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

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  • Jozef Barunik
  • Lukas Vacha

Abstract

We introduce wavelet-based methodology for estimation of realized variance allowing its measurement in the time-frequency domain. Using smooth wavelets and Maximum Overlap Discrete Wavelet Transform, we allow for the decomposition of the realized variance into several investment horizons and jumps. Basing our estimator in the two-scale realized variance framework, we are able to utilize all available data and get feasible estimator in the presence of microstructure noise as well. The estimator is tested in a large numerical study of the finite sample performance and is compared to other popular realized variation estimators. We use different simulation settings with changing noise as well as jump level in different price processes including long memory fractional stochastic volatility model. The results reveal that our wavelet-based estimator is able to estimate and forecast the realized measures with the greatest precision. Our time-frequency estimators not only produce feasible estimates, but also decompose the realized variation into arbitrarily chosen investment horizons. We apply it to study the volatility of forex futures during the recent crisis at several investment horizons and obtain the results which provide us with better understanding of the volatility dynamics.

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  • Jozef Barunik & Lukas Vacha, 2012. "Realized wavelet-based estimation of integrated variance and jumps in the presence of noise," Papers 1202.1854, arXiv.org, revised Feb 2013.
    • Handle: RePEc:arx:papers:1202.1854
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    5. Faria, Gonçalo & Verona, Fabio, 2018. "Forecasting stock market returns by summing the frequency-decomposed parts," Journal of Empirical Finance, Elsevier, vol. 45(C), pages 228-242.
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    8. Barunik, Jozef & Krehlik, Tomas & Vacha, Lukas, 2016. "Modeling and forecasting exchange rate volatility in time-frequency domain," European Journal of Operational Research, Elsevier, vol. 251(1), pages 329-340.
    9. Kraicová Lucie & Baruník Jozef, 2017. "Estimation of long memory in volatility using wavelets," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 21(3), pages 1-22, June.
    10. Barunik, Jozef & Vacha, Lukas, 2018. "Do co-jumps impact correlations in currency markets?," Journal of Financial Markets, Elsevier, vol. 37(C), pages 97-119.
    11. Faria, Gonçalo & Verona, Fabio, 2018. "The equity risk premium and the low frequency of the term spread," Research Discussion Papers 7/2018, Bank of Finland.
    12. Barunik, Jozef & Barunikova, Michaela, 2015. "Revisiting the long memory dynamics of implied-realized volatility relation: A new evidence from wavelet band spectrum regression," FinMaP-Working Papers 43, Collaborative EU Project FinMaP - Financial Distortions and Macroeconomic Performance: Expectations, Constraints and Interaction of Agents.
    13. Takaki Hayashi & Yuta Koike, 2017. "Multi-scale analysis of lead-lag relationships in high-frequency financial markets," Papers 1708.03992, arXiv.org, revised May 2020.
    14. Gonçalo Faria & Fabio Verona, 2021. "Time-frequency forecast of the equity premium," Quantitative Finance, Taylor & Francis Journals, vol. 21(12), pages 2119-2135, December.
    15. Faria, Gonçalo & Verona, Fabio, 2020. "Frequency-domain information for active portfolio management," Research Discussion Papers 2/2020, Bank of Finland.
    16. Kshatriya, Saranya & Prasanna, Krishna, 2021. "Jump Interdependencies: Stochastic linkages among international stock markets," The North American Journal of Economics and Finance, Elsevier, vol. 57(C).
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    20. Semeyutin, Artur & Gozgor, Giray & Lau, Chi Keung Marco & Xu, Bing, 2021. "Effects of idiosyncratic jumps and co-jumps on oil, gold, and copper markets," Energy Economics, Elsevier, vol. 104(C).
    21. Jozef Barunik & Michaela Barunikova, 2012. "Revisiting the fractional cointegrating dynamics of implied-realized volatility relation with wavelet band spectrum regression," Papers 1208.4831, arXiv.org, revised Feb 2013.
    22. Faria, Gonçalo & Verona, Fabio, 2020. "Frequency-domain information for active portfolio management," Bank of Finland Research Discussion Papers 2/2020, Bank of Finland.
    23. Kim C. Raath & Katherine B. Ensor, 2023. "Wavelet-L2E Stochastic Volatility Models: an Application to the Water-Energy Nexus," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 150-176, May.

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