Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-13T10:19:31.456Z Has data issue: false hasContentIssue false
  • English
  • Français

TEMPORAL SHAPING OF SIMULATED TIME SERIES WITH CYCLICAL SAMPLE PATHS

Published online by Cambridge University Press:  09 January 2017

Weiwei Chen ,
Alok Baveja  and
Benjamin Melamed
Weiwei Chen
Affiliation:
Department of Supply Chain Management, Rutgers University, Rutgers Business School – Newark and New Brunswick, 1 Washington Park, Newark, NJ 07901, USA E-mail: wchen@business.rutgers.edu
Alok Baveja
Affiliation:
Department of Supply Chain Management, Rutgers University, Rutgers Business School – Newark and New Brunswick, 100 Rockafeller Road, Piscataway, NJ 08854, USA E-mail: baveja@business.rutgers.edu; melamed@business.rutgers.edu
Benjamin Melamed
Affiliation:
Department of Supply Chain Management, Rutgers University, Rutgers Business School – Newark and New Brunswick, 100 Rockafeller Road, Piscataway, NJ 08854, USA E-mail: baveja@business.rutgers.edu; melamed@business.rutgers.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

Temporal shaping of time series is the activity of deriving a time series model with a prescribed marginal distribution and some sample path characteristics. Starting with an empirical sample path, one often computes from it an empirical histogram (a step-function density) and empirical autocorrelation function. The corresponding cumulative distribution function is piecewise linear, and so is the inverse distribution function. The so-called inversion method uses the latter to generate the corresponding distribution from a uniform random variable on [0,1), histograms being a special case. This paper shows how to manipulate the inverse histogram and an underlying marginally uniform process, so as to “shape” the model sample paths in an attempt to match the qualitative nature of the empirical sample paths, while maintaining a guaranteed match of the empirical marginal distribution. It proposes a new approach to temporal shaping of time series and identifies a number of operations on a piecewise-linear inverse histogram function, which leave the marginal distribution invariant. For cyclical processes with a prescribed marginal distribution and a prescribed cycle profile, one can also use these transformations to generate sample paths which “conform” to the profile. This approach also improves the ability to approximate the empirical autocorrelation function.

Keywords

ARM processesautocorrelation functionshistogramsmodel fittingmodeling time seriestemporal shapingTES processes
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 32 , Issue 1 , January 2018 , pp. 126 - 143
Copyright
Copyright © Cambridge University Press 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Bertsekas, D.P. (1999). Nonlinear programming, 2nd ed. Athena Scientific, Belmont, Massachusetts, USA.Google Scholar
2. Bratley, P., Fox, B.L., & Schrage, L.E. (1987). A guide to simulation. Springer-Verlag, New York, NY, USA.Google Scholar
3. Cario, M.C. & Nelson, B.L. (1996). Autoregressive to anything: Time-series input processes for simulation. OR Letters 19: 51–58.Google Scholar
4. Cario, M.C. & Nelson, B.L. (1998). Numerical methods for fitting and simulating autoregressive-to-anything processes. INFORMS Journal on Computing 10(1): 72–81.Google Scholar
5. Feller, W. (1971). An introduction to probability theory and its applications, vol. 2, 2nd ed. John Wiley & Sons, Inc., New York, NY, USA.Google Scholar
6. Liu, B. & Munson, D.C. (1982). Generation of a random sequence having a jointly specified marginal distribution and autocovariance. IEEE Transactions on Acoustics, Speech and Signal Processing 30(6): 973–983.Google Scholar
7. Lewis, P.A.W. & McKenzie, E. (1991). Minification processes and their transformations. Journal of Applied Probability 28: 45–57.Google Scholar
8. Jagerman, D.L. & Melamed, B. (1992). The transition and autocorrelation structure of TES processes part I: General theory. Stochastic Models 8(2): 193–219.CrossRefGoogle Scholar
9. Jagerman, D.L. & Melamed, B. (1992). The transition and autocorrelation structure of TES processes part II: Special cases. Stochastic Models 8(3): 499–527.CrossRefGoogle Scholar
10. Jagerman, D.L. & Melamed, B. (1994). The spectral structure of TES processes. Stochastic Models 10(3): 599–618.CrossRefGoogle Scholar
11. Jagerman, D.L. & Melamed, B. (1995). Bidirectional estimation and confidence regions for TES processes. Proceedings of MASCOTS ’95, Durham, North Carolina, pp. 94–98.Google Scholar
12. Jelenkovic, P. & Melamed, B. (1995). Automated TES modeling of compressed video. Proceedings of IEEE INFOCOM ’95, Boston, Massachusetts, pp. 746–752.CrossRefGoogle Scholar
13. Jelenkovic, P. & Melamed, B. (1995). Algorithmic modeling of TES processes. IEEE Transactions on Automatic Control 40(7): 1305–1312.Google Scholar
14. Melamed, B. (1991). TES: A class of methods for generating autocorrelated uniform variates. ORSA Journal on Computing 3(4): 317–329.CrossRefGoogle Scholar
15. Melamed, B. (1993). An overview of TES processes and modeling methodology. In Donatiello, L. & Nelson, R. (eds.), Performance evaluation of computer and communications systems. Springer-Verlag Berlin Heidelberg Lecture Notes in Computer Science, pp. 359–393.Google Scholar
16. Melamed, B. (1999). ARM processes and modeling methodology. Stochastic Models 15(5): 903–929.CrossRefGoogle Scholar