Standard and seasonal long memory in volatility: an application to Spanish inflation

Abstract

The historical series of many economic variables, such as inflation, are characterized by a strong persistent behaviour in the form of long memory, not only in the long run or at zero frequency but often also at seasonal frequencies. In financial series, long memory is not apparent in levels but strong persistence in higher order moments such as volatility has been proven to be a stylized fact in stock returns. Interest in economic time series has, however, focused on the persistence of levels and little attention has been paid to higher order dependence, which can be important for assessing the stability of the series. We propose a semiparametric analysis of the standard and seasonal persistence of the volatility of a monthly Spanish inflation series. The conclusions can be summarized in three main results. First volatility shows strong persistence implying an unstable trend in prices, but its structure depends on the proxy used, the absolute values, the squares or the logarithms of squares. Second, the structure of the persistence of volatility changed with the first oil crisis in 1973, with a persistent trend in both periods, in contrast with levels. Third, the Taylor effect, which is well documented in financial series, does not apply in this series.