Search Advanced

Quantitative Finance and Economics

2018, Volume 2, Issue 1: 622-644. doi: 10.3934/QFE.2018.1.137
Previous Article Next Article
Research article Special Issues

The memory of volatility

  • Faculty of Economics and Management, Leibniz University Hannover, Königsworther Platz 1,30167 Hannover, Germany
  • Received: 04 August 2017 Accepted: 26 September 2017 Published: 13 March 2018

  • JEL Codes: G11

  • The focus of the volatility literature on forecasting and the predominance of the conceptually simpler HAR model over long memory stochastic volatility models has led to the fact that the actual degree of memory estimates has rarely been considered. Estimates in the literature range roughly between 0.4 and 0.6 -that is from the higher stationary to the lower non-stationary region. This difference, however, has important practical implications -such as the existence or nonexistence of the fourth moment of the return distribution. Inference on the memory order is complicated by 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 stock indices and exchange rates. On the one hand, we find that the variance of exchange rates is subject to spurious long memory and the true memory parameter is in the higher stationary range. Stock index variances, on the other hand, are free of low frequency contaminations and the memory is in the lower non-stationary range. These results are obtained using state of the art local Whittle methods that allow consistent estimation in presence of perturbations or low frequency contaminations.

    Citation: Kai R. Wenger, Christian H. Leschinski, Philipp Sibbertsen. The memory of volatility[J]. Quantitative Finance and Economics, 2018, 2(1): 622-644. doi: 10.3934/QFE.2018.1.137

    Related Papers:

  • The focus of the volatility literature on forecasting and the predominance of the conceptually simpler HAR model over long memory stochastic volatility models has led to the fact that the actual degree of memory estimates has rarely been considered. Estimates in the literature range roughly between 0.4 and 0.6 -that is from the higher stationary to the lower non-stationary region. This difference, however, has important practical implications -such as the existence or nonexistence of the fourth moment of the return distribution. Inference on the memory order is complicated by 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 stock indices and exchange rates. On the one hand, we find that the variance of exchange rates is subject to spurious long memory and the true memory parameter is in the higher stationary range. Stock index variances, on the other hand, are free of low frequency contaminations and the memory is in the lower non-stationary range. These results are obtained using state of the art local Whittle methods that allow consistent estimation in presence of perturbations or low frequency contaminations.


    加载中
    [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.
  • Reader Comments
  • © 2018 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索
Quantitative Finance and Economics
5.3

Metrics

Article views(3398) PDF downloads(1642) Cited by(3)

Preview PDF
Download XML
Export Citation
Article outline

Figures and Tables

Tables(14)

Other Articles By Authors

Related pages

Tools

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog