×

zbMATH — the first resource for mathematics

Common price and volatility jumps in noisy high-frequency data. (English) Zbl 1398.62281
This paper deals with testing high-frequency financial data for simultaneous jumps in price and volatility. The investigated data model is of the form \[ Y_{i} = X_{i/n} + \epsilon_i \] with the latent log-price process \(X\) satisfying \[ X_t = X_0 + \int_0^t b_s d s + \int_0^t \sigma_s d W_s + P(t), \] where \(P\) is another specific random process generating jumps. To test for simultaneous jumps in price and volatility, first price jumps are localized via thresholding, and afterwards local tests for volatility jumps based on self-scaling test statistics are performed. The asymptotic distribution of this test statistic is analyzed, such that the testing procedure can be properly calibrated.
Details on a possible implementation are provided, as well as a simulation study which reveals the investigated procedure to be robust w.r.t. the microstructure noise \(\epsilon_i\). The procedure is furthermore applied to real NASDAQ data.

MSC:
62P05 Applications of statistics to actuarial sciences and financial mathematics
62M09 Non-Markovian processes: estimation
62G10 Nonparametric hypothesis testing
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
PDF BibTeX XML Cite
Full Text: DOI Euclid
References:
[1] Aït-Sahalia, Y., J. Fan, R. J. A. Laeven, C. D. Wang, and X. Yang (2017). Estimation of the continuous and discontinuous leverage effects., Journal of the American Statistical Association,112(520), 1744-1758.
[2] Aït-Sahalia, Y. and J. Jacod (2010). Is Brownian motion necessary to model high-frequency data?, The Annals of Statistics38(5), 3093-3128. · Zbl 1327.62118
[3] Aït-Sahalia, Y. and J. Jacod (2014)., High-frequency financial econometrics. Princeton, NJ: Princeton University Press. · Zbl 1298.91018
[4] Aït-Sahalia, Y., L. Zhang, and P. A. Mykland (2005). How often to sample a continuous-time process in the presence of market microstructure noise., Review of Financial Studies18, 351-416. · Zbl 1151.62365
[5] Altmeyer, R. and M. Bibinger (2015). Functional stable limit theorems for quasi-efficient spectral covolatility estimators., Stochastic Processes and their Applications125(12), 4556-4600. · Zbl 1327.62188
[6] Andersen, T. G. and T. Bollerslev (1998). Answering the skeptics: Yes, standard volatility models do provide accurate forecasts., International Economic Review39(4), 885-905.
[7] Andersen, T. G., T. Bollerslev, F. X. Diebold, and P. Labys (2001). The distribution of realized exchange rate volatility., Journal of the American Statistical Association96(453), 42-55. · Zbl 1015.62107
[8] Bandi, F. and R. Renò (2016). Price and volatility co-jumps., Journal of Financial Economics119(1), 107-146.
[9] Barndorff-Nielsen, O. E., P. R. Hansen, A. Lunde, and N. Shephard (2008). Designing realised kernels to measure the ex-post variation of equity prices in the presence of noise., Econometrica76(6), 1481-1536. · Zbl 1153.91416
[10] Barndorff-Nielsen, O. E. and N. Shephard (2002). Econometric analysis of realized volatility and its use in estimating stochastic volatility models., Journal of the Royal Statistical Society64(2), 253-280. · Zbl 1059.62107
[11] Bibinger, M. (2011). Efficient covariance estimation for asynchronous noisy high-frequency data., Scandinavian Journal of Statistics38, 23-45. · Zbl 1246.91148
[12] Bibinger, M., N. Hautsch, P. Malec, and M. Reiß (2014). Estimating the quadratic covariation matrix from noisy observations: Local method of moments and efficiency., The Annals of Statistics42(4), 1312-1346. · Zbl 1302.62190
[13] Bibinger, M., N. Hautsch, P. Malec, and M. Reiß (2017). Estimating the spot covariation of asset prices – statistical theory and empirical evidence., Journal of Business & Economic Statistics,forthcoming.
[14] Bibinger, M., M. Jirak, and M. Vetter (2017). Nonparametric change-point analysis of volatility., The Annals of Statistics45(4), 1542-1578. · Zbl 1421.62163
[15] Bibinger, M. and M. Reiß (2014). Spectral estimation of covolatility from noisy observations using local weights., Scandinavian Journal of Statistics41(1), 23-50. · Zbl 1349.62441
[16] Bibinger, M. and L. Winkelmann (2015). Econometrics of co-jumps in high-frequency data with noise., Journal of Econometrics184(2), 361 - 378. · Zbl 1331.91200
[17] Bloom, N. (2009). The impact of uncertainty shocks., Econometrica77(3), 623-685. · Zbl 1176.91114
[18] Clinet, S. and Y. Potiron (2017). Efficient asymptotic variance reduction when estimating volatility in high frequency data., arxive:1701.01185. · Zbl 1398.62288
