Summary
A one-step optimization procedure is suggested for parameter estimation in autoregressive fractionally integrated moving average (ARFIMA) processes. Comparisons are made between the proposed procedure and the well known two-step procedure of Haslett and Raftery (1989) using simulation results. The invertibility condition is handled by a convenient transformation. The optimization procedure is performed using the simulated annealing method.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
BARNDORFF-NIELSEN, O. E. and SCHOU, G. (1973): On the reparametrization of autoregressive models by partial autocorrelations. Journal Multivar. Analysis, 3, 408–419.
GEWEKE, J. F. and PORTER-HUDAK, S. (1983): The estimation and application of long memory time series models. Journal of Time Series Analysis, 4, 221–238.
GRANGER, C. W. J. and JOYEAUX, R. (1980): An introduction to longmemory time series models and fractional differencing. Journal of Time Series Anal, 1, 15–29.
HASLETT, J. and RAFTERY, A. (1989): Space-time modeling with long-memory dependence: Assessing Ireland’s wind power resource (with discussion). Journal of the Royal Statistical Society, C, 38, 1–50.
HOSKING, J. R. M. (1981): Fractional differencing. Biometrika, 68, 165–176.
HOSKING, J. R. M. (1984): Modeling persistence in hydrological time series using fractional differencing. Water Resources Research, 20(12), 1898–1908.
KIRKPATRICK, S. (1984): Optimization by simulated annealing: Quantitative studies. Journal of Statistical Physics, 34, 975–986.
METROPOLIS, N.; ROSENBLUTH, A. W.; ROSENBLUTH, M. N.; TELLER, A. H. and TELLER, E. (1953): Equations of state calculations by fast computing machines, Journal Chemical Physics, 21, 1087–1091.
MONAHAN, J. F. (1984): A note on enforcing stationarity in autoregressive moving models, Biometrika, 71, 403–404.
PAI, J. S. and RAVISHANKER, N. (1996): Exact likelihood function forms for an ARFIMA process. In: H.H. Bock and W. Polasek (eds.): Data Analysis and Information System. Springer-Verlag, Heidelberg, 323–331.
PRESS, W. H.; TEUKOLSKY, S. A.; VETTERLING, W. T. and FLANNERY, B. P. (1992): Numerical recipes. Cambridge University Press, Cambridge.
SOWELL, F. B. (1992): Maximum likelihood estimation of stationary univariate fractionally integrated time series models. Journal of Econometrics, 53, 165–188.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1997 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Pai, J.S. (1997). A One-Step Optimization Procedure for ARFIMA Processes. In: Klar, R., Opitz, O. (eds) Classification and Knowledge Organization. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59051-1_18
Download citation
DOI: https://doi.org/10.1007/978-3-642-59051-1_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-62981-8
Online ISBN: 978-3-642-59051-1
eBook Packages: Springer Book Archive