메뉴 건너뛰기




Volumn 123, Issue 7, 2013, Pages 2475-2499

Some limit theorems for hawkes processes and application to financial statistics

Author keywords

Discretisation of stochastic processes; Hawkes processes; Limit theorems; Point processes; Statistics of random processes

Indexed keywords

FINANCE; RANDOM PROCESSES; STATISTICS; STOCHASTIC SYSTEMS;

EID: 84885063010     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spa.2013.04.007     Document Type: Article
Times cited : (191)

References (28)
  • 2
    • 84874579362 scopus 로고    scopus 로고
    • Trade-throughs: Empirical facts and application to lead-lag measures
    • F. Abregel, B.K. Chakrabarti, A. Chakrabart, M. Mitra (Eds.), New Economic Windows, Springer, Berlin, Heidelberg
    • F. Abergel, F. Pomponio, Trade-throughs: empirical facts and application to lead-lag measures, in: F. Abregel, B.K. Chakrabarti, A. Chakrabart, M. Mitra (Eds.), Econophysics of Order-Driven Markets, in: New Economic Windows, Springer, Berlin, Heidelberg, 2011.
    • (2011) Econophysics of Order-Driven Markets
    • Abergel, F.1    Pomponio, F.2
  • 4
    • 25844435205 scopus 로고    scopus 로고
    • How often to sample a continuous-time process in the presence of market microstructure noise
    • DOI 10.1093/rfs/hhi016
    • Y. Ait-Sahalia, P.A. Mykland, L. Zhang, How often to sample a continuous-time process in the presence of market microstructure noise, The Review of Financial Studies 18 (2005) 351-416. (Pubitemid 41389276)
    • (2005) Review of Financial Studies , vol.18 , Issue.2 , pp. 351-416
    • Ait-Sahalia, Y.1    Mykland, P.A.2    Zhang, L.3
  • 5
    • 78649734954 scopus 로고    scopus 로고
    • Ultra high frequency volatility estimation with dependent microstructure noise
    • Y. Ait-Sahalia, P.A. Mykland, L. Zhang, Ultra high frequency volatility estimation with dependent microstructure noise, Journal of Econometrics 160 (2011) 160-175.
    • (2011) Journal of Econometrics , vol.160 , pp. 160-175
    • Ait-Sahalia, Y.1    Mykland, P.A.2    Zhang, L.3
  • 6
    • 0008108418 scopus 로고    scopus 로고
    • Understanding, optimizing, using and forecasting realized volatility and correlation
    • T. Andersen, T. Bollerslev, F.X. Diebold, P. Labys, (Understanding, optimizing, using and forecasting) Realized volatility and correlation, in: "Great Realizations Risk, 2000, pp. 105-108.
    • (2000) Great Realizations Risk , pp. 105-108
    • Andersen, T.1    Bollerslev, T.2    Diebold, F.X.3    Labys, P.4
  • 7
    • 84861315065 scopus 로고    scopus 로고
    • Modelling microstructure noise with mutually exciting point processes
    • E. Bacry, S. Delattre, M. Hoffmann, J.F. Muzy, Modelling microstructure noise with mutually exciting point processes, Quantitative Finance 13 (2013) 65-77.
    • (2013) Quantitative Finance , vol.13 , pp. 65-77
    • Bacry, E.1    Delattre, S.2    Hoffmann, M.3    Muzy, J.F.4
  • 8
    • 56349136475 scopus 로고    scopus 로고
    • Designing realised kernels to measure the ex-post variation of equity prices in the presence of noise
    • O. Barndorff-Nielsen, P. Hansen, A. Lunde, N. Stephard, Designing realised kernels to measure the ex-post variation of equity prices in the presence of noise, Econometrica 76 (6) (2008) 1481-1536.
    • (2008) Econometrica , vol.76 , Issue.6 , pp. 1481-1536
    • Barndorff-Nielsen, O.1    Hansen, P.2    Lunde, A.3    Stephard, N.4
  • 10
    • 79956347891 scopus 로고    scopus 로고
    • Modelling financial high frequency data using point processes
    • T. Mikosch, J.-P. Kreiss, R.A. Davis, T.G. Andersen (Eds.), Springer, Berlin, Heidelberg
    • L. Bauwens, N. Hautsch, Modelling financial high frequency data using point processes, in: T. Mikosch, J.-P. Kreiss, R.A. Davis, T.G. Andersen (Eds.), Handbook of Financial Time Series, Springer, Berlin, Heidelberg, 2009.
    • (2009) Handbook of Financial Time Series
    • Bauwens, L.1    Hautsch, N.2
  • 11
    • 0036508533 scopus 로고    scopus 로고
    • Power spectra of general shot noises and Hawkes point processes with a random excitation
    • DOI 10.1239/aap/1019160957
    • P. Bremaud, L. Massoulie, Power spectra of general shot noises and hawkes point processes with a random excitation, Advances in Applied Probability 34 (2002) 205-222. (Pubitemid 34726721)
    • (2002) Advances in Applied Probability , vol.34 , Issue.1 , pp. 205-222
    • Bremaud, P.1    Massoulie, L.2
  • 12
    • 0003508387 scopus 로고    scopus 로고
    • An introduction to the theory of point processes
    • second ed., Probability and its Applications (New York), Springer-Verlag, New York
