A discrete log-normal process to sequentially generate a multifractal time series

Journal of Statistical Mechanics: Theory and Experiment

Volumn 2011, Issue 12, 2011, Pages

  Perpete N ^a   Schmitt, F G ^b  

^a UNIVERSITÉ LILLE 1   (France)

^b Laboratoire d Océanologie et de Géosciences   (France)

Author keywords

dynamical processes (theory); fluctuations (theory); intermittency; stochastic processes (theory)

Indexed keywords

EID: 84855477999     PISSN: None     EISSN: 17425468     Source Type: Journal    
DOI: 10.1088/1742-5468/2011/12/P12013     Document Type: Article

References (58)

1. Hentschel H G E and Procaccia I 1983 Physica D 8 435
2. Benzi R, Paladin G, Parisi G and Vulpiani A 1984 J. Phys. A: Math. Gen. 17 3521
3. Parisi G and Frisch U 1985 On the singularity structure of fully developed turbulence Turbulence and Predictability in Geophysical Fluid Dynamics and Climate Dynamics ed M Ghil et al (Amsterdam: North-Holland) pp84-7
4. Meneveau C and Sreenivasan K R 1987 Phys. Rev. Lett. 59 1424
5. Frisch U 1995 Turbulence (Cambridge: Cambridge University Press)
6. Schertzer D, Lovejoy S, Schmitt F G, Chigirinskaya Y and Marsan D 1997 Fractals 5 427
7. Schertzer D and Lovejoy S 1987 J. Geophys. Res. 92 9692
8. Deidda R 1999 Phys. Chem. Earth B 24 73
9. Seuront L and Schmitt F G 2004 Geophys. Res. Lett. 31 L03306
10. Turiel A, Nieves V, Garcia-Ladona E, Font J, Rio M-H and Larnicol G 2009 Ocean Sci. 5 447
11. Lovejoy S and Schertzer D 2010 Atmos. Res. 96 1
12. Schmitt F, Schertzer D and Lovejoy S 1999 Appl. Stoch. Models Data Anal. 15 29
13. Muzy J-F, Delour J and Bacry E 2000 Eur. Phys. J. B 17 537
14. Calvet L 2008 Multifractal Volatility: Theory, Forecasting and Pricing (Amsterdam: Elsevier Science)
15. Aubry J-M and Jaffard S 2002 Commun. Math. Phys. 227 483
16. Anselmet F, Gagne Y, Hopfinger E A and Antonia R A 1984 J. Fluid Mech. 140 63
17. Arneodo A et al 1996 Europhys. Lett. 34 411
18. Schmitt F G 2006 Physica A 368 377
19. Lashermes B, Roux S G, Abry P and Jaffard S 2008 Eur. Phys. J. B 61 201
20. Ivanova K and Ausloos M 1999 Eur. Phys. J. B 8 665
21. Yaglom A M 1966 Sov. Phys. Dokl. 11 49
22. Schertzer D and Lovejoy S 1984 On the dimension of atmospheric motions Turbulence and Chaotic Phenomena in Fluids ed T Tatsumi (Amsterdam: North Holland) pp505-12
23. Schmitt F, Lavallee D, Schertzer D and Lovejoy S 1992 Phys. Rev. Lett. 68 305
24. Arneodo A, Muzy J-F and Sornette D 1998 Eur. Phys. J. B 2 277
25. Lux T 2000 Quant. Finance 1 632
26. Schmitt F, Vannitsem S and Barbosa A 1998 J. Geophys. Res. 103(D8) 23181
27. de Montera L, Barthese L, Mallet C and Gole P 2009 J. Hydrometeorol. 10 493
28. Mandelbrot B B 1989 PAGEOPH 131 5
29. Muzy J F, Bacry E and Arneodo A 1991 Phys. Rev. Lett. 67 3515
30. Brown G, Michon G and Peyriere J 1992 J. Stat. Phys. 66 775
31. Barral J, Coppens M-O and Mandelbrot B B 2003 J. Math. Pures Appl. 82 1555
32. Schmitt F G and Chainais P 2007 Eur. Phys. J. B 58 149
33. Schmitt F G and Marsan D 2001 Eur. Phys. J. B 20 3
34. Bacry E and Muzy J-F 2003 Commun. Math. Phys. 236 449
35. Gurvich A S and Zubkovski S L 1963 Izv. Akad. Nauk. SSSR Ser. Geofiz. 1856
36. Pond S and Stewart R W 1965 Izv. Akad. Nauk SSSR, Phys. Ocean Atmos. 1 914
37. Mandelbrot B B 1974 J. Fluid Mech. 62 331
38. Schertzer D and Lovejoy S 1992 Physica A 185 187
39. Schmitt F, Schertzer D, Lovejoy S and Brunet Y 1994 Nonlinear Proc. Geophys. 1 95
40. Lashermes B, Abry P and Chainais P 2004 Int. J. Wav. Mult. Infor. Proc. 2 497
41. Muzy J F, Bacry E and Kozhemyak A 2006 Phys. Rev. E 73 066114
42. Kahane J-P 1985 Ann. Sc. Math. Québec 9 105
43. Samorodnitsky G and Taqqu M S 1994 Stable non-Gaussian Random Processes Stochastic Models with Infinite Variance (London: Chapman and Hall)
44. Polya G and Szego D 1967 Problems and Theorems in Analysis (Berlin: Springer)
45. Weron R 1996 Stat. Probab. Lett. 28 165
46. Kokoszka P S and Taqqu M S 1995 Stoch. Proc. Appl. 60 19
47. Kokoszka P S and Taqqu M S 1994 J. Time Ser. Anal. 15 203
48. Granger C W J and Joyeux R 1980 J. Time Ser. Anal. 1 15
49. Hosking J R M 1981 Biometrika 68 165
50. Montanari A, Rosso R and Taqqu M S 1997 Water Resour. Res. 33 1035
51. Barbulescu A and Pelican E 2009 ARIMA models for the analysis of the precipitation evolution Recent Advances in Computers ed N E Mastorakis et al (Rodos: WSEAS Press) pp221-6
52. Bertacca M, Rosso R, Berizzi F and Mese E D 2005 IEEE Trans. Geosci. Remote Sensing 43 2484
53. Kavasseri R G and Seetharaman K 2009 Renew. Energy 34 1388
54. Stanislavsky A A et al 2009 Astrophys. J. 693 1877
55. Harmantzis F C and Hatzinakos D 2005 Heavy network traffic modeling and simulation using stable FARIMA Performance Challenges for Efficient Next Generation Networks vol 6A-C ed X J Liang et al (Beijing: Beijing University Post Telecommunication Press) pp435-50
56. Song L, Bondon P, Cao Y and Cheng Q 2008 A time-varying FARIMA model for internet traffic CISP 2008: 1st Int. Congr. on Image and Signal Processing vol 5 Proceedings ed D Li and G Deng (IEEE Computer Soc.) pp83-7
57. Stoev S and Taqqu M S 2004 Fractals 12 95
58. Stoev S and Taqqu M S 2005 J. Time Ser. Anal. 26 211