Volatility of unevenly sampled fractional Brownian motion: An application to ice core records

Abstract

The analysis of many natural time series and especially those related to ice core records often suffers from uneven sampling intervals. For fractional Brownian motion, we show that standard estimates of the volatility can be strongly biased due to uneven sampling. Taking these limitations into account, we study high-resolution records of temperature proxies obtained from Antarctic ice cores. We find that the volatility properties reveal a strong nonlinear component in the temperature time series for time scales of 5–200 kyr extending earlier results. These findings suggest in particular that temperature increments over these time scales appear in clusters of big and small increments—a big (positive or negative) change is most likely followed by a big (positive or negative) change and a small change is most likely followed by a small change