Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-09T22:30:07.687Z Has data issue: false hasContentIssue false
  • English
  • Français

SIGNAL EXTRACTION IN LONG MEMORY STOCHASTIC VOLATILITY

Published online by Cambridge University Press:  14 October 2014

Josu Arteche
Josu Arteche*
Affiliation:
University of the Basque Country UPV/EHU
*
*Address correspondence to Josu Arteche, Dept. of Econometrics and Statistics, University of the Basque Country UPV/EHU, Bilbao 48015, Spain; e-mail: [email protected].
Get access Rights & Permissions [Opens in a new window]

Abstract

Long memory in stochastic volatility (LMSV) models are flexible tools for the modeling of persistent dynamic volatility, which is a typical characteristic of financial time series. However, their empirical applicability is limited because of the complications inherent in the estimation of the model and in the extraction of the volatility component. This paper proposes a new technique for volatility extraction, based on a semiparametric version of the optimal Wiener–Kolmogorov filter in the frequency domain. Its main characteristics are its simplicity and generality, because no parametric specification is needed for the volatility component and it remains valid for both stationary and nonstationary signals. The applicability of the proposal is shown in a Monte Carlo and in a daily series of returns from the Dow Jones Industrial index.

Type
ARTICLES
Information
Econometric Theory , Volume 31 , Issue 6 , December 2015 , pp. 1382 - 1402
Copyright
Copyright © Cambridge University Press 2014 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Arteche, J. (2006) Semiparametric estimation in perturbed long memory series. Computational Statistics and Data Analysis 51, 2118–2141.CrossRefGoogle Scholar
Arteche, J. (2012) Semiparametric inference in correlated long memory signal plus noise models. Econometric Reviews 31, 440–474.Google Scholar
Arteche, J. & Robinson, P.M. (2000) Semiparametric inference in seasonal and cyclical long memory processes. Journal of Time Series Analysis 21, 1–25.Google Scholar
Bell, W. (1984) Signal extraction for nonstationary time series. Annals of Statistics 12, 646–664.Google Scholar
Breidt, F.J., Crato, N., & de Lima, P. (1998) The detection and estimation of long memory in stochastic volatility. Journal of Econometrics 83, 325–348.Google Scholar
Brillinger, D.R. (1975) Time Series: Data Analysis and Theory. Holt, Rinehart and Winston, Inc.Google Scholar
Brockwell, P.J. & Davies, R.A. (2006) Time Series: Theory and Methods. Springer.Google Scholar
Giraitis, L., Kokoska, P., & Leipus, R. (2000) Stationary ARCH models: Dependence structure and central limit theorem. Econometric Theory 16, 3–22.Google Scholar
Harvey, A.C. (1998) Long memory in stochastic volatility. In Knight, J. & Satchell, S. (eds.), Forecasting Volatility in Financial Markets, pp. 307–320. Butterworth-Heinemann.Google Scholar
Harvey, A.C., Ruiz, E., & Shephard, N. (1994) Multivariate stochastic variance models. Review of Economic Studies 61, 247–264.Google Scholar
Hidalgo, J. & Yajima, Y. (2002) Prediction and signal extraction of strongly dependent processes in the frequency domain. Econometric Theory 18, 584–624.Google Scholar
Hurvich, C.M., Moulines, E., & Soulier, P. (2005) Estimating long memory in volatility. Econometrica 73, 1283–1328.Google Scholar
Robinson, P.M. (1995) Gaussian semiparametric estimation of long-range dependence. Annals of Statistics 23, 1630–1661.Google Scholar
Shimotsu, K. (2010) Exact local Whittle estimation of fractional integration with unknown mean and time trend. Econometric Theory 26, 501–540.CrossRefGoogle Scholar
Taqqu, M.S. & Teverovsky, V. (1996) Semi-parametric Graphical Estimation Techniques for Long-Memory Data . Lecture Notes in Statistics, vol. 115, pp. 420–432.CrossRefGoogle Scholar
Velasco, C. (1999a) Non-stationary log-periodogram regression. Journal of Econometrics 91, 325–371.Google Scholar
Velasco, C. (1999b) Gaussian semiparametric estimation of non-stationary time series. Journal of Time Series Analysis 20, 87–127.Google Scholar
Velasco, C. (2003) Nonparametric frequency domain analysis of nonstationary multivariate time series. Journal of Statistical Planning and Inference 116, 209–247.Google Scholar
Zaffaroni, P. (2004) Stationarity and memory of ARCH(∞) models. Econometric Theory 20, 147–160.CrossRefGoogle Scholar
Supplementary material: File

Arteche supplementary data

Supplementary material

Download Arteche supplementary data(File)
File 43.4 KB
Supplementary material: PDF

Arteche supplementary data

Supplementary material

Download Arteche supplementary data(PDF)
PDF 834.8 KB