TY - JOUR

T1 - Evaluation of the ARTAFIT method for fitting time-series input processes for simulation

AU - Biller, Bahar

AU - Nelson, Barry L.

PY - 2008

Y1 - 2008

N2 - Time-series input processes occur naturally in the stochastic simulation of many service, communications, and manufacturing systems, and there are a variety of time-series input models available to match a given collection of properties, typically a marginal distribution and an autocorrelation structure specified via the use of one or more time lags. The focus of this paper is the situation in which the collection of properties are not “given,” but data are available from which a time-series input model is to be estimated. The input model we consider is the very flexible autoregressive-to-anything (ARTA) model of Cario and Nelson [Cario, M. C., B. L. Nelson. 1996. Autoregressive to anything: Time-series input processes for simulation. Oper. Res. Lett. 19 51–58]. Recently, we developed a statistically valid algorithm (ARTAFIT) for fitting this model to stationary univariate time-series data using marginal distributions from the Johnson translation system. In this paper, we perform a comprehensive numerical study to assess the performance of our algorithm relative to the two most commonly used approaches: (a) fitting the marginal distribution but ignoring the autocorrelation structure, and (b) fitting separately the marginal distribution as in (a) and the autocorrelation structure using the sample autocorrelation function. We find that ARTAFIT, which fits the marginal distribution and the autocorrelation structure jointly, outperforms both (a) and (b), and we demonstrate the importance of taking dependencies into account while developing input models for stochastic simulation.

AB - Time-series input processes occur naturally in the stochastic simulation of many service, communications, and manufacturing systems, and there are a variety of time-series input models available to match a given collection of properties, typically a marginal distribution and an autocorrelation structure specified via the use of one or more time lags. The focus of this paper is the situation in which the collection of properties are not “given,” but data are available from which a time-series input model is to be estimated. The input model we consider is the very flexible autoregressive-to-anything (ARTA) model of Cario and Nelson [Cario, M. C., B. L. Nelson. 1996. Autoregressive to anything: Time-series input processes for simulation. Oper. Res. Lett. 19 51–58]. Recently, we developed a statistically valid algorithm (ARTAFIT) for fitting this model to stationary univariate time-series data using marginal distributions from the Johnson translation system. In this paper, we perform a comprehensive numerical study to assess the performance of our algorithm relative to the two most commonly used approaches: (a) fitting the marginal distribution but ignoring the autocorrelation structure, and (b) fitting separately the marginal distribution as in (a) and the autocorrelation structure using the sample autocorrelation function. We find that ARTAFIT, which fits the marginal distribution and the autocorrelation structure jointly, outperforms both (a) and (b), and we demonstrate the importance of taking dependencies into account while developing input models for stochastic simulation.

KW - simulation

KW - statistical analysis

U2 - 10.1287/ijoc.1070.0261

DO - 10.1287/ijoc.1070.0261

M3 - Journal article

VL - 20

SP - 485

EP - 498

JO - INFORMS Journal on Computing

JF - INFORMS Journal on Computing

SN - 1091-9856

IS - 3

ER -