Skip to main content
Log in

Level changes in volatility models

  • Symposium
  • Published:
Annals of Finance Aims and scope Submit manuscript

Abstract

Level shifts confound the estimation of persistence. This paper shows analytically, in simulations, and using high-frequency stock price data that models for financial volatility that feature a separate source of randomness in the volatility equation are less susceptible to this effect. Such models include recently proposed time series models for realized volatility, as opposed to GARCH models for daily observations, which are highly sensitive to unknown shifts, as has been shown before.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Andersen T., Bollerslev T., Diebold F.X.: Roughing it up: including jump components in the measurement, modeling and forecasting of return volatility. Rev Econ Stat 89(4), 701–720 (2007)

    Article  Google Scholar 

  • Andreou E., Ghysels E.: Detecting multiple breaks in financial market volatility dynamics. J Appl Economet 17, 579–600 (2002)

    Article  Google Scholar 

  • Bai J.: Least quares estimation of a shift in linear processes. J Time Ser Anal 15(5), 453–472 (1994)

    Article  Google Scholar 

  • Bai J.: Estimating multiple breaks one at a time. Economet Theory 13, 315–352 (1997)

    Article  Google Scholar 

  • Bai J., Perron P.: Estimating and testing linear models with multiple structural changes. Econometrica 66(1), 47–78 (1998)

    Article  Google Scholar 

  • Barndorff-Nielsen O.E., Hansen P.R., Lunde A., Shephard N.: Designing realised kernels to measure the ex-post variation of equity prices in the presence of noise. Econometrica 76, 1481–1536 (2008)

    Article  Google Scholar 

  • Berkes I., Gombay E., Horvath L., Kokoszka P.: Sequential change-point detection in GARCH(p,q) models. Economet Theory 20, 1140–1167 (2004)

    Google Scholar 

  • Bollerslev T.: Generalized autoregressive conditional heteroskedasticity. J Economet 31, 307–327 (1986)

    Article  Google Scholar 

  • Chen C., Tiao G.C.: Random level-shift time series models, ARIMA approximations, and level-shift detection. J Bus Econ Stat 8(1), 83–97 (1990)

    Article  Google Scholar 

  • Choi K., Zivot E.: Long memory and structural changes in the forward discount: an mpirical investigation. J Int Money Finance 26(3), 342–362 (2007)

    Article  Google Scholar 

  • Corsi F.: A simple approximate long memory model of realized volatility. J Financ Economet 7(2), 174–196 (2009)

    Article  Google Scholar 

  • Davidson J., Sibbertsen P.: Generating schemes for long memory processes: regimes, aggregation and linearity. J Economet 128, 253–282 (2005)

    Article  Google Scholar 

  • Diebold F.X.: Modeling the persistence of conditional variances: a comment. Economet Rev 5, 51–56 (1986)

    Article  Google Scholar 

  • Diebold F.X., Inoue A.: Long memory and regime switching. J Economet 105, 131–159 (2001)

    Article  Google Scholar 

  • Engle R.F.: Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica 50(4), 987–1007 (1982)

    Article  Google Scholar 

  • Engle R.F., Bollerslev T.: Modeling the persistence of conditional variances. Economet Rev 5, 1–50 (1986)

    Article  Google Scholar 

  • Fouque J.P., Papanicolaou G., Sircar K.R., Sølna K.: Short time-scale in S&P 500 volatility. J Comput Finance 6, 1–23 (2003)

    Google Scholar 

  • Francq C., Roussignol M., Zakoïan J.M.: Conditional heteroskedasticity driven by hidden Markov chains. J Time Ser Anal 22, 197–220 (2001)

    Article  Google Scholar 

  • Frühwirth-Schnatter S.: Full Bayesian analysis of switching Gaussian state space models. Ann Inst Stat Math 53(1), 31–49 (2001)

    Article  Google Scholar 

  • Granger C.W.J., Hyung N.: Occasional structural breaks and long memory with an application to the S&P500 absolute stock returns. J Empir Finance 3, 399–421 (2004)

    Article  Google Scholar 

  • Granger C.W.J., Teräsvirta T.: A simple nonlinear time series model with misleading linear properties. Econ Lett 62, 161–165 (2001)

    Article  Google Scholar 

  • Gray S.: Modeling the conditional distribution of interest rates as a regime-switching process. J Financ Econ 42, 27–62 (1996)

