat_upper: Upper confidence bound

models Dictionary

Key = category name, Value = Fitted Prophet model object

Key Features

• Pure anomaly detection without business logic (no hardcoded top N)
• Automatic daily aggregation by grouping dimension
• Prophet model training with seasonality (daily, weekly, yearly)
• Counterfactual prediction for intervention analysis
• Scaled anomaly index [-100, 100] for interpretability

Best Practices

• Ensure sufficient training data (180+ days recommended)
• Use cutoff_date to define pre/post intervention periods
• Use agg_func=None if data already at daily category level
• Apply your own filtering logic on anomaly_summary (top N, thresholds, etc.)
• Chain with DID analysis for causal inference on selected categories

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