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Volatility estimators are especially valuable in modelling financial returns and capturing time-variability of financial series.

In this article, we discuss advanced metrics of volatility and measures of integrated quarticity. Besides, we implement the estimators in Pandas, NumPy and SciPy python libraries.

The provided code involves statistical or financial calculations using Python's NumPy and Pandas libraries, along with the gamma function from the SciPy library.

Furthermore, we estimate additional volatility estimators that we build upon realized quarticity, realized quad-power quarticity and realized tri-power quarticity.

The function realized_quarticity calculates the quarticity of a given series. First, it takes the natural logarithm of the input series and then calculates the difference between consecutive elements. After this, it raises each element of the resulting series to the power of 4, sums the results, and then multiplies by the length of the series. Finally, it divides by 3.

The subsequent code applies the realized_quarticity function to a DataFrame df grouped by the date of the index, and aggregates the results of the function for each group.

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