Autoregressive Fractionally Integrated Moving Average Processes Research Articles

Estimation of the ARFIMA (p, d, q) fractional differencing parameter (d) using the classical rescaled adjusted range technique

Derived from the general ARMA (p, q) class of short-term dependent models, the Autoregressive Fractionally Integrated Moving Average (ARFIMA) specification provides a means of modelling long-term dependence in time-series data. In financial and economic time-series, the application of the ARFIMA model has been predominantly by the Maximum Likelihood (ML) methods, and the Geweke and Porter-Hudak (GPH) two step procedure. Extending the application of the classical rescaled adjusted range to long-term dependent ARFIMA (p, d, q) processes, estimates of the fractional differencing parameter (d) may also be derived by the Hurst exponent.

Stationary persistent time series misspecified as nonstationary arima

Long-memory processes, such as Autoregressive Fractionally Integrated Moving-Average processes—ARFIMA—are likely to lead the observer to make serious misspecification errors. Nonstationary ARFIMA processes can easily be misspecified as ARIMA models, thus confusing a fractional degree of integration with an integer one. Stationary persistent ARFIMA processes can be misspecified as nonstationary ARIMA models, thus leading to a serious increase of out-of-sample forecast errors. In this paper, we discuss three prototypical misspecification cases and derive the corresponding increase in mean square forecasting error for different lead times.

Bayesian modelling of ARFIMA processes by Markov chain Monte Carlo methods

This article describes Bayesian inference for autoregressive fractionally integrated moving average (ARFIMA) models using Markov chain Monte Carlo methods. The posterior distribution of the model parameters, corresponding to the exact likelihood function is obtained through the partial linear regression coefficients of the ARFIMA process. A Metropolis-Rao-Blackwellizallization approach is used for implementing sampling-based Bayesian inference. Bayesian model selection is discussed and implemented.

Bayesian modelling of ARFIMA processes by Markov chain Monte Carlo methods

This article describes Bayesian inference for autoregressive fractionally integrated moving average (ARFIMA) models using Markov chain Monte Carlo methods. The posterior distribution of the model parameters, corresponding to the exact likelihood function is obtained through the partial linear regression coefficients of the ARFIMA process. A Metropolis-Rao-Blackwellizallization approach is used for implementing sampling-based Bayesian inference. Bayesian model selection is discussed and implemented.