A seasonal analysis of Chinese births.

Abstract

Chinese cultural patterns of birthing tend to follow a long cycle of a year or more and an annual seasonal cycle. Data on seasonality of births by month of occurrence are modeled with a Box/Jenkins seasonal model with a deterministic seasonality and a stochastic seasonality for Chinese populations in Singapore (1961-86), Malaysia (1966-85), Hong Kong (1971-86), and Taiwan (1964-86). The seasonality of marriages by month of registration was also estimated with least squares regressions. The effect of economic development on seasonality was examined by modeling Chinese birth data for 2 periods: 1961-69 and 1974-86. The Chinese lunar calendar is 12 moons lasting 29-30 days, and a new moon, embolism, is added every 2-3 years to accommodate the Western calendar. In the modeling of births, the deterministic seasonal component is represented by a sin/cos function while the stochastic seasonality is represented as a seasonal autoregressive moving average (ARMA). Methodology is explained. An ARMA model and a subset of ARMA models for the residuals are generated as well as the full model using the maximum likelihood method for all the subsets and choosing a model that minimizes Akaike's information criterion or Schwarz's Bayesian criterion. Data were checked with the Ljung/Box/Pierce Q statistic. The null hypothesis was tested. Data series were adjusted for the length of the month. Unlike double differencing used in ARMA modeling, the subtraction of seasonal means was used because double differencing increased the standard deviations. The results for Malaysia and Hong Kong show deterministic seasonality. A Taiwanese, model, which uses month of registration not occurrence, was more difficult to model, and deterministic seasonality is assumed. The 4 countries were similar: birth peaks in October in Singapore, Malaysia, and Hong Kong and in November in Taiwan. The birth troughs were more variable. Malaysia and Hong Kong models showed a stochastic component as well. Economic development has not changed the seasonality for Singapore. Marriages follow the expected pattern peaking during the Chinese New Year (Jeanuary-February) for Taiwan, and peaks in November and December for Singapore and Hong Kong due to early registration of marriages. Marriage seasonality only explained the seasonality of 1st births. A caveat is that regression models that attempt to eliminate seasonality of births through use of dummy variables may have misleading results.