The Analysis of Seasonal Long Memory: The Case of Spanish Inflation*
用半参数方法分析西班牙月度通胀数据的季节性长记忆特征，发现该序列在部分季节频率存在长记忆，且1973年前后周期行为不同，之后出现单位根表明冲击有持久效应。
Abstract This paper describes semiparametric techniques recently proposed for the analysis of seasonal or cyclical long memory and applies them to a monthly Spanish inflation series. One of the conclusions is that this series has long memory not only at the origin but also at some but not all seasonal frequencies, suggesting that the fractional difference operator (1− L 12 ) d should be avoided. Moreover, different persistent cycles are observed before and after the first oil crisis. Whereas the cycles seem stationary in the former period, we find evidence of a unit root after 1973, which implies that a shock has a permanent effect. Finally, it is shown how to compute the exact impulse responses and the coefficients in the autoregressive expansion of parametric seasonal long memory models. These two quantities are important to assess the impact of aleatory shocks such as those produced by a change of economic policy and for forecasting purposes, respectively.