[19] Comte, F. and E. Renault (1998). Long memory in continuous-time stochastic volatility models., Mathematical Finance8(4), 291-323. · Zbl 1020.91021
[20] Duffie, D., J. Pan, and K. Singleton (2000). Transform analysis and asset pricing for affine jump-diffusions., Econometrica68(6), 1343-1376. · Zbl 1055.91524
[21] Fan, J. and Y. Wang (2007). Multi-scale jump and volatility analysis for high-frequency data., Journal of the American Statistical Association102(480), 1349-1362. · Zbl 1332.62403
[22] Hansen, P. R. and A. Lunde (2006). Realized variance and market microstructure noise., Journal of Business & Economic Statistics24(2), 127-161.
[23] Hautsch, N. and M. Podolskij (2013). Preaveraging-based estimation of quadratic variation in the presence of noise and jumps: Theory, implementation, and empirical evidence., Journal of Business & Economic Statistics31(2), 165-183.
[24] Jacod, J. (2008). Asymptotic properties of realized power variations and related functionals of semimartingales., Stochastic Processes and their Applications118(4), 517-559. · Zbl 1142.60022
[25] Jacod, J., C. Klüppelberg, and G. Müller (2017). Testing for non-correlation between price and volatility jumps., Journal of Econometrics197(2), 284-297. · Zbl 1422.91781
[26] Jacod, J., Y. Li, P. A. Mykland, M. Podolskij, and M. Vetter (2009). Microstructure noise in the continous case: the pre-averaging approach., Stochastic Processes and their Applications119, 2803-2831. · Zbl 1166.62078
[27] Jacod, J. and P. A. Mykland (2015). Microstructure noise in the continuous case: Approximate efficiency of the adaptive pre-averaging method., Stochastic Processes and their Applications125, 2910 - 2936. · Zbl 1314.62095
[28] Jacod, J. and P. Protter (2012)., Discretization of processes. Springer. · Zbl 1259.60004
[29] Jacod, J. and V. Todorov (2010). Do price and volatility jump together?, The Annals of Applied Probability20(4), 1425-1469. · Zbl 1203.62139
[30] Kalnina, I. and D. Xiu (2017). Nonparametric Estimation of the Leverage Effect: A Trade-Off Between Robustness and Efficiency., Journal of the American Statistical Association112(517), 384-396.
[31] Koike, Y. (2016). Estimation of integrated covariances in the simultaneous presence of nonsynchronicity, microstructure noise and jumps., Econometric Theory32(3), 533-611. · Zbl 1441.62779
[32] Lee, S. and P. A. Mykland (2008). Jumps in finacial markets: A new nonparametric test and jump dynamics., Review of Financial Studies21(6), 2535-2563.
[33] Lee, S. and P. A. Mykland (2012). Jumps in equilibrium prices and market microstructure noise., Journal of Econometrics168(2), 396-406. · Zbl 1443.62360
[34] Liu, J., F. Longstaff, and J. Pan (2003). Dynamic asset allocation with event risk., Journal of Finance58(1), 231-259.
[35] Mancini, C. (2009). Non-parametric threshold estimation for models with stochastic diffusion coefficient and jumps., Scandinavian Journal of Statistics36(4), 270-296. · Zbl 1198.62079
[36] Mancini, C., V. Mattiussi, and R. Reno (2015). Spot volatility estimation using delta sequences., Finance and Stochastics19(2), 261-293. · Zbl 1310.91149
[37] Munk, A. and J. Schmidt-Hieber (2010a). Lower bounds for volatility estimation in microstructure noise models. In J. O. Berger, T. T. Cai, and I. M. Johnstone (Eds.), Borrowing Strength: Theory Powering Applications - A Festschrift for Lawrence D. Brown, Volume 6 of Collections, pp. 43-55. Beachwood, Ohio, USA: Institute of Mathematical Statistics.
[38] Munk, A. and J. Schmidt-Hieber (2010b). Nonparametric estimation of the volatility function in a high-frequency model corrupted by noise., Electronic Journal of Statistics4, 781-821. · Zbl 1329.62366
[39] Pastor, L. and P. Veronesi (2012). Uncertainty about government policy and stock prices., Journal of Finance67(4), 1219-1264.
[40] Reiß, M. (2011). Asymptotic equivalence for inference on the volatility from noisy observations., The Annals of Statistics39(2), 772-802. · Zbl 1215.62113
[41] Tauchen, G. and V. Todorov (2011). Volatility jumps., Journal of Business and Economic Statistics29(3), 356-371. · Zbl 1219.91156
[42] Todorov, V. (2010). Variance risk-premium dynamics: The role of jumps., Review of Financial Studies23(1), 345-383.
[43] Winkelmann, L., M. Bibinger, and T. Linzert (2016). Ecb monetary policy surprises: Identification through cojumps in interest rates., Journal of Applied Econometrics31(4), 613-629.
[44] Zhang, L. (2006). Efficient estimation of stochastic volatility using noisy observations: A multi-scale approach., Bernoulli12(6), 1019-1043. · Zbl 1117.62119
[45] Zu, Y. and H. · Zbl 1311.91198
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.