    Article  Google Scholar 

  • Hamilton J.D.: A new approach to the economic analysis of nonstationary time series and the business cycle. Econometrica 57(2), 357–384 (1989)

    Article  Google Scholar 

  • Hamilton J.D., Susmel R.: Autoregressive conditional heteroskedasticity and changes in regime. J Economet 64, 307–333 (1994)

    Article  Google Scholar 

  • Han H., Park J.Y.: Time series properties of ARCH processes with persistent covariates. J Economet 146, 275–292 (2008)

    Article  Google Scholar 

  • Hendry D.F., Neale A.J.: A Monte Carlo study of the effects of structural breaks on tests for unit roots. In: Hackl, P., Westlund, A.H. (eds) Economic Structural Change, Analysis and Forecasting, pp. 95–119. Springer, New York (1991)

    Google Scholar 

  • Hillebrand E.: Neglecting parameter changes in GARCH models. J Economet 129, 121–138 (2005)

    Article  Google Scholar 

  • Hillebrand E., Medeiros M.C.: Estimating and forecasting GARCH models in the presence of structural breaks and regime switches. In: Rapach, D.E., Wohar, M. (eds) Forecasting in the Presence of Structural Breaks and Model Uncertainty, pp. 303–325. Elsevier, Emerald (2008)

    Chapter  Google Scholar 

  • Hyung N., Poon S.H., Granger C.W.J.: A source of long memory in volatility. In: Rapach, D.E., Wohar, M. (eds) Forecasting in the Presence of Structural Breaks and Model Uncertainty, pp. 329–380. Elsevier, Emerald (2008)

    Chapter  Google Scholar 

  • Kaufmann S., Frühwirth-Schnatter S.: Bayesian analysis of switching ARCH models. J Time Ser Anal 23(4), 425–458 (2002)

    Article  Google Scholar 

  • Kokoszka P., Leipus R.: Testing for parameter changes in ARCH models. Lithuanian Math J 39(2), 182–195 (1999)

    Article  Google Scholar 

  • Kokoszka P., Leipus R.: Changepoint estimation in ARCH models. Bernoulli 6, 513–539 (2000)

    Article  Google Scholar 

  • Lamoureux C.G., Lastrapes W.D.: Persistence in variance, structural change, and the GARCH model. J Bus Econ Stat 8, 225–234 (1990)

    Article  Google Scholar 

  • Lobato I.N., Savin N.E.: Real and spurious long-memory properties of stock-market data. J Bus Econ Stat 16, 261–268 (1998)

    Article  Google Scholar 

  • Lumsdaine R.: Consistency and asymptotic normality of the quasi-maximum likelihood estimator in IGARCH(1,1) and covariance stationary GARCH(1,1) models. Econometrica 64, 575–596 (1996)

    Article  Google Scholar 

  • Medeiros M.C., Veiga A.: Modeling multiple regimes in financial volatility with a flexible coefficient GARCH(1,1) model. Economet Theory 25, 117–161 (2009)

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Ng S., Vogelsang T.J.: Analysis of vector autoregressions in the presence of shifts in mean. Economet Rev 21(3), 353–381 (2002)

    Article  Google Scholar 

  • Perron P.: The great crash, the oil price shock, and the unit root hypothesis. Econometrica 57(6), 1361–1401 (1989)

    Article  Google Scholar 

  • Perron P.: Testing for a unit root in a time series with a changing mean. J Bus Econ Stat 8(2), 153–162 (1990)

    Article  Google Scholar 

  • Rapach D.E., Strauss J.K.: Structural breaks and GARCH models of exchange rate volatility. J Appl Economet 23(1), 65–90 (2008)

    Article  Google Scholar 

  • Rapach D.E., Strauss J.K., Wohar M.: Forecasting stock return volatility in the presence of structural breaks. In: Rapach, D.E., Wohar, M. (eds) Forecasting in the Presence of Structural Breaks and Model Uncertainty, pp. 81–416. Elsevier, Emerald (2008)

    Google Scholar 

  • Smith A.: Level shifts and the illusion of long memory in economic time series. J Bus Econ Stat 23(3), 321–335 (2005)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Eric Hillebrand.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Craioveanu, M., Hillebrand, E. Level changes in volatility models. Ann Finance 8, 277–308 (2012). https://doi.org/10.1007/s10436-010-0163-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10436-010-0163-5

Keywords

JEL Classification

Navigation