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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: [email protected]
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: [email protected]; [email protected]
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: [email protected]; [email protected]
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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 

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