CYCLICAL VARIATIONS IN CRIME RATES CANNOT BE ACCURATELY IDENTIFIED BY SIMPLE OBSERVATION OF GRAPHICAL PRESENTATIONS OR OTHER DESCRIPTIVE METHODS. THE PURPOSE OF THIS RESEARCH IS TO PROVIDE A SYSTEMATIC STATISTICAL ANALYSIS OF CYCLICAL MOVEMENTS MONTHLY AND YEARLY HOMICIDE RATES IN THE UNITED STATES AND TO EXAMINE THE POTENTIAL USE OF TIME-SERIES ANALYSES OF CRIME RATES FOR PREDICTING VIOLENT CRIMES. THE MONTHLY DATA ANALYZED COVER 1963-1974, AND THE YEARLY DATA COVER 1900-1974. APPROACHES TO THE STUDY OF TIME-SERIES ANALYSES OF CRIME RATES ARE DISTINGUISHED BY THE INVESTIGATION OF SEASONAL AND CYCLICAL MOVEMENTS OF CRIME RATES, AND THE INVESTIGATION OF SOCIOECONOMIC DETERMINANTS OF VIOLENT CRIMES. THE IDENTIFICATION OF LEADING INDICATORS HAS BEEN SUGGESTED FOR COMBINING THESE TWO APPROACHES IN ORDER TO DEVELOP A FORECASTING MODEL OF CRIME RATES. CONSTRUCTION OF A FORECASTING MODEL REQUIRES STUDYING TIME SERIES AS A SEQUENCE OF OBSERVATIONS IN TIME, DESIGNED TO COMPLEMENT FREQUENCY ANALYSIS. THE AUTO-REGRESSIVE MOVING AVERAGE (ARMA) IS THE FORECASTING MODEL USED TO DESCRIBE THE BEHAVIOR OF THE TIME SERIES. SPECTRAL ANALYSIS, A STATISTICAL TECHNIQUE WHICH IDENTIFIES CYCLICAL COMPONENTS OF A TIME SERIES BY REDUCING A STATIONARY TIME SERIES TO A NUMBER OF CYCLES, WAS USED TO DETERMINE THE RELATIVE CONTRIBUTION OF EACH CYCLE TO TOTAL VARIANCE OF THE TIME SERIES AND ITS STATISTICAL SIGNIFICANCE. CROSS-SPECTRAL ANALYSIS, WHICH ATTEMPTS TO DISCOVER THE STATISTICAL RELATIONSHIP BETWEEN TWO STATIONARY TIME SERIES, WAS CONDUCTED ON THE FOLLOWING VARIBLES: SEASONALLY ADJUSTED UNEMPLOYMENT RATES FOR MALES AGED 20 TO 24 AND MONTHLY DATA ON HOMICIDE RATES FOR 1963 TO 1974. THEN IT WAS USED TO ATTAIN OBJECTIVES CONSIDERING A GIVEN RANGE OF FREQUENCIES: (1) IDENTIFICATION OF CYCLICAL COMPONENTS OF EACH SERIES; (2) ESTABLISHMENT OF THE DEGREE OF ASSOCIATION BETWEEN THE CYCLES OF THE TWO TIME SERIES; AND (3) ESTABLISHMENT OF THE LEAD-LAG RELATIONSHIP BETWEEN THE CYCLES OF EACH SERIES. THE ANALYSIS DEMONSTRATED THAT THE EMPIRICAL KNOWLEDGE OF THE BEHAVIOR OF TIME SERIES COULD BE USED AS A BASIS FOR CONSTRUCTING FORECASTING MODELS. THIS COULD SUPPORT FUTURE RESEARCH SEEKING TO IDENTIFY SOCIOECONOMIC AND DEMOGRAPHIC CORRELATES OF CRIME RATES. TABULAR DATA, FORMULAS, FIGURES, NOTES, AND REFERENCES ARE PROVIDED. (JCP)