Analysis of Long-Term Ecological Data Using Categorical Time Series Regression

Abstract

We propose a time series analysis method based on the use of categorized variables and ordinary least squares regression. It has several advantages over Box–Jenkins models and time series regression with continuous variables, including model specification based on ecological information, parsimonious representations of the functional forms of model terms and interactions, robust treatment of the high uncertainty associated with long-term ecological data, and interpretive features based on linear combinations of the regression coefficients. Aspects of model building, significance testing, and interpretation of results are discussed and illustrated with a fisheries example involving an annual measure of white perch (Morone americana) stock size in the Delaware River/Bay from 1929 to 1974. Variation in white perch dynamics is analyzed using the following explanatory variables: lagged values of stock, hydrographic variables (freshwater flow and water temperature), and pollution-related variables (sewage loading, dredging activity, and dissolved oxygen). Potential statistical problems with the new method involving multicollinearity, autocorrelated errors, and other violations of ordinary least squares are identified.