Premium
A GENERALIZED FRACTIONALLY INTEGRATED AUTOREGRESSIVE MOVING‐AVERAGE PROCESS
Author(s) -
Chung ChingFan
Publication year - 1996
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.1996.tb00268.x
Subject(s) - autoregressive fractionally integrated moving average , mathematics , autoregressive model , estimator , autoregressive–moving average model , econometrics , moving average model , moving average , statistics , autoregressive integrated moving average , long memory , time series , volatility (finance)
. 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.