Review of Quantitative Finance and Accounting

, Volume 33, Issue 3, pp 233–252

US stock market volatility persistence: evidence before and after the burst of the IT bubble

  • J. Cuñado
  • L. A. Gil-Alana
  • F. Perez de Gracia
Original Research

Abstract

In this paper we test whether the US stock market volatility presents a different behavior before and after the burst of the IT bubble. Using long range dependence techniques we examine the order of integration in the absolute and squared returns in three daily stock market indices (DJIA, S&P and NASDAQ). The results indicate that both absolute and squared returns present long memory behavior. In general, the highest orders of integration in the volatility processes correspond to the NASDAQ index. The results also show that in most cases the volatility is more persistent in the bear market than in the bull market.

Keywords

Volatility Bull market Bear market Long range dependence Absolute returns Squared returns 

JEL Classification

G10 G12 C32 

References

  1. Andrews DWK (1993) Tests for parameter instability and structural change with unknown change point. Econometrica 61:821–856CrossRefGoogle Scholar
  2. Andrews DWK (2003) Tests for parameter instability and structural change with unknown change point. A corrigendum. Econometrica 71:395–397CrossRefGoogle Scholar
  3. Ang A, Bekaert G (2002) International asset allocation with regime shifts. Rev Financ Stud 15:1137–1187CrossRefGoogle Scholar
  4. Aydogan K, Booth GG (1988) Are there long cycles in common stock returns? South Econ J 55:141–149CrossRefGoogle Scholar
  5. Bai J, Perron P (1998) Estimating and testing linear models with multiple structural changes. Econometrica 66:47–78CrossRefGoogle Scholar
  6. Baillie RT (1996) Long memory processes and fractional integration in econometrics. J Econom 73:5–59CrossRefGoogle Scholar
  7. Barkoulas JT, Baum CF (1996) Long term dependance in stock returns. Econ Lett 53:253–259CrossRefGoogle Scholar
  8. Barkoulas JT, Baum CF, Travlos N (2000) Long memory in the Greek stock market. Appl Financ Econ 10:177–184CrossRefGoogle Scholar
  9. Beran J (1994) Statistics for long memory processes. Chapman and Hall, New YorkGoogle Scholar
  10. Beran J, Terrin N (1996) Testing for a change of the long memory parameter. Biometrika 83:627–638CrossRefGoogle Scholar
  11. Bollerslev T, Wright JH (2000) High frequency data, frequency domain inference and volatility forecasting. Rev Econ Stat 83:596–602Google Scholar
  12. Bos C, Franses PH, Ooms M (2001) Inflation, forecast intervals and long memory regression models. Int J Forecast 18:243–264CrossRefGoogle Scholar
  13. Bry G, Boschan C (1971) Cyclical analysis of time series: selected procedures and computer programs. NBER, New YorkGoogle Scholar
  14. Campbell JY, Lettau M, Malkiel BG, Xu X (2001) Have individual stocks become more volatile? An empirical exploration of idiosyncratic risk. J Finance 56:1–43CrossRefGoogle Scholar
  15. Cavalcante J, Assaf A (2004) Long range dependence in the returns and volatility of the Brazilian stock market. Eur Rev Econ Finance 3:5–22Google Scholar
  16. Chambers M (1998) Long memory and aggregation in macroeconomic time series. Int Econ Rev 39:1053–1072CrossRefGoogle Scholar
  17. Chordia T, Roll R, Subrahmanyam A (2001) Market liquidity and trading volume. J Finance LVI:501–531CrossRefGoogle Scholar
  18. Cioczek-George R, Mandelbrot BB (1995) A class of micropulses and anti persistent fractional Brownian motion. Stoch Process Appl 60:1–18CrossRefGoogle Scholar
  19. Cotter J (2005) Uncovering long memory in high frequency UK futures. Eur J Finance 11:325–337CrossRefGoogle Scholar
  20. Crato N (1994) Some international evidence regarding the stochastic behaviour of stock returns. Appl Financ Econ 4:33–39CrossRefGoogle Scholar
  21. Diebold FX, Inoue A (2001) Long memory and regime switching. J Econom 105:131–159CrossRefGoogle Scholar
