The effect of round-off error on long memory processes
We study how the round-off (or discretization) error changes the statistical properties of a Gaussian long memory process. We show that the autocovariance and the spectral density of the discretized process are asymptotically rescaled by a factor smaller than one, and we compute exactly this scaling factor. Consequently, we find that the discretized process is also long memory with the same Hurst exponent as the original process. We consider the properties of two estimators of the Hurst exponent, namely the local Whittle (LW) estimator and the Detrended Fluctuation Analysis (DFA). By using analytical considerations and numerical simulations we show that, in presence of round-off error, both estimators are severely negatively biased in finite samples. Under regularity conditions we prove that the LW estimator applied to discretized processes is consistent and asymptotically normal. Moreover, we compute the asymptotic properties of the DFA for a generic (i.e. non Gaussian) long memory process and we apply the result to discretized processes.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Harris, Lawrence, 1990. "Estimation of Stock Price Variances and Serial Covariances from Discrete Observations," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 25(03), pages 291-306, September.
- Eduardo Rossi & Paolo Santucci de Magistris, 2014.
"Estimation of Long Memory in Integrated Variance,"
Taylor & Francis Journals, vol. 33(7), pages 785-814, October.
- Eduardo Rossi & Paolo Santucci de Magistris, 2012. "Estimation of long memory in integrated variance," DEM Working Papers Series 017, University of Pavia, Department of Economics and Management.
- Eduardo Rossi & Paolo Santucci de Magistris, 2011. "Estimation of long memory in integrated variance," CREATES Research Papers 2011-11, School of Economics and Management, University of Aarhus.
- Szpiro, George G., 1998. "Tick size, the compass rose and market nanostructure," Journal of Banking & Finance, Elsevier, vol. 22(12), pages 1559-1569, December.
- Clifford Hurvich & Eric Moulines & Philippe Soulier, 2004.
"Estimating Long Memory in Volatility,"
- Hansen, Peter R. & Lunde, Asger, 2014.
"Estimating The Persistence And The Autocorrelation Function Of A Time Series That Is Measured With Error,"
Cambridge University Press, vol. 30(01), pages 60-93, February.
- Peter R. Hansen & Asger Lunde, 2010. "Estimating the Persistence and the Autocorrelation Function of a Time Series that is Measured with Error," CREATES Research Papers 2010-08, School of Economics and Management, University of Aarhus.
- Gottlieb, Gary & Kalay, Avner, 1985. " Implications of the Discreteness of Observed Stock Prices," Journal of Finance, American Finance Association, vol. 40(1), pages 135-53, March.
- Saint-Paul, Gilles, 2010.
"A "quantized" approach to rational inattention,"
TSE Working Papers
10-144, Toulouse School of Economics (TSE), revised 10 Jan 2011.
- Hosking, Jonathan R. M., 1996. "Asymptotic distributions of the sample mean, autocovariances, and autocorrelations of long-memory time series," Journal of Econometrics, Elsevier, vol. 73(1), pages 261-284, July.
- Dittmann, Ingolf & Granger, Clive W. J., 2000.
"Properties of nonlinear transformations of fractionally integrated processes,"
2000,25, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
- Dittmann, Ingolf & Granger, Clive W. J., 2002. "Properties of nonlinear transformations of fractionally integrated processes," Journal of Econometrics, Elsevier, vol. 110(2), pages 113-133, October.
- Dittmann, Ingolf & Granger, Clive W.J., 2000. "Properties of Nonlinear Transformations of Fractionally Integrated Processes," University of California at San Diego, Economics Working Paper Series qt0kk9x0mc, Department of Economics, UC San Diego.
- Bali, Rakesh & Hite, Gailen L., 1998. "Ex dividend day stock price behavior: discreteness or tax-induced clienteles?," Journal of Financial Economics, Elsevier, vol. 47(2), pages 127-159, February.
- Velasco, Carlos, 2000. "Non-Gaussian Log-Periodogram Regression," Econometric Theory, Cambridge University Press, vol. 16(01), pages 44-79, February.
When requesting a correction, please mention this item's handle: RePEc:arx:papers:1107.4476. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators)
If references are entirely missing, you can add them using this form.