Journal ArticleDOI
A generalized fractionally differencing approach in long-memory modeling
Liudas Giraitis,Remigijus Leipus +1 more
TLDR
In this paper, the authors extend the class of fractional ARIMA models to extend it to the case of long-term time series with long-range periodical behavior at a finite number of spectrum frequencies.Abstract:
We extend the class of fractional ARIMA models to the class of fractional ARUMA models, which describe long-memory time series with long-range periodical behavior at a finite number of spectrum frequencies. The exact asymptotics of the covariance function and the spectrum at the points of peaks and zeros are given. To obtain asymptotic expansions, Gegenbauer polynomials are used. Consistent parameter estimation is discussed using Whittle's estimate.read more
Citations
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Journal ArticleDOI
A seasonal fractional ARIMA Model applied to the Nile River monthly flows at Aswan
TL;DR: In this article, a seasonal fractional autoregressive integrated moving average (ARIMA) model is introduced, with both short and long-term persistent periodic components, and the estimation of the parameters is carried out by applying the Whittle's approximation to the Gaussian maximum likelihood function, which yields asymptotically consistent estimates.
Journal ArticleDOI
A k‐Factor GARMA Long‐memory Model
TL;DR: A k‐factor extension of the Gegenbauer and GARMA models that allows for long‐memory behavior to be associated with each of k frequencies in [0, 0.5].
Posted Content
Semiparametric inference in seasonal and cyclical long memory processes
Josu Arteche,Peter M. Robinson +1 more
TL;DR: In this article, the authors introduce Seasonal/Cyclical Asymmetric Long Memory (SCALM) processes that allow differing rates of increase on either side of such a pole.
Journal ArticleDOI
Forecasting electricity spot market prices with a k-factor GIGARCH process
TL;DR: In this article, the conditional mean and variance forecasts using a dynamic model following a k-factor GIGARCH process were investigated using the classical RMSE criteria, and the conditional variance of the prediction error was calculated.
Posted Content
Gaussian Estimation of Parametric Spectral Density with Unknown Pole
Liudas Giraitis,Javier Hidalgo +1 more
TL;DR: In this paper, a parametric spectral density with power-law behavior about a fractional pole at the unknown frequency w was considered, and the authors established Vn-consistency and asymptotic normality.
References
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Book
Time Series: Theory and Methods
TL;DR: In this article, the mean and autocovariance functions of ARIMA models are estimated for multivariate time series and state-space models, and the spectral representation of the spectrum of a Stationary Process is inferred.
Journal ArticleDOI
An introduction to long‐memory time series models and fractional differencing
TL;DR: Generation and estimation of these models are considered and applications on generated and real data presented, showing potentially useful long-memory forecasting properties.
Journal ArticleDOI
The estimation and application of long memory time series models
John Geweke,Susan Porter-Hudak +1 more
TL;DR: In this article, a new estimator of the long memory parameter in these models is proposed, based on the simple linear regression of the log periodogram on a deterministic regressor.
Journal ArticleDOI
Large-Sample Properties of Parameter Estimates for Strongly Dependent Stationary Gaussian Time Series
Robert Fox,Murad S. Taqqu +1 more
TL;DR: In this paper, a strongly dependent Gaussian sequence has a spectral density that satisfies the conditions that the spectral density is consistent and asymptotically normal under appropriate conditions, which are satisfied by fractional Gaussian noise and fractional ARMA.