1/f (One-Over-F) Noise (or Related Topics)
in Financial Data

Prof. Clive W.J. Granger and Prof. Robert F. Engle won the 2003 Nobel Prize in Economics! See the press release

stock price/index usually fluctuates as 1/f2 noise, whereas stock volatility/trading volume fluctuates as 1/f noise.

    + 2007

  1. V Gontis and B Kaulakys (2007), "Modeling long-range memory trading activity by stochastic differential equations", Physica A, 382(1):114-120.
    [ abstract]

    + 2006

  2. V Gontis and B Kaulakys (2006), "Long-range memory model of trading activity and volatility", Journal of Statistical Mechanics, P10016.
    [ abstract]

    + 2004

  3. V Gontis and B Kaulakys (2004), "Modelling financial markets by the multiplicative sequence of trades", Physica A, 344(1-2):128-133.
    [ abstract]

  4. V Gontis and B Kaulakys (2004), "Multiplicative point process as a model of trading activity", Physica A, 343:505-514.
    [ abstract]

    + 2001

  5. Giovanni Bonanno, Fabrizio Lillo, Rosario N Mantegna (2001), "1/f and 1/f2 noise in financial time series", in Proceedings of 16th International Conference on Noise in Physical Systems and 1/f Fluctuations (World Scientific), pp 791-796.

  6. BJW Fleming, D Yu, RG Harrison, D Jubb (2001), "Wavelet-based detection of coherent structures and self-affinity in financial data", European Physical Journal B, 20:543-546.

  7. Blake LeBaron (2001), "Stochastic volatility as a simple generator of apparent financial power laws and long memory", Quantitative Finance, 1(6):621-631.
    [ abstract]

  8. Andrew Lo (2001), "Fat tails, long memory, and the stock market since the 1960's", in Economic Notes (Banca Monte dei Paschi di Siena).

  9. PM Robinson (2001), "The memory of stochastic volatility models", Journal of Econometrics, 101(2):195-218.

  10. HE Stanley, V Plerou (2001), "Scaling and universality in economics: empirical results and theoretical interpretation", Quantitative Finance, 1(6):563-567.
    [ abstract]

    + 2000

  11. Tim Bollerslev, Jun Cai, Frank M. Song (2000), "Intraday periodicity, long memory volatility, and macroeconomic announcement effects in the US Treasury bond market", Journal of Empirical Finance, 7(1):37-55.

  12. Tim Bollerslev, Jonathan H Wright (2000), "Semiparametric estimation of long-memory volatility dependencies: the role of high-frequency data", Journal of Econometrics, 98(1):81-106.

  13. P Gopikrishnan, V Plerou, X Gabaix, HE Stanley (2000), "Statistical properties of share volume traded in financial markets", Physical Review E, 62:R4493-R4496.

  14. Ming Liu (2000), "Modeling long memory in stock market volatility", Journal of Econometrics, 99(1):139-171.

    + 1999

  15. CF Baum, JT Barkoulas, M Caglayan (1999), "Long memory or structural breaks: can either explain nonstationary real exchange rates under the current float?", Journal of International Financial Markets, Institutions, and Money, 9:359-376.

  16. CS Bos, PH Franses, M Ooms (1999), "Long memoey and level shifts: re-analyzing inflation rates", Empirical Economics, 24:427-449.

  17. Andrew Lo, A Craig MacKinlay (1999), A Non-Random Walk Down Wall Street (Princeton Univ Press). [ISBN 0-6910-5774-5]
    [ sample texts from the publisher]

  18. W Willinger, MS Taqqu, V Teverovsky (1999), "Stock price return indices and long-range dependence", Finance and Stochastics, 3:1-13.

    + 1998

  19. IN Lobato, NE Savin (1998), "Real and spurious long-memory properties of stock-market data (with comments)", Journal of Business and Economic Statistics, 16:261-283.

    + 1997

  20. ed. Benoit B Mandelbrot (1997), Fractals and Scaling in Finance: Discountinuity, Concentration, Risk , (Springer-Verlag) [ISBN 0-3879-8363-5].

  21. Joseph Haubrich, Andrew Lo (1997), "The sources and nature and long-range dependence in the business cycle", Working Paper LFE-97-1024 (MIT).

    + 1996

  22. Rosario N Mantegna, H. Eugene Stanley (1996), "Turbulence and financial markets" (Sceintific Correspondence), Nature, 383:587-588.

    + 1993

  23. Z Ding, CWJ Granger, R Engle (1993), "A long memory property of stock market returns and a new model", Journal of Empirical Finance, 1:83-106.

    + 1991

  24. Wentian Li (1991), "Absence of 1/f spectra in Dow Jones daily average", International Journal of Bifurcation and Chaos, 1(3):583-597.
    [ abstract]

  25. Andrew Lo (1991), "Long-term memory in stock market prices", Econometrica, 59:1279-1313.
    [ abstract] [ PDF ]

    + 1990

  26. Susan Porter-Hudak (1990), "An application of the seasonal fractionally differenced model to the monetary aggregates", Journal of the American Statistical Association, 85(410):338-344.