On fractionally integrated autoregressive moving-average time series models with conditional heteroscedasticity

Shiqing LING, Wai Keung LI

Research output: Contribution to journalArticle

164 Citations (Scopus)

Abstract

This article considers fractionally integrated autoregressive moving-average time series models with conditional heteroscedasticity, which combines the popular generalized autoregressive conditional heteroscedastic (GARCH) and the fractional (ARMA) models. The fractional differencing parameter d can be greater than 1/2, thus incorporating the important unit root case. Some sufficient conditions for stationarity, ergodicity, and existence of higher-order moments are derived. An algorithm for approximate maximum likelihood (ML) estimation is presented. The asymptotic properties of ML estimators, which include consistency and asymptotic normality, are discussed. The large-sample distributions of the residual autocorrelations and the square-residual autocorrelations are obtained, and two portmanteau test statistics are established for checking model adequacy. In particular, non-stationary FARIMA(p, d, q)-GARCH(r, s) models are also considered. Some simulation results are reported. As an illustration, the proposed model is also applied to the daily returns of the Hong Kong Hang Seng index (1983–1984). Copyright © 1997 American Statistical Association.
Original languageEnglish
Pages (from-to)1184-1194
JournalJournal of the American Statistical Association
Volume92
Issue number439
DOIs
Publication statusPublished - 1997

Fingerprint

Residual Autocorrelation
Conditional Heteroscedasticity
Moving Average Model
Autoregressive Moving Average
Time Series Models
Fractional Differencing
Portmanteau Test
ARMA Model
Higher Order Moments
Unit Root
Stationarity
Ergodicity
Asymptotic Normality
Maximum Likelihood Estimation
Maximum Likelihood Estimator
Model Checking
Asymptotic Properties
Test Statistic
Fractional
Sufficient Conditions

Bibliographical note

Ling, S., & Li, W. K. (1997). On fractionally integrated autoregressive moving-average time series models with conditional heteroscedasticity. Journal of the American Statistical Association, 92(439), 1184-1194. doi: 10.1080/01621459.1997.10474076

Keywords

  • Fractional differencing
  • Maximum likelihood estimation
  • Portmanteau tests
  • Stationarity and ergodicity