Some aspects of the serial correlation function as applied to a model of a fish swimming in a tank

Abstract

The objectives of this study were twofold. The first was to find a model based on time series analysis that would give a reasonably accurate simulation of the behaviour o f a normal fish under normal conditions in a tank. The tank under consideration was built by Dr. Herman Kleerekoper of Texas A&M University and was equipped with a grid of 44 x 44 photoelectric cells on ten centimeter centers. The tank was monitored by a PDP - 8 computer and the coordinates of a triggered cell and the elapsed time from the beginning of an experiment were recorded on magnetic tape. The data was transformed into polar coordinates and correlogram analysis was used as an aid in determining that an autoregressive scheme could be used. It was found that a fourth order autoregressive scheme was satisfactory for polar R and a third order scheme for polar 0. Some estimates of the mean and variance of the error were made and also a decision concerning the number of observations needed. A technique for estimating the parameters was discussed and confidence limits were established. The second objective of this work was to develop some algorithms that would aid in analyzing very long time series. First an algorithm was designed to generate artificial fish paths in the tank so that the effect of various time series techniques could be verified. Secondly, an algorithm was developed which displayed only the oscillations in a long correlogram which were different from those which preceded it. Three criteria were used and the user was given the opportunity to set two tolerances and a Type I error.