Evaluation of order determination procedures in ARMA models

Autoregression-moving average (ARMA) models provide insight into many biological systems. One of the most difficult decisions in ARMA modeling is identifying the order of the model. Many procedures have been proposed. The purpose of this study was to compare Pandit and Wu\u27s multi-objective test criterion with Akaike\u27s information criterion and Schwartz\u27s Bayesian criterion, SBC. Several versions of the criteria were compared for 10 processes which were simulations of ARMA models ranging in order from (1,1) to (8,7). Batches of 100 realizations were generated for each model. The performance of the criteria varied depending on how closely a process complied with the assumptions, length of series and alpha levels chosen. The error variance and method of parameter estimation had no effect on the relative merits of the criteria. The proposed strategy uses Pandit and Wu\u27s (2p,2p-1) portfolio and SBC (or F-ratio, if sample size $\le$125) to identify a neighborhood for the model on the first pass. The portfolio is modified to include all models between adjacent primary models which define the neighborhood. In the second pass, a model is selected using SBC. Three classical time series were assessed by this strategy. The results compare favorably to those in the literature. The proposed strategy was utilized to identify a sensible heat loss model for non-laying hens. The ARMA(2,0) model which was selected for all four hens, explained 70 to 89% of the total variation. The proposed strategy was also used to identify a tympanic temperature model for steers housed in a constant thermoneutral environment. The ARMA(3,0) model was adequate for both animals in the study, although the model accounted for only 15 to 27% of the total variation. This dissertation is divided into four sections. The first contains a literature review of time series relative to dynamic systems. The second provides a comparison of order determination procedures and introduces a new strategy. The third describes the utilization of proposed strategy in modeling biological processes. The last section discusses various aspects in the construction of simulation software