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.
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References
Arteche J (2002) Semiparametric robust tests on seasonal or cyclical long memory time series. J Time Ser Anal 23: 251–285
Arteche J (2004) Gaussian semiparametric estimation in long memory in stochastic volatility and signal plus noise models. J Econom 119: 131–154
Arteche J (2006) Semiparametric estimation in perturbed long memory series. Comput Stat Data Anal 52: 2118–2141
Arteche J (2007) The analysis of seasonal long memory: the case of Spanish inflation. Oxf Bull Econ Stat 69: 749–772
Arteche J, Robinson PM (1999) Seasonal and cyclical long memory. In: Ghosh S (ed) Asymptotics, nonparametrics and time series. Marcel Dekker, Inc., New York, pp 115–148
Arteche J, Robinson PM (2000) Semiparametric inference in seasonal and cyclical long memory processes. J Time Ser Anal 21: 1–25
Baillie RT, Bollerslev T, Mikkelsen HO (1996a) Fractionally integrated generalized autoregressive conditional heteroskedasticity. J Econom 74: 3–30
Baillie RT, Chung CF, Tieslau MA (1996b) Analysing inflation by the fractionally integrated ARFIMA-GARCH model. J Appl Econom 11: 23–40
Bollerslev T, Mikkelsen HO (1996) Modeling and pricing long memory in stock market volatility. J Econom 73: 151–184
Bordignon S, Caporin M, Lisi F (2007) Generalized long-memory GARCH models for intra-daily volatility. Comput Stat Data Anal 51: 5900–5912
Bos CS, Koopman J, Ooms M (2007) Long memory modelling of inflation with stochastic variance and structural breaks. CREATES Research Paper 2007-44
Breidt FJ, Crato N, de Lima P (1998) The detection and estimation of long memory in stochastic volatility. J Econom 83: 325–348
Broto C, Ruiz E (2009) Testing for conditional heterocedasticity in the components of inflation. Stud Nonlinear Dyn Econom 13(2): 1–28
Ding Z, Granger CWJ (1996) Modeling volatility persistence of speculative returns: a new approach. J Econom 73: 185–215
Ding Z, Granger CWJ, Engle RF (1993) A long-memory property of stock market returns and a new model. J Empir Financ 1: 83–106
Gil-Alana LA (2001) Seasonal long memory in the US monthly monetary aggregate. Appl Econ Lett 8: 573–575
Gil-Alana LA (2002) Seasonal long memory in the aggregate output. Econ Lett 74: 333–337
Giraitis L, Kokoska P, Leipus R (2000) Stationary ARCH models: dependence structure and central limit theorem. Econom Theory 16: 3–22
Giraitis L, Robinson PM, Surgailis D (2004) LARCH, leverage and long memory. J Financ Econom 2: 177–210
Granger CWJ (1966) The typical spectral shape of an economic variable. Econometrica 34: 150–161
Granger CWJ, Ding Z (1995) Some properties of absolute return. An alternative measure of risk. Annales d’Economie et de Statistique 40: 67–91
Granger CWJ, Ding Z (1996) Varieties of long memory models. J Econom 73: 61–77
Harvey AC (1998) Long memory in stochastic volatitility. In: Knight J., Satchell S. (eds) Forecasting volatility in financial markets. Butterworth-Haineman, Oxford, pp 307–320
Hurvich CM, Moulines E, Soulier P (2005) Estimating long memory in volatility. Econometrica 73: 1283–1328
Kumar MS, Okimoto T (2007) Dynamics of persistence in international inflation rates. J Money Credit Bank 39: 1457–1479
Malmsten H, Teräsvirta T (2004) Stylized facts of financial time series and three popular models of volatility. SSE/EFI working papers series in economics and finance, Stockholm School of Economics
Mora-Galán A, Pérez A, Ruiz E (2004) Stochastic volatility models and the Taylor effect. Working paper 04-63, Statistics and econometrics series 15. Universidad Carlos III de Madrid
Porter-Hudak S (1990) An application of seasonal fractionally differenced model to the monetary aggregates. J Am Stat Assoc 85: 338–344
Ray BK (1993) Long-range forecasting of IBM product revenues using a seasonal fractionally differenced ARMA model. Int J Forecast 9: 255–269
Robinson PM (1991) Testing for strong serial correlation and dynamic conditional heteroskedasticity in multiple regression. J Econom 47: 67–84
Surgailis D, Viano MC (2002) Long memory properties and covariance structure of the EGARCH model. ESAIM Probab Stat 6: 311–329
Taylor SJ (1986) Modelling financial time series. Wiley, New York
Zaffaroni P (2004) Stationarity and memory of ARCH(∞) models. Econom Theory 20: 147–160
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Arteche, J. Standard and seasonal long memory in volatility: an application to Spanish inflation. Empir Econ 42, 693–712 (2012). https://doi.org/10.1007/s00181-010-0446-8
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DOI: https://doi.org/10.1007/s00181-010-0446-8