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.

Fractionally Differenced Gegenbauer Processes with Long Memory: A Review

“…Several statistical modelling methodologies have been developed, among which we mention the fractional Gaussian noise process of Abrahams and Dempster (1979), the seasonal fractionally integrated autoregressive moving average (SARFIMA) model of Porter-Hudak (1990), the flexible seasonal fractionally integrated process (flexible ARFISMA) of Hassler (1994), the k-GARMA process of Woodward, Cheng and Gray (1998), the seasonal long range dependent process of Palma and Chan (2005), the seasonal fractionally integrated process of Reisen, Rodrigues and Palma (2006) and the seasonal ARFIMA model of Bisognin and Lopes (2009). Statistical inference for seasonal long memory processes has been dealt with by Giraitis and Leipus (1995), Chung (1996), Arteche and Robinson (2000), Velasco and Robinson (2000), Giraitis, Hidalgo and Robinson (2001), Palma (2007), Arteche (2007), Koopman, Ooms and Carnero (2007), Bisognin and Lopes (2009), Hsu and Tsai (2009) and Arteche (2012).…”