  22. Ding Z, Granger CWJ, Engle RF (1993) A long memory property of stock markets and a new model. J Empir Finance 1:83–106CrossRefGoogle Scholar
  23. Edwards S, Gomez Biscarri J, Perez de Gracia F (2003) Stock market cycles, financial liberalization and volatility. J Int Money Finance 22:925–955CrossRefGoogle Scholar
  24. Elder J, Jin HJ (2007) Long memory in commodity futures volatility: a wavelet perspective. J Futures Mark 27:411–437CrossRefGoogle Scholar
  25. Engle RF, Smith AD (1999) Stochastic permanent breaks. Rev Econ Stat 81:553–574CrossRefGoogle Scholar
  26. García del Barrio P, Gil-Alana LA (2007) Unemployment persistente in Spain. Time series and panel data approaches using disaggregated data. Appl Econ 38:1–18CrossRefGoogle Scholar
  27. Geweke J, Porter-Hudak S (1983) The estimation and application of long memory time series models. J Time Ser Anal 4:221–238CrossRefGoogle Scholar
  28. Gil-Alana LA (2000) Fractional integration in the purchasing power parity. Econ Lett 69:285–288CrossRefGoogle Scholar
  29. Gil-Alana LA (2003) Fractional integration in the volatility of asset returns. Eur Rev Econ Finance 2:41–52Google Scholar
  30. Gil-Alana LA (2005) Long memory in daily absolute and squared returns in the Spanish stock market. Adv Invest Anal Portf Manag 1:198–217Google Scholar
  31. Gil-Alana LA (2006) Fractional integration in daily stock market indices. Rev Financ Econ 15:28–48CrossRefGoogle Scholar
  32. Gil-Alana LA (2008) Fractional integration and structural breaks at unknown periods of time. J Time Ser Anal 29:163–185Google Scholar
  33. Gil-Alana LA, Robinson PM (1997) Testing of unit roots and other nonstationary hypotheses in macroeconomic time series. J Econom 80:241–268CrossRefGoogle Scholar
  34. Gil-Alana LA, Cunado J, Perez de Gracia F (2008) Stochastic volatility in the Spanish stock market. A long memory model with a structural break. Eur J Finance 14:23–31CrossRefGoogle Scholar
  35. Gomez Biscarri J, Perez de Gracia F (2004) Stock market cycles and stock market development in Spain. Span Econ Rev 6:127–151CrossRefGoogle Scholar
  36. Gonzalez L, Powell JG, Shi J, Wilson A (2005) Two centuries of bull and bear market cycles. Int Rev Econ Finance 14:469–486CrossRefGoogle Scholar
  37. Granger CWJ (1980) Long memory relationships and the aggregation of dynamic models. J Econom 14:227–238CrossRefGoogle Scholar
  38. Granger CWJ, Ding Z (1995a) Some properties of absolute returns. An alternative measure of risk. Ann Econ Stat 40:67–91Google Scholar
  39. Granger CWJ, Ding Z (1995b) Stylized facts on the temporal and distributional properties of daily data from speculative markets. Working Paper, UCSDGoogle Scholar
  40. Granger CWJ, Ding Z (1996) Varieties of long memory models. J Econom 73:61–78CrossRefGoogle Scholar
  41. Granger CWJ, Hyung N (2004) Occasional structural breaks and long memory with an application to the S&P 500 absolute stock returns. J Empir Finance 11:399–421CrossRefGoogle Scholar
  42. Greene MT, Fielitz BD (1977) Long term dependence in common stock returns. J Financ Econ 5:339–349CrossRefGoogle Scholar
  43. Greenspan A (1996) Minutes of the federal open market commitee. www.federalreserve.gov/transcript/1996/19960924meeting.pdf
  44. Guidolin M, Timmermann A (2005) Economic implications of the bull and bear regimes in UK stock and bond returns. Econ J 115:111–143CrossRefGoogle Scholar
  45. Henry OT (2002) Long memory in stock returns: some international evidence. Appl Financ Econ 12:725–729CrossRefGoogle Scholar
  46. Hiemstra C, Jones JD (1997) Another look at long memory in common stock returns. J Empir Finance 29:373–401CrossRefGoogle Scholar
  47. Jones CP, Walker MD, Wilson JW (2004) Analyzing stock market volatility using extreme day measures. J Financ Res 27:585–601CrossRefGoogle Scholar
