Data for this study were obtained from the Uniform Crime Reports issued by the North Carolina Department of Justice. The Auto Regressive Moving Average (ARMA) model, derived empirically from the data, was used instead of the traditional regression, model which is built on the basis of previous theory and research. Findings included no significant trends in arrest data for all drug offenders for 1976 to 1979, and a seasonal fluctuation of high marijuana arrest rates during the summer months and low arrest rates in the winter months. Findings imply that, at least for the recent past, there has been no significant increase or decrease in the use of drugs. The use of arrest statistics for future research of demographic data on offenders, potential risk groups, and the effects of social environments is recommended. 3 tables, 3 figures, 2 notes and 22 references.