Estimation par le minimum de distance de Hellinger dʼun processus ARFIMA

Kamagaté, Adama; Hili, Ouagnina

doi:10.1016/j.crma.2012.07.005

Cited by 3 publications

(4 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this paper, we generalize the results of Kamagaté and Hili [7] to the multivariate case. We consider an m-dimensional ARFIMA stationary process ( ) ( ) ( ) , , , 1 t y t y m after inversion of the process, we establish the consistence and asymptotic normality by using the minimum Hellinger distance.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Minimum Hellinger Distance Estimation of a Stationary Multivariate Long Memory Arfima Process

Mbeke¹,

Hili²

2018

Jour. Math. Sci. Adv. Appl.

Self Cite

View full text Add to dashboard Cite

show abstract

Section: Introductionmentioning

confidence: 99%

“…Mayoral [9] proposed by minimum distance a new method for estimating the parameters of stationary and non-stationary ARFIMA ( ) Kamagaté and Hili [7] and [8] estimated by the minimum Hellinger distance method a stationary univariate ARFIMA process and by the quasi maximum likelihood approach a non-stationary multivariate ARFIMA process.…”

Section: Introductionmentioning

confidence: 99%

Minimum Hellinger Distance Estimation of a Stationary Multivariate Long Memory Arfima Process

Mbeke¹,

Hili²

2018

Jour. Math. Sci. Adv. Appl.

Self Cite

View full text Add to dashboard Cite

show abstract

“…The quasi-maximum likelihood approach for a non-stationary multivariate ARFIMA process is derived by Kamagate and Hili [13]. Kamagate and Hili [12] determined the minimum Hellinger distance estimate (MHDE) of a general ARFIMA model. Mbeke and Hili [16] extended this work to the multivariate case.…”

Section: Introductionmentioning

confidence: 99%

Minimum Hellinger distance estimates for a periodically time-varying long memory parameter

Amimour¹,

Belaide²,

Hili³

2022

Comptes Rendus. Mathématique

Self Cite

View full text Add to dashboard Cite

show abstract

“…Our study is essentially based on the long range dependence process as in Kamagaté and Hili (2012). Kamagaté and Hili (2012) and Kamagaté and Hili (2013) estimated by the Minimum Hellinger Distance method a stationary univariate ARFIMA process and by the quasi maximum likelihood approach a non-stationary multivariate ARFIMA process. K.S.…”

Section: Introductionmentioning

confidence: 99%

Estimation of a stationary multivariate ARFIMA process

Mbeke¹,

Hili²

2018

JAS

Self Cite

View full text Add to dashboard Cite

In this note, we consider an m-dimensional stationary multivariate long memory ARFIMA (AutoRegressive Fractionally Integrated Moving Average) process, which is defined as : A(L)D(L) (y 1 (t), . . . , y m (t)) = B(L) (ε 1 (t), . . . , ε m (t)) , where M denotes the transpose of the matrix M . We determine the minimum Hellinger distance estimator (MHDE) of the parameters of a stationary multivariate long memory ARFIMA. This method is based on the minimization of the Hellinger distance between the random function of f n (.) and a theoretical probability density f θ (.). We establish, under some assumptions, the almost sure convergence of the estimator and its asymptotic normality.Résumé. Dans cette note, nous considérons un processus ARFIMA (AutoRegressive Fractionally Integrated Moving Average) stationnaire multivariéà longue mémoire défini par : A(L)D(L) (y 1 (t), . . . , y m (t)) = B(L) (ε 1 (t), . . . , ε m (t)) , où M représente la transposée de la matrice M . Nous déterminons le minimum de distance de Hellinger d'un estimateur (MHDE) de paramètres d'un processus ARFIMA stationnaire multivariéà longue mémoire. Cette méthode consisteà minimiser la distance de Hellinger entre la densité de probabilité théorique f θ (.) et une fonction aléatoire f n (.). Sous quelques hypothèses, nousétablissons la convergence presque sûre de l'estimateur et sa normalité asymptotique.In this paper, we generalize the results of Kamagaté and Hili (2012) to the multivariate case. We consider an m-dimensional ARFIMA stationary process (y 1 (t), . . . , y m (t)) following d < 1 2 which is generated bywhere M denotes the transpose of the matrix M . After the invertibility of the above process, we establish the consistence and asymptotic normality by using the Minimum Hellinger Distance method. The reasons for choosing this estimation technic lie in the fact that these estimators obtained are efficient and robust (cf.

show abstract

Estimation par le minimum de distance de Hellinger dʼun processus ARFIMA

Cited by 3 publications

References 6 publications

Minimum Hellinger Distance Estimation of a Stationary Multivariate Long Memory Arfima Process

Minimum Hellinger Distance Estimation of a Stationary Multivariate Long Memory Arfima Process

Minimum Hellinger distance estimates for a periodically time-varying long memory parameter

Estimation of a stationary multivariate ARFIMA process

Contact Info

Product

Resources

About