Publication Cover
Statistics
A Journal of Theoretical and Applied Statistics
Volume 58, 2024 - Issue 2
30
Views
0
CrossRef citations to date
0
Altmetric
Research Article

Long-range dependence and rational Gaussian noise

Pages 364-382 | Received 06 Sep 2023, Accepted 13 Apr 2024, Published online: 23 Apr 2024

References

  • Tsay RS. Analysis of financial time series. 3rd ed. Hoboken (NJ): Wiley; 2010.
  • Engle R. Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica. 1982;50(4):987–1007. doi: 10.2307/1912773
  • Bollerslev T. Generalized autoregressive conditional heteroskedasticity. J Econom. 1986;31:307–327. doi: 10.1016/0304-4076(86)90063-1
  • Ding Z, Granger CWJ, Engle RF. A long memory property of stock market returns and a new model. J Empir Finance. 1993;1(1):83–106. doi: 10.1016/0927-5398(93)90006-D
  • Caporale GM, Gil-Alana L, Plastun A. Long memory and data frequency in financial markets. J Stat Comput Simul. 2019;89(10):1763–1779. doi: 10.1080/00949655.2019.1599377
  • Christensen BJ, Nielsen MØ. The effect of long memory in volatility on stock market fluctuations. Rev Econ Stat. 2007;89(4):684–700. doi: 10.1162/rest.89.4.684
  • Lillo F, Farmer JD. The long memory of the efficient market. Stud Nonlinear Dyn Econom. 2004;8(3):Article ID 1.
  • Ling S, Li WK. On fractionally integrated autoregressive moving-average time series models with conditional heteroscedasticity. J Am Stat Assoc. 1997;92(439):1184–1194. doi: 10.1080/01621459.1997.10474076
  • Baillie R, Bollerslev T, Mikkelsen HO. Fractionally integrated generalized autoregressive conditional heteroskedasticity. J Econom. 1996;74(1):3–30. doi: 10.1016/S0304-4076(95)01749-6
  • Feng L, Shi Y. Fractionally integrated GARCH model with tempered stable distribution: a simulation study. J Appl Stat. 2017;44(16):2837–2857. doi: 10.1080/02664763.2016.1266310
  • Elliott R, Van Der Hoek J. A general fractional white noise theory and applications to finance. Math Financ. 2003;13(2):301–330. doi: 10.1111/mafi.2003.13.issue-2
  • Bayraktar E, Poor HV, Sircar KR. Estimating the fractal dimension of the s&p500 index using wavelet analysis. Int J Theor Appl Finance. 2004;7:615–643. doi: 10.1142/S021902490400258X
  • Doran J, Ronn EI, Goldberg RS. A simple model for time – varying expected returns on the s&p 500 index. J Invest Manag. 2009. Second Quarter. Available from: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1503581.
  • Bollerslev T, Kretschmer U, Pigorsch C, et al. A discrete-time model for daily S&P 500 returns and realized variations: jumps and leverage effects. J Econom. 2009;150:151–166. doi: 10.1016/j.jeconom.2008.12.001
  • Kılıç DK, Uğur Ö. Multiresolution analysis of S&P 500 time series. Ann Oper Res. 2018;260:197–216. doi: 10.1007/s10479-016-2215-3
  • Granger CWJ, Joyeux R. An introduction to long-memory time series models and fractional differencing. J Time Ser Anal. 1980;1(1):15–29. doi: 10.1111/jtsa.1980.1.issue-1
  • Qian H. Fractional brownian motion and fractional gaussian noise. In: Rangarajan G, Ding, MZ, editors. In processes with long-range correlations: theory and applications lecture notes in physics. Vol. 621; 2003. p. 22–33.
  • Li M. Modeling autocorrelation functions of long-range dependent teletraffic series based on optimal approximation in Hilbert space – a further study. Appl Math Model. 2007;31(3):625–631. doi: 10.1016/j.apm.2005.11.029
  • Dieker T. Simulation of fractional brownian motion [M.Sc. thesis]. Amsterdam: University of Twente; 2004.
  • Koutsoyiannis D. The hurst phenomenon and fractional Gaussian noise made easy. Hydrol Sci J. 2002;47(4):573–595. doi: 10.1080/02626660209492961
  • Aldasoro I, Gambacorta L, Giudici P, et al. The drivers of cyber risk. J Financ Stab. 2022;60:Article ID 100989. doi: 10.1016/j.jfs.2022.100989
  • Agosto A, Giudici P. A poisson autoregressive model to understand COVID-19 contagion dynamics. Risks. 2020;8(3):77. doi: 10.3390/risks8030077
  • Sonkavde G, Dharrao DS, Bongale AM, et al. Forecasting stock market prices using machine learning and deep learning models: a systematic review, performance analysis and discussion of implications. Int J Financ Stud. 2023;11(94):1–22.
  • Mukherjee S, Sadhukhan B, Sarkar N, et al. Stock market prediction using deep learning algorithms. CAAI Trans Intell Technol. 2023;8(1):82–94. doi: 10.1049/cit2.v8.1
  • Yang SD, Ali ZA, Wong BM. Fluid-GPT (fast learning to understand and investigate dynamics with a generative pre-trained transformer): efficient predictions of particle trajectories and erosion. Ind Eng Chem Res. 2023;62:15278–15289. doi: 10.1021/acs.iecr.3c01639
  • Brown T, Mann B, Ryder N. Language models are few-shot learners. Adv Neural Inf Process Syst. 2020;33:1877–1901.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.