Realized wavelet-based estimation of integrated variance and jumps in the presence of noise

Details Realized wavelet-based estimation of integrated variance and jumps in the presence of noise Realized wavelet-based estimation of integrated variance and jumps in the presence of noise

2012-02-08

arxiv.org/abs/1202.1854v1

Economy

Quantitative Finance

Statistical Finance

Scientific paper

This paper proposes generalization of the popular realized volatility framework by allowing its measurement in the time-frequency domain and bringing robustness to both noise as well as jumps. Based on the generalization of Fan and Wang (2007) approach using smooth wavelets and Maximum Overlap Discrete Wavelet Transform, we present new, general theory for wavelet decomposition of integrated variance. Using wavelets, we not only gain decomposition of the realized variance into several investment horizons, but we are also able to estimate the jumps consistently. Basing our estimator in the two-scale realized variance framework of Zhang et al. (2005), we are able to utilize all available data and get unbiased estimator in the presence of noise as well. The theory is also tested in a large numerical study of the small sample performance of the estimators and compared to other popular realized variation estimators under different simulation settings with changing noise as well as jump level. The results reveal that our wavelet-based estimator is able to estimate and forecast the realized measures with the greatest precision. Another notable contribution lies in the application of the presented theory. Our time-frequency estimators not only produce more efficient estimates, but also decompose the realized variation into arbitrarily chosen investment horizons. The results thus provide a better understanding of the dynamics of stock markets.

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