Rolling Windows

A rolling window computes a statistic over a moving slice of the most recent n points, sliding forward one point at a time — you already used this exact pattern for moving averages in the Quant Finance Fundamentals course's Backtesting module. The same technique applies to ANY statistic, not just the mean:

def rolling_std(series, window):
    result = []
    for i in range(window - 1, len(series)):
        chunk = series[i - window + 1 : i + 1]
        mean = sum(chunk) / window
        variance = sum((x - mean) ** 2 for x in chunk) / window
        result.append(variance ** 0.5)
    return result

A rolling standard deviation tracks how VOLATILE the series has been recently — rising rolling std means the series has gotten choppier; falling means it's calmed down.

A rolling z-score flags anomalies relative to RECENT behavior, not the series' entire history:

def rolling_zscore(series, window):
    result = []
    for i in range(window - 1, len(series)):
        chunk = series[i - window + 1 : i + 1]
        mean = sum(chunk) / window
        variance = sum((x - mean) ** 2 for x in chunk) / window
        std = variance ** 0.5
        result.append(0.0 if std == 0 else (series[i] - mean) / std)
    return result

A value that's only slightly above the series' ALL-TIME average might still be a big local anomaly if recent values have all clustered tightly together — a rolling z-score catches that; a single global z-score computed once over the whole series would miss it entirely. This is exactly how real-time anomaly detection systems (fraud detection, server monitoring) actually work.