Create a function to detect anomalies in sales trends using Pandas and NumPy.

To detect anomalies in sales trends using Pandas and NumPy, common statistical methods include the Z-score, Interquartile Range (IQR), and rolling Z-score. These methods identify data points significantly deviating from the central tendency or expected range, indicating potential anomalies.

Anomaly Detection Mechanics

* Z-score: This method quantifies how many standard deviations a data point is from the mean. A common threshold, like |x - mean| / std > 3, flags values that are statistically very unlikely to occur under a normal distribution. It's effective for detecting global outliers in normally distributed data.
Interquartile Range (IQR): This robust method defines outliers as data points falling below Q1 - 1.5 IQR or above Q3 + 1.5 * IQR. It is particularly useful when data is skewed or contains extreme values, as it's less sensitive to them than methods relying on the mean and standard deviation.
Rolling Z-score: This is crucial for time series data, as it adapts to evolving trends and seasonality. Instead of a global mean/std, it calculates these statistics over a defined recent window (e.g., 30 days). This allows detection of deviations from recent* behavior, flagging (current_sales - rolling_mean) / rolling_std > threshold.

Trade-offs and Example

The Z-score method assumes a normal distribution of sales data; deviations from this can lead to false positives or negatives. The IQR method is more robust to skewed distributions or the presence of existing outliers, as it relies on quartiles rather than the mean and standard deviation. For trend anomalies, the rolling Z-score is often preferred.

import pandas as pd
import numpy as np
def detect_anomalies_rolling_zscore(df: pd.DataFrame, column: str, window: int = 30, threshold: float = 3.0) -> pd.DataFrame:
    """Detects anomalies using a rolling Z-score."""
    df['rolling_mean'] = df[column].rolling(window=window, min_periods=1).mean()
    df['rolling_std'] = df[column].rolling(window=window, min_periods=1).std()
    df['rolling_zscore'] = np.abs((df[column] - df['rolling_mean']) / df['rolling_std'])
    df['is_anomaly'] = df['rolling_zscore'] > threshold
    return df

In the interview, also mention…

For production-grade anomaly detection in complex time series, consider more sophisticated algorithms like Isolation Forest or Prophet. Isolation Forest is an unsupervised machine learning algorithm effective at isolating anomalies in high-dimensional datasets. Prophet, developed by Facebook, is specifically designed for forecasting time series data with strong seasonal effects and can identify anomalies by flagging points that deviate significantly from its forecast. When scaling these operations on large datasets, distributed processing frameworks like Apache Spark can parallelize computations, leveraging window functions for rolling metrics across partitions.