Determining the hurst exponent for time series data

• US 6,144,877 A
• Filed: 08/11/1998
• Issued: 11/07/2000
• Est. Priority Date: 08/11/1998
• Status: Expired due to Fees

• Current Assignee: The United States of America, as represented by the Secretary, Department of Health and Human Services
• Original Assignee: United States Department Of Health And Human Services (Government of the United States of America)
• Inventors: DePetrillo, Paolo B.
• Primary Examiner(s): LAYNO, CARL HERNANDZ
• Application Number:
  US09/132,462
• Time in Patent Office: 819 Days
• Field of Search: 600/515
• US Class Current: 600/515
• CPC Class Codes: A61B 5/318 Heart-related electrical modalities, e.g. electrocardiography [ECG]
• CPC Class Codes: G06F 17/10 Complex mathematical operations function generation by table look-up G06F1/03; evaluation of elementary functions by calculation G06F7/544

Abstract

Statistical information is determined for time series data of a measurable activity. The time series data of the measurable activity is obtained and comprises data elements representative of the measurable activity. A Hurst exponent is determined from the time series data and is the statistical information of the time series data.

Claims

1. A method using a computer for determining statistical information for time series data for a measurable activity, the method comprising the steps of:

obtaining the time series data of the measurable activity, the time of the series data comprising a plurality of data elements representative of the measurable activity; and

using a computer to determine a Hurst exponent from the time series data, the Hurst exponent being the statistical information of the time series data.

2. A method according to claim 1, wherein the step of determining the Hurst exponent comprises the step of:

determining a plurality of lengths L(r) for a plurality of sampling resolutions r for a plurality of self-similar fractal curves for the time series data.

3. A method according to claim 2, wherein the length L(r) and the sampling resolution r are related by:

##EQU3## where the plurality of data elements of the time series data are represented by S₁ S₂,S₃, . . . , S_N, r=1,2,3, . . . , M, I is the integer part of (N-r-n+1)/r, and n≧

1 is an embedding dimension.

4. A method according to claim 2, wherein the step of determining the Hurst exponent further comprises the step of:

determining a linear relationship between log (r) and log [L(r)/r].

5. A method according to claim 4, wherein the step of determining the Hurst exponent further comprises the step of:

determining a slope of the linear relationship between log (r) and log [L(r)/r].

6. A method according to claim 5, wherein the step of determining the Hurst exponent further comprises the step of:

determining the Hurst exponent from the slope of the linear relationship between log (r) and log [L(r)/r].

7. A method according to claim 1, wherein obtaining the time series data comprises measuring the measurable activity to obtain the time series data.

8. A method according to claim 1, wherein obtaining the time series data comprises retrieving the time series data from a computer-readable medium.

9. A method according to claim 1, wherein the measurable activity is a biologically generated activity.

10. A method according to claim 1, wherein the time series data are representative of measurements of heart rate variability.

11. A method according to claim 1, further comprising the step of:

detecting a biological condition using the Hurst exponent.

12. A method according to claim 11, wherein the biological condition is alcoholism.

13. A method according to claim 11, wherein the biological condition is related to a change in serotonin activity in a biological subject.

14. A method according to claim 11, wherein the biological condition is related to the heart of a biological subject.

15. A method according to claim 11, wherein the biological condition is a psychiatric disorder.

16. An apparatus for determining statistical information for time series data for a measurable activity, comprising:

means for obtaining the time series data of the measurable activity, the time series data comprising a plurality of data elements representative of the measurable activity; and

means for determining a Hurst exponent from the time series data, the Hurst exponent being the statistical information of the time series data.

17. An apparatus according to claim 16, wherein said means for determining the Hurst exponent comprises:

means for determining a plurality of lengths L(r) for a plurality of sampling resolutions r for a plurality of self-similar fractal curves for the time series data.

18. An apparatus according to claim 17, wherein the length L(r) and the sampling resolution r are related by:

##EQU4## where the plurality of data elements of the time series data are represented by S₁,S₂,S₃, . . . , S_N, r= 1,2,3, . . . , M, I is the integer part of (N-r-n+1)/r, and n≧

1 is an embedding dimension.