    • D.J. Daley, D. Vere-Jones, An Introduction to the Theory of Point Processes. Vol. 1: Elementary Theory and Methods, second ed., in: Probability and its Applications (New York), Springer-Verlag, New York, 2003.
    • (2003) Elementary Theory and Methods , vol.1
    • Daley, D.J.1    Vere-Jones, D.2
  • 14
    • 84859447054 scopus 로고    scopus 로고
    • Multivariate hawkes processes: An application to financial data
    • P. Embrechts, J.T. Liniger, L. Lu, Multivariate Hawkes processes: an application to financial data, Journal of Applied Probability 48 (2011) 367-378.
    • (2011) Journal of Applied Probability , vol.48 , pp. 367-378
    • Embrechts, P.1    Liniger, J.T.2    Lu, L.3
  • 17
    • 0002920214 scopus 로고
    • Spectra of some self-exciting and mutually exciting point processes
    • A.G. Hawkes, Spectra of some self-exciting and mutually exciting point processes, Biometrika 58 (1971) 83-90.
    • (1971) Biometrika , vol.58 , pp. 83-90
    • Hawkes, A.G.1
  • 18
    • 0001915688 scopus 로고
    • Spectra of some mutually exciting point processes with associated variables
    • P.A.W. Lewis (Ed.), Wiley, New York
    • A.G. Hawkes, Spectra of some mutually exciting point processes with associated variables, in: P.A.W. Lewis (Ed.), Stochastic Point Processes, Wiley, New York, 1972.
    • (1972) Stochastic Point Processes
    • Hawkes, A.G.1
  • 19
    • 0001446567 scopus 로고
    • A cluster process representation of a self-exciting process
    • A.G. Hawkes, D. Oakes, A cluster process representation of a self-exciting process, Journal of Applied Probability 11 (1974) 493-503.
    • (1974) Journal of Applied Probability , vol.11 , pp. 493-503
    • Hawkes, A.G.1    Oakes, D.2
  • 21
    • 84884128241 scopus 로고    scopus 로고
    • Estimation of the lead-lag effect from nonsynchronous data
    • M. Hoffmann, M. Rosenbaum, N. Yoshida, Estimation of the lead-lag effect from nonsynchronous data, Bernoulli 19 (2013) 426-461.
    • (2013) Bernoulli , vol.19 , pp. 426-461
    • Hoffmann, M.1    Rosenbaum, M.2    Yoshida, N.3
  • 22
    • 0000531113 scopus 로고
    • Multivariate point processes: Predictable projection, radon-nikodym derivatives, representation of martingales
    • J. Jacod, Multivariate point processes: predictable projection, Radon-Nikodym derivatives, representation of martingales, Zeitschrift fur Wahrscheinlichkeitstheorie und Verwandte Gebiete 31 (1974-1975) 235-253.
    • (1974) Zeitschrift Fur Wahrscheinlichkeitstheorie Und Verwandte Gebiete , vol.31 , pp. 235-253
    • Jacod, J.1
  • 23
    • 0003757289 scopus 로고
    • Limit theorems for stochastic processes
    • (Fundamental Principles of Mathematical Sciences), Springer-Verlag, Berlin
    • J. Jacod, A.N. Shiryaev, Limit Theorems for Stochastic Processes, in: Grundlehren der Mathematischen Wissenschaften (Fundamental Principles of Mathematical Sciences), vol. 288, Springer-Verlag, Berlin, 1987.
    • (1987) Grundlehren Der Mathematischen Wissenschaften , vol.288
    • Jacod, J.1    Shiryaev, A.N.2
  • 24
    • 51249182136 scopus 로고
    • The asymptotic behaviour of maximum likelihood estimators for stationary point processes
    • Y. Ogata, The asymptotic behaviour of maximum likelihood estimators for stationary point processes, Annals of the Institute of Statistical Mathematics 30 (1978) 243-261.
    • (1978) Annals of the Institute of Statistical Mathematics , vol.30 , pp. 243-261
    • Ogata, Y.1
  • 25
    • 77957600568 scopus 로고    scopus 로고
    • Adaptive estimation for hawkes processes; application to genome analysis
    • P. Reynaud-Bouret, S. Schbath, Adaptive estimation for Hawkes processes; application to genome analysis, Annals of Statistics 38 (2010) 2781-2822.
    • (2010) Annals of Statistics , vol.38 , pp. 2781-2822
    • Reynaud-Bouret, P.1    Schbath, S.2
  • 26
    • 79954611545 scopus 로고    scopus 로고
    • A new approach for the dynamics of ultra high frequency data: The model with uncertainty zones
    • C.Y. Robert, M. Rosenbaum, A new approach for the dynamics of ultra high frequency data: The model with uncertainty zones, Journal of Financial Econometrics 9 (2011) 344-366.
    • (2011) Journal of Financial Econometrics , vol.9 , pp. 344-366
    • Robert, C.Y.1    Rosenbaum, M.2
  • 27
    • 79957801014 scopus 로고    scopus 로고
    • A new microstructure noise index
    • M. Rosenbaum, A new microstructure noise index, Quantitative Finance 6 (2011) 883-899.
    • (2011) Quantitative Finance , vol.6 , pp. 883-899
    • Rosenbaum, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.