Exact Likelihood Function Forms for an ARFIMA Process
We present four closed form expressions for the exact likelihood function for a Gaussian ARFIMA process, which is useful in modeling time series with long memory and short memory behavior. Use is made of the relationship between the ARFIMA process and the corresponding fractional Gaussian noise process. Application to the simpler short memory ARMA process is illustrated.
KeywordsCovariance Autocorrelation Verse Sowell
Unable to display preview. Download preview PDF.
- Beran, J. (1994): Statistics for long-memory processes. Chapman and Hall, New York.Google Scholar
- Box, G.E.P., and Jenkins, G.M. (1976): Time Series Analysis: Forecasting and Control Holden Day, San Francisco.Google Scholar
- Brockwell, P.J., and Davis, R.A. (1987): Time Series: Theory and methods. Springer-Verlag, New York.Google Scholar
- 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.Google Scholar
- Marriott, J.M., Ravishanker, N., Gelfand, A.E., and Pai, J.S. (1995): Bayesian analysis for ARMA processes: Complete sampling based inference under exact likelihoods. In: D. Barry, K. Chaloner and J. Geweke (eds.): Bayesian Statistics and Econometrics: Essays in honor of Arnold Zellner. John Wiley, New York.Google Scholar
- Pai, J.S., and Ravishanker, N. (1995): Bayesian modeling of ARFIMA processes by Markov Chain Monte Carlo methods. Journal of Forecasting, forthcoming.Google Scholar
- Pai, J.S., and Ravishanker, N. (1994): Bayesian analysis of ARFIMA processes. Technical Report, University of Connecticut.Google Scholar