The purpose of this paper is to examine the time series property of fertility change and fluctuation in postwar Japan. At first, we tested the null hypothesis in which the macro-fertility index has a unit root by various procedures. It was not rejected against an alternative hypothesis of trend stationarity. We conclude that the change of fertility has moved according to a random walk with a drift, not a "deterministic" trend. Therefore, fertility is influenced by probability factors over the long-term ; hence, there is the possibility that fertility will be reversed upward by an exogenous shock in the future. It is well said that the structure of fertility index had changed in Japan after 1966, the year of Hinoe-Uma. We examined this structural change with the step-wise Chow test and reconfirmed it. The presence of this structural change, however, does not modify the above conclusion of a unit root in fertility index. Assuming that there is a unit root in macro-fertility index, we decomposed TFR into a long-term and a short term factor, and we showed that the avoidance of a notification of birth due to superstition reached about several per cent in the year of Hinoe-Uma. Moreover, as an extension of above conclusions, we examined the possibility of applying the Butz-Ward model to Japanese data. We made clear that the model could not be adopted because there was no cointegration between fertility variable and economic variables of family income and women's wages. The approach using time series analysis, though it has limitations for structural investigation, is a useful tool to explain features of time series change. In this sense, this paper provides a new view on demographic studies.