Export file:


  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text


  • Citation Only
  • Citation and Abstract

The memory of volatility

Faculty of Economics and Management, Leibniz University Hannover, Königsworther Platz 1, 30167 Hannover, Germany

Special Issue: Volatility of Prices of Financial Assets

The focus of the volatility literature on forecasting and the predominance of theconceptually simpler HAR model over long memory stochastic volatility models has led to the factthat the actual degree of memory estimates has rarely been considered. Estimates in the literaturerange roughly between 0.4 and 0.6 - that is from the higher stationary to the lower non-stationaryregion. This difference, however, has important practical implications - such as the existence or nonexistenceof the fourth moment of the return distribution. Inference on the memory order is complicatedby the presence of measurement error in realized volatility and the potential of spurious long memory.In this paper we provide a comprehensive analysis of the memory in variances of international stockindices and exchange rates. On the one hand, we find that the variance of exchange rates is subject tospurious long memory and the true memory parameter is in the higher stationary range. Stock indexvariances, on the other hand, are free of low frequency contaminations and the memory is in the lowernon-stationary range. These results are obtained using state of the art local Whittle methods that allowconsistent estimation in presence of perturbations or low frequency contaminations.
  Article Metrics


1.Andersen TG, Bollerslev T, Diebold FX, et al. (2001) The distribution of realized exchange rate volatility. J Am Statist Associ 96: 42–55.    

2.Andersen TG, Bollerslev T, Diebold FX, et al. (2003) Modeling and forecasting realized volatility. Econom 71: 579–625.    

3.Andrews DWK, Sun Y (2004) Adaptive Local Polynomial Whittle Estimation of Long-range Dependence. Econom 72: 569–614.    

4.Arteche J (2004) Gaussian semiparametric estimation in long memory in stochastic volatility and signal plus noise models. J Econom 119: 131–154.    

5.Arteche J, Orbe J (2016) A bootstrap approximation for the distribution of the Local Whittle estimator. Comput Stat Data Anal 100: 645–660.    

6.Barndorff-Nielsen OE, Hansen PR, Lunde A, et al. (2009) Realized kernels in practice: Trades and quotes. Econom J 12: C1–C32.    

7.Barndorff-Nielsen OE, Shephard N (2002) Econometric analysis of realized volatility and its use in estimating stochastic volatility models. J Royal Stat Soc: Ser B (Statist Methodol) 64: 253–280.    

8.Chiriac R, Voev V (2011) Modelling and forecasting multivariate realized volatility. J Appl Econom 26: 922–947.    

9.Corsi F (2009) A simple approximate long-memory model of realized volatility. J Financ Econom 7: 174–196.

10.Deo RS, Hurvich CM, Lu Y (2006) Forecasting realized volatility using a long-memory stochastic volatility model: estimation, prediction and seasonal adjustment. J Econom 131: 29–58.    

11.Deo RS, Hurvich CM (2001) On the log periodogram regression estimator of the memory parameter in long memory stochastic volatility models. Econom Theory 17: 686–710.    

12.Diebold FX, Inoue A (2001) Long memory and regime switching. J Econom 105: 131-159.    

13.Frederiksen P, Nielsen FS, Nielsen M (2012) Local polynomial Whittle estimation of perturbed fractional processes. J Econom 167: 426–447.    

14.Geweke J, Porter-Hudak S (1983) The estimation and application of long memory time series models. J Time Ser Anal 4: 221–238.    

15.Giraitis L, Leipus R, Surgailis D (2007) Recent advances in ARCH modelling. Long Memory Econom 3–38.

16.Giraitis L, Leipus R, Surgailis D (2009) ARCH infinity models and long memory properties. Handb Financ Time Ser 71–84.

17.Gourieroux C, Jasiak J (2001) Memory and infrequent breaks. Econom Lett 70: 29–41.    

18.Granger CWJ, Ding Z (1996) Varieties of long memory models. J Econom 73: 61–77.    

19.Granger CWJ, Hyung N (2004) Occasional structural breaks and long memory with an application to the S&P 500 absolute stock returns. J Empir Financ 11: 399–421.    

20.Heber G, Lunde A, Shephard N, et al. (2009) Oxford-Man Institutes realized library, version 0.2, Oxford-Man Institute, University of Oxford.

21.Hou J, Perron P (2014) Modified local Whittle estimator for long memory processes in the presence of low frequency (and other) contaminations. J Econom 182: 309–328.    

22.Hurvich CM, Moulines E, Soulier P (2005) Estimating long memory in volatility. Econom 73: 1283–1328.    

23.Hurvich CM, Ray BK (2003) The local Whittle estimator of long-memory stochastic volatility. J Financ Econom 1: 445–470.    

24.Iacone F (2010) Local Whittle estimation of the memory parameter in presence of deterministic components. J Time Ser Anal 31: 37–49.    

25.Künsch HR (1987) Statistical aspects of self-similar processes. Proc First World Congr Bernoulli Soc 1: 67–74.

26.Leccadito A, Rachedi O, Urga G (2015) True versus spurious long memory: Some theoretical results and a monte carlo comparison. Econom Rev 34: 452–479.    

27.Leschinski C, Sibbertsen P (2017) Origins of Spurious Long Memory. Hann Econ Pap.

28.Lu YK, Perron P (2010) Modeling and forecasting stock return volatility using a random level shift model. J Empir Financ 17: 138–156.    

29.Martens M, Dijk DV, de Pooter M (2009) Forecasting S&P 500 volatility: Long memory, level shifts, leverage effects, day-of-the-week seasonality, and macroeconomic announcements. Int J Forecast 25: 282–303.    

30.McCloskey A, Perron P (2013) Memory parameter estimation in the presence of level shifts and deterministic trends. Econom Theory 29: 1196–1237.    

31.Mikosch T, Stărică C (2004) Nonstationarities in financial time series, the long-range dependence, and the IGARCH effects. Rev Econ Stat 86: 378–390.    

32.Perron P, Qu Z (2010) Long-memory and level shifts in the volatility of stock market return indices. J Bus Econ Stat 28: 275–290.    

33.Qu Z (2011) A test against spurious long memory. J Bus Econ Stat 29: 423–438.    

34.Robinson PM (1995a) Gaussian semiparametric estimation of long range dependence. Annals Stat 23: 1630–1661.

35.Robinson PM (1995b) Log-periodogram regression of time series with long range dependence. Annals Stat 23: 1048–1072.

36.Sibbertsen P, Leschinski C, Busch M (2017) A multivariate test against spurious long memory. J Econom (in press).

37.Velasco C (1999) Gaussian Semiparametric Estimation of Non-stationary Time Series. J Time Ser Anal 20: 87–127.    

38.Xu J, Perron P (2014) Forecasting return volatility: Level shifts with varying jump probability and mean reversion. Int J Forecast 30: 449–463.    

© 2018 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Article outline

Show full outline
Copyright © AIMS Press All Rights Reserved