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An Application of a Short Memory Model with Random Level Shifts to the Volatility of Latin American Stock Market Returns

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  • Rodríguez, Gabriel

    (Pontificia Universidad Católica del Perú)

  • Tramontana, Roxana

    (Pontificia Universidad Católica del Perú)

Abstract

Empirical research indicates that the volatility of stock return time series have long memory. However, it has been demonstrated that short memory processes contaminated with random level shifts can often be confused as being long memory. Often this feature is referred to as spurious long memory. This paper represents an empirical study of the random level shift (RLS) model using the approach of Lu and Perron (2010) and Li and Perron (2013) for the volatility of daily stocks returns data for ve Latin American countries. The RLS model consists of the sum of a short term memory component and a level shift component, where the level shift component is governed by a Bernoulli process with a shift probability . The estimation results suggest that the level shifts in the volatility of daily stocks returns data are infrequent but once they are taken into account, the long memory characteristic and the GARCH e¤ects disappear. An out-of-sample forecasting exercise is also provided.

Suggested Citation

  • Rodríguez, Gabriel & Tramontana, Roxana, 2015. "An Application of a Short Memory Model with Random Level Shifts to the Volatility of Latin American Stock Market Returns," Working Papers 2015-004, Banco Central de Reserva del Perú.
    • Handle: RePEc:rbp:wpaper:2015-004
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    References listed on IDEAS

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    1. Perron, Pierre & Wada, Tatsuma, 2009. "Let's take a break: Trends and cycles in US real GDP," Journal of Monetary Economics, Elsevier, vol. 56(6), pages 749-765, September.
    2. Lobato, Ignacio N & Savin, N E, 1998. "Real and Spurious Long-Memory Properties of Stock-Market Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(3), pages 261-268, July.
    3. Alberto Humala & Gabriel Rodriguez, 2013. "Some stylized facts of return in the foreign exchange and stock markets in Peru," Studies in Economics and Finance, Emerald Group Publishing Limited, vol. 30(2), pages 139-158, May.
    4. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    5. Tatsuma Wada & Pierre Perron, 2006. "State Space Model with Mixtures of Normals: Specifications and Applications to International Data," Boston University - Department of Economics - Working Papers Series WP2006-029, Boston University - Department of Economics.
    6. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
    7. Lu, Yang K. & Perron, Pierre, 2010. "Modeling and forecasting stock return volatility using a random level shift model," Journal of Empirical Finance, Elsevier, vol. 17(1), pages 138-156, January.
    8. Bollerslev, Tim & Ole Mikkelsen, Hans, 1996. "Modeling and pricing long memory in stock market volatility," Journal of Econometrics, Elsevier, vol. 73(1), pages 151-184, July.
    9. Tatsuma Wada & Pierre Perron, 2005. "An Alternative Trend-Cycle Decomposition using a State Space Model with Mixtures of Normals: Specifications and Applications to International Data," Boston University - Department of Economics - Working Papers Series WP2005-43, Boston University - Department of Economics.
    10. Granger, Clive W. J. & Hyung, Namwon, 2004. "Occasional structural breaks and long memory with an application to the S&P 500 absolute stock returns," Journal of Empirical Finance, Elsevier, vol. 11(3), pages 399-421, June.
    11. Hansen, Peter Reinhard & Lunde, Asger, 2006. "Consistent ranking of volatility models," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 97-121.
    12. Peter R. Hansen & Asger Lunde & James M. Nason, 2011. "The Model Confidence Set," Econometrica, Econometric Society, vol. 79(2), pages 453-497, March.
    13. Jushan Bai & Pierre Perron, 1998. "Estimating and Testing Linear Models with Multiple Structural Changes," Econometrica, Econometric Society, vol. 66(1), pages 47-78, January.
    14. Robert F. Engle & Aaron D. Smith, 1999. "Stochastic Permanent Breaks," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 553-574, November.
    15. Diebold, Francis X. & Inoue, Atsushi, 2001. "Long memory and regime switching," Journal of Econometrics, Elsevier, vol. 105(1), pages 131-159, November.
    16. Perron, Pierre & Qu, Zhongjun, 2010. "Long-Memory and Level Shifts in the Volatility of Stock Market Return Indices," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(2), pages 275-290.
    17. Perron, Pierre, 1989. "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 57(6), pages 1361-1401, November.
    18. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-384, March.
    19. Baillie, Richard T. & Bollerslev, Tim & Mikkelsen, Hans Ole, 1996. "Fractionally integrated generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 74(1), pages 3-30, September.
    20. Gourieroux, Christian & Jasiak, Joann, 2001. "Memory and infrequent breaks," Economics Letters, Elsevier, vol. 70(1), pages 29-41, January.
    21. Junior A. Ojeda Cunya & Gabriel Rodríguez, 2016. "An application of a random level shifts model to the volatility of Peruvian stock and exchange rate returns," Macroeconomics and Finance in Emerging Market Economies, Taylor & Francis Journals, vol. 9(1), pages 34-55, March.
    22. Lobato, Ignacio N & Savin, N E, 1998. "Real and Spurious Long-Memory Properties of Stock-Market Data: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(3), pages 280-283, July.
    23. Perron, Pierre, 1990. "Testing for a Unit Root in a Time Series with a Changing Mean," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(2), pages 153-162, April.
    24. Jushan Bai & Pierre Perron, 2003. "Computation and analysis of multiple structural change models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(1), pages 1-22.
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    Cited by:

    1. Dennis Alvaro & Ángel Guillén & Gabriel Rodríguez, 2017. "Modelling the volatility of commodities prices using a stochastic volatility model with random level shifts," Review of World Economics (Weltwirtschaftliches Archiv), Springer;Institut für Weltwirtschaft (Kiel Institute for the World Economy), vol. 153(1), pages 71-103, February.
    2. Gabriel Rodríguez, 2016. "Modeling Latin-American Stock and Forex Markets Volatility: Empirical Application of a Model with Random Level Shifts and Genuine Long Memory [Modelando la volatilidad de los mercados bursátiles y cam," Documentos de Trabajo / Working Papers 2016-416, Departamento de Economía - Pontificia Universidad Católica del Perú.
    3. Gabriel Rodríguez & José Carlos Gonzáles Tanaka, 2016. "An Empirical Application of a Random Level Shifts Model with Time-Varying Probability and Mean Reversion to the Volatility of Latin-American Forex Markets Returns [Una aplicación empírica de un modelo," Documentos de Trabajo / Working Papers 2016-415, Departamento de Economía - Pontificia Universidad Católica del Perú.

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    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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