A GENERALIZED FRACTIONALLY INTEGRATED AUTOREGRESSIVE MOVING‐AVERAGE PROCESS
- 1 March 1996
- journal article
- Published by Wiley in Journal of Time Series Analysis
- Vol. 17 (2) , 111-140
- https://doi.org/10.1111/j.1467-9892.1996.tb00268.x
Abstract
This paper considers the long memory Gegenbauer autoregressive movingaverage (GARMA) process that generalizes the fractionally integrated ARMA (ARFIMA) process to allow for hyperbolic and sinusoidal decay in autocorrelations. We propose the conditional sum of squares method for estimation (which is asymptotically equivalent to the maximum likelihood estimation) and develop the asymptotic theory. Many results are in sharp contrast to those of the ARFIMA model. Simulations are conducted to assess the performance of the proposed estimators in small sample applications. Two applications to the sunspot data and the US inflation rates based on the wholesale price index are provided.Keywords
This publication has 26 references indexed in Scilit:
- On the power of the KPSS test of stationarity against fractionally-integrated alternativesPublished by Elsevier ,1999
- Estimating a generalized long memory processPublished by Elsevier ,1999
- Small sample bias in conditional sum-of-squares estimators of fractionally integrated ARMA modelsEmpirical Economics, 1993
- Asymptotic Properties of the LSE in a Regression Model with Long-Memory Stationary ErrorsThe Annals of Statistics, 1991
- An Application of the Seasonal Fractionally Differenced Model to the Monetary AggregatesJournal of the American Statistical Association, 1990
- Efficient Parameter Estimation for Self-Similar ProcessesThe Annals of Statistics, 1989
- ON GENERALIZED FRACTIONAL PROCESSESJournal of Time Series Analysis, 1989
- On Estimation of a Regression Model with Long-Memory Stationary ErrorsThe Annals of Statistics, 1988
- Generalized autoregressive conditional heteroskedasticityJournal of Econometrics, 1986
- On Large-Sample Estimation for the Mean of a Stationary Random SequenceThe Annals of Statistics, 1974