Comptes Rendus
Probability theory, Statistics
Minimum Hellinger distance estimates for a periodically time-varying long memory parameter
Comptes Rendus. Mathématique, Volume 360 (2022), pp. 1153-1162.

We consider a purely fractionally deferenced process driven by a periodically time-varying long memory parameter. We will build an estimate for the vector parameters using the minimum Hellinger distance estimation. The results are investigated through simulation studies.

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Accepted:
Published online:
DOI: 10.5802/crmath.381
Classification : 37M10, 62M10, 91B84

Amine Amimour 1; Karima Belaide 1; Ouagnina Hili 2

1 Department of Mathematics, Applied Mathematics Laboratory, University of Bejaia, Bejaia Algeria
2 Laboratory of Mathematics and New Technologies of Information, National Polytechnic Institute Felix HOUPHOUET-BOIGNY, Yamoussoukro, P.O. Box 1093, Ivory Coast
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Amine Amimour; Karima Belaide; Ouagnina Hili. Minimum Hellinger distance estimates for a periodically time-varying long memory parameter. Comptes Rendus. Mathématique, Volume 360 (2022), pp. 1153-1162. doi : 10.5802/crmath.381. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.381/

[1] Amine Amimour; Karima Belaide A long memory time series with a periodic degree of fractional differencing (2020) (https://arxiv.org/abs/2008.01939)

[2] Amine Amimour; Karima Belaide On the invertibility in periodic ARFIMA models (2020) (https://arxiv.org/abs/2008.02978)

[3] Amine Amimour; Karima Belaide Local asymptotic normality for a periodically time varying long memory parameter, Commun. Stat., Theory Methods, Volume 51 (2022) no. 9, pp. 2936-2952 | DOI | MR | Zbl

[4] Mohamed Bentarzi; Marc Hallin On the invertibility of periodic moving-average models, J. Time Ser. Anal., Volume 15 (1994) no. 3, pp. 263-268 | DOI | MR | Zbl

[5] Rudolf Beran Minimum Hellinger distance estimates for parametric models, Ann. Stat., Volume 5 (1977) no. 3, pp. 445-463 | DOI | MR