ARCH, GARCH, and ARMAX Models for Forecasting Pathogen Indicators and Advisories at Marine Recreational Sites

Abstract

Despite the wide ranging applications of time series methodologies for stochastic processes, they have not been used for environmental economics (except climate change). To fill this gap, we introduce time series methodology for the environmental econometrics, presenting autoregressive, moving average, ARCH, GARCH, and ARMAX models. These models are applied to establish a functional relationship between pathogen indicator and meteorological and environmental variables using time series data associated with Huntington Beach, Ohio. According to ARCH, turbidity, dew point, flow, and rainfall are statistically significant variables. Other models produced roughly similar results because of the short lag order. Models confirm the lag order of one using Akaike, Schwartz, and Hannan-Quinn selection criteria, reflecting very short memory of the pathogen indicator series. However, the time series did not support GARCH variance structure. These models not only under forecasted observations at both ends of the distribution of the data, but also simultaneously underforecasted advisories.