  48. Kurozumi E (2005) Detection of structural change in the long run persistence in a univariate time series. Oxf Bull Econ Stat 67:181–206CrossRefGoogle Scholar
  49. Lo AW (1991) Long term memory in stock prices. Econometrica 59:1279–1313CrossRefGoogle Scholar
  50. Lobato IN, Savin NE (1998) Real and spurious long memory properties of stock market data. J Bus Econ Stat 16:261–268CrossRefGoogle Scholar
  51. Maheu JM, McCurdy TH (2000) Identifying bull and bear markets in stock returns. J Bus Econ Stat 18:100–112CrossRefGoogle Scholar
  52. Mandelbrot BB (1971) When can price be arbitraged efficiently? A limit to the validity of the random walk and martingale models. Rev Econ Stat 53:225–236CrossRefGoogle Scholar
  53. Marelli E (2004) Evolution of unemployment structures and regional specialization in the EU. Econ Syst 28:35–59CrossRefGoogle Scholar
  54. Nishina K, Maghrebi N, Holmes MJ (2006) Are volatility expectations characterized by regime shifts? Evidence from implied volatility indices. Discussion Papers in Economics and Business 06–20Google Scholar
  55. Ohanissian A, Russell JR, Tsay RS (2008) True or spurious long memory? A new test. J Bus Econ Stat 26:161–175CrossRefGoogle Scholar
  56. Parke WR (1999) What is fractional integration? Rev Econ Stat 81:632–638CrossRefGoogle Scholar
  57. Phillips PCB, Shimotsu K (2004) Local Whittle estimation in nonstationary and unit root cases. Ann Stat 32:656–692CrossRefGoogle Scholar
  58. Phillips PCB, Shimotsu K (2005) Exact local Whittle estimation of fractional integration. Ann Stat 33:1890–1933CrossRefGoogle Scholar
  59. Robinson PM (1978) Statistical inference for a random coefficient autoregressive model. Scand J Stat 5:163–168Google Scholar
  60. Robinson PM (1994) Efficient tests of nonstationary hypotheses. J Am Stat Assoc 89:1420–1437CrossRefGoogle Scholar
  61. Robinson PM (1995) Gaussian semiparametric estimation of long range dependence. Ann Stat 23:1630–1661CrossRefGoogle Scholar
  62. Robinson PM (2003) Long memory time series. In: Robinson PM (ed) Time series with long memory. Oxford University Press, Oxford, pp 1–48Google Scholar
  63. Sadique S, Silvapulle P (2001) Long term memory in stock market returns: international evidence. Int J Finance Econ 6:59–67CrossRefGoogle Scholar
  64. Schwert GW (1998) Stock market volatility: 10 years after the crash. Brook-Wharton Pap Financ Serv I:65–114Google Scholar
  65. Shiller RJ (2001) Irrational exuberance. Princeton University Press, PrincetonGoogle Scholar
  66. Sibbertsen P (2004) Long memory in volatilities of German stock returns. Empir Econ 29:477–488CrossRefGoogle Scholar
  67. Sowell F (1992) Maximum likelihood estimation of stationary univariate fractionally integrated time series models. J Econom 53:165–188CrossRefGoogle Scholar
  68. Taqqu MS, Willinger W, Sherman R (1997) Proof of a fundamental result in self-similar traffic modelling. Comp Commun Rev 27:5–23CrossRefGoogle Scholar
  69. Teverosky V, Taqqu MS (1997) Testing for long range dependence in the presence of shifting means or slowly decaying trend using a variance-type estimator. J Time Ser Anal 18:279–304CrossRefGoogle Scholar
  70. Tolvi J (2003) Long memory model in a small economy. Econ Bull 7:1–13Google Scholar
  71. Tu J (2006) Are bull and bear markets economically important? MimeoGoogle Scholar
  72. Turner CM, Startz R, Nelson CR (1989) A markov model of heteroscedasticity, risk and learning in the stock market. J Financ Econ 25:3–22CrossRefGoogle Scholar
  73. Velasco C (1999) Gaussian semiparametric estimation of nonstationary time series. J Time Ser Anal 20:87–127CrossRefGoogle Scholar
  74. Yajima Y (1985) Estimation of long memory time series models. Aust J Stat 27:303–320CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • J. Cuñado
    • 1
  • L. A. Gil-Alana
    • 1
  • F. Perez de Gracia
    • 1
  1. 1.Department of EconomicsUniversidad de NavarraPamplonaSpain

Personalised recommendations