19. An apparatus according to claim 17, wherein said means for determining the Hurst exponent further comprises:

means for determining a linear relationship between log (r) and log [L(r)/r].

20. An apparatus according to claim 19, wherein said means for determining the Hurst exponent further comprises:

means for determining a slope of the linear relationship between log (r) and log [L(r)/r].

21. An apparatus according to claim 20, wherein said means for determining the Hurst exponent further comprises:

means for determining the Hurst exponent from the slope of the linear relationship between log (r) and log [L(r)/r].

22. An apparatus according to claim 16, wherein said means for obtaining the time series data comprises means for measuring the measurable activity to obtain the time series data.

23. An apparatus according to claim 16, wherein said means for obtaining the time series data comprises means for retrieving the time series data from a computer-readable medium.

24. An apparatus according to claim 16, wherein the measurable activity is a biologically generated activity.

25. An apparatus according to claim 16, wherein the time series data are representative of measurements of heart rate variability.

26. An apparatus according to claim 16, further comprising:

means for detecting a biological condition using the Hurst exponent.

27. An apparatus according to claim 26, wherein the biological condition is alcoholism.

28. An apparatus according to claim 26, wherein the biological condition is related to a change in serotonin activity in a biological subject.

29. An apparatus according to claim 26, wherein the biological condition is related to the heart of a biological subject.

30. An apparatus according to claim 26, wherein the biological condition is a psychiatric disorder.

31. A computer-readable medium embodying code segments for determining statistical information for time series data for a measurable activity, comprising:

code segments for obtaining the time series data of the measurable activity, the time series data comprising a plurality of data elements representative of the measurable activity; and

code segments for determining a Hurst exponent from the time series data, the Hurst exponent being the statistical information of the time series data.

32. A computer-readable medium according to claim 31, wherein said code segments for determining the Hurst exponent comprise:

code segments for determining a plurality of lengths L(r) for a plurality of sampling resolutions r for a plurality of self-similar fractal curves for the time series data.

33. A computer-readable medium according to claim 32, wherein the length L(r) and the sampling resolution r are related by:

##EQU5## where the plurality of data elements of the time series data are represented by S₁,S₂,S₃, . . . , S_N, r=1,2,3, . . . , M, I is the integer part of (N-r-n+1)/r, and n≧

1 is an embedding dimension.

34. A computer-readable medium according to claim 32, wherein said code segments for determining the Hurst exponent further comprise:

code segments for determining a linear relationship between log (r) and log [L(r)/r].

35. A computer-readable medium according to claim 34, wherein said code segments for determining the Hurst exponent further comprise:

code segments for determining a slope of the linear relationship between log (r) and log [L(r)/r].

36. A computer-readable medium according to claim 35, wherein said code segments for determining the Hurst exponent further comprise:

code segments for determining the Hurst exponent from the slope of the linear relationship between log (r) and log [L(r)/r].

37. A computer-readable medium according to claim 31, wherein said code segments for obtaining the time series data comprise code segments for measuring the measurable activity to obtain the time series data.

38. A computer-readable medium according to claim 31, wherein said code segments for obtaining the time series data comprise code segments for retrieving the time series data from a computer-readable medium.

39. A computer-readable medium according to claim 31, wherein the measurable activity is a biologically generated activity.

40. A computer-readable medium according to claim 31, wherein the time series data are representative of measurements of heart rate variability.

41. A computer-readable medium according to claim 31, further comprising:

code segments for detecting a biological condition using the Hurst exponent.

42. A computer-readable medium according to claim 41, wherein the biological condition is alcoholism.

43. A computer-readable medium according to claim 41, wherein the biological condition is related to a change in serotonin activity in a biological subject.

44. A computer-readable medium according to claim 41, wherein the biological condition is related to the heart of a biological subject.

45. A computer-readable medium according to claim 41, wherein the biological condition is a psychiatric disorder.