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How precise is the finite sample approximation of the asymptotic distribution of realised variation measures in the presence of jumps?

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Abstract

This paper studies the impact of jumps on volatility estimation and inference based on various realised variation measures such as realised variance, realised multipower variation and truncated realised multipower variation. We review the asymptotic theory of those realised variation measures and present a new estimator for the asymptotic ‘variance’ of the centered realised variance in the presence of jumps. Next, we compare the finite sample performance of the various estimators by means of detailed Monte Carlo studies. Here we study the impact of the jump activity, of the jump size of the jumps in the price and of the presence of additional independent or dependent jumps in the volatility. We find that the finite sample performance of realised variance and, in particular, of log-transformed realised variance is generally good, whereas the jump-robust statistics tend to struggle in the presence of a highly active jump process.

Finally, we investigate the impact of jumps on inference on volatility empirically, where we study high frequency data from the Standard & Poor’s Depository Receipt (SPY).

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  1. CREATES, School of Economics and Management, Aarhus University, 8000, Aarhus C, Denmark

    Almut E. D. Veraart

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Veraart, A.E.D. How precise is the finite sample approximation of the asymptotic distribution of realised variation measures in the presence of jumps?. AStA Adv Stat Anal 95, 253–291 (2011). https://doi.org/10.1007/s10182-011-0158-1

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