Statistical analysis of the seasonal variation in demographic data

There has been little agreement as to whether reproduction or similar demographic events occur seasonally and, especially, whether there is any universal seasonal pattern. One reason is that the seasonal pattern may vary in different populations and at different times. Another reason is that different statistical methods have been used. Every statistical model is based on certain assumed conditions and hence is designed to identify specific components of the seasonal pattern. Therefore, the statistical method applied should be chosen with due consideration. In this study we present, develop, and compare different statistical methods for the study of seasonal variation. Furthermore, we stress that the methods are applicable for the analysis of many kinds of demographic data. The first approaches in the literature were based on monthly frequencies, on the simple sine curve, and on the approximation that the months are of equal length. Later, "the population at risk" and the fact that the months have different lengths were considered. Under these later assumptions the targets of the statistical analyses are the rates. In this study we present and generalize the earlier models. Furthermore, we use trigonometric regression methods. The trigonometric regression model in its simplest form corresponds to the sine curve. We compare the regression methods with the earlier models and reanalyze some data. Our results show that models for rates eliminate the disturbing effects of the varying length of the months, including the effect of leap years, and of the seasonal pattern of the population at risk. Therefore, they give the purest analysis of the seasonal pattern of the demographic data in question, e.g., rates of general births, twin maternities, neural tube defects, and mortality. Our main finding is that the trigonometric regression methods are more flexible and easier to handle than the earlier methods, particularly when the data differ from the simple sine curve.