Skip to main content
SpringerLink
Log in

Small sample bias in conditional sum-of-squares estimators of fractionally integrated ARMA models

  • Seasonality, Cointegration and Fractional Integration
  • Published:
Empirical Economics Aims and scope Submit manuscript

Abstract

This paper considers estimation of the parameters for the fractionally integrated class of processes known as ARFIMA. We consider the small sample properties of a conditional sum-of-squares estimator that is asymptotically equivalent to MLE. This estimator has the advantage of being relatively simple and can estimate all the parameters, including the mean, simultaneously. The simulation evidence we present indicates that estimation of the mean can make a considerable difference to the small sample bias and MSE of the other parameter estimates.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Agiakloglou, Newbold P, Wohar M (1992) Bias in an estimator of the fractional differencing parameter. Journal of Time Series Analysis, forthcoming

  • Baillie RT, Chung CF, Tieslau MA (1992) The long memory and variability of inflation: A reappraisal of the friedman hypothesis. Michigan State University Working Paper 9102

  • Box GEP, Jenkins GM (1976) Time series analysis: forecasting and control, second edition, Holden-Day San Francisco

    Google Scholar 

  • Cheung YW, Diebold FX (1993) On maximum-likelihood estimation of the differencing parameter of fractionally integrated noise with unknown mean. Journal of Econometrics, forthcoming

  • Diebold FX, Rudebusch GD (1989) Long memory and persistence in aggregate output. Journal of Monetary Economics 24:189–209

    Google Scholar 

  • Diebold FX, Rudebusch GD (1991) Is consumption too smooth? Long memory and the deaton paradox. The Review of Economics and Statistics 73:1–9

    Google Scholar 

  • Engel RF (1982) Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflations. Econometrica 50:987–1008

    Google Scholar 

  • Fox R, Taqqu MS (1986) Large sample properties of parameter estimates for strongly dependent stationary gaussian time series. Annals of Statistics 14:517–532

    Google Scholar 

  • Geweke J, Porter-Hudak S (1983) The estimation and application of long memory time series models. Journal of Time Series Analysis 4:221–238

    Google Scholar 

  • Granger CWJ (1980) Long memory relationships and the aggregation of dynamic models. Journal of Econometrics 14:227–238

    Google Scholar 

  • Granger CWJ (1981) Some properties of time series data and their use in econometric model specification. Journal of Econometrics 16:121–130

    Google Scholar 

  • Granger CWJ, Joyeux R (1980) An introduction to long memory time series models and fractional differencing. Journal of Time Series Analysis 1:15–39

    Google Scholar 

  • Hosking JRM (1981) Fractional differencing. Biometrika 68:165–176

    Google Scholar 

  • Hosking JRM (1984). Modeling persistence in hydrological time series using fractional differencing. Water Resources Research 20:1898–1908

    Google Scholar 

  • Li WK, McLeod AI (1986) Fractional time series modeling. Biometrika 73:217–221

    Google Scholar 

  • Newbold P (1974) The exact likelihood function for a mixed autoregressive-moving average process. Biometrika 61:423–426

    Google Scholar 

  • Phillips PCB (1987) Time series regression with a unit root. Econometrica 55:277–301

    Google Scholar 

  • Pierce DA (1971) Least squares estimation in the regression model with autoregressive-moving average errors. Biometrika 58:299–312

    Google Scholar 

  • Samarov A, Taqqu MS (1988) On the efficiency of the sample mean in long-memory noise. Journal of Time Series Analysis 9:191–200

    Google Scholar 

  • Shea GS (1989) Ex-post rational price approximations and the empirical reliability of the presentvalue relation. Journal of Applied Econometrics 4:139–159

    Google Scholar 

  • Shea GS (1991) Uncertainty and implied variance bounds in long-memory models of the interest rate term structure. Empirical Economics 16:287–312

    Google Scholar 

  • Sowell FB (1992a) Maximum likelihood estimation of stationary univariate fractionally integrated time series models. Journal of Econometrics 53:165–188

    Google Scholar 

  • Sowell FB (1992b) Modelling long-run behavior with the fractional ARIMA model. Journal of Monetary Economics 29:277–302

    Google Scholar 

  • Taqqu MS (1975) Weak convergence to fractional brownian motion and to the Rosenblatt process. Zeitschrift Wahrscheinlichkeitstheorie verw. Gebiete 31:287–302

    Google Scholar 

  • Yajima Y (1988) On estimation of A regression model with long-memory stationary errors. Annals of Statistics 16:791–807

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Economics, Michigan State University, 101 Marshall Hall, 48824-1038, East Lansing, Michigan, USA

    Ching-Fan Chung & Richard T. Baillie

Authors
  1. Ching-Fan Chung
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Richard T. Baillie
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

We gratefully acknowledge helpful comments from the editor, Baldev Raj, and three anonymous referees.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chung, CF., Baillie, R.T. Small sample bias in conditional sum-of-squares estimators of fractionally integrated ARMA models. Empirical Economics 18, 791–806 (1993). https://doi.org/10.1007/BF01205422

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01205422

JEL Classification System-Number

Search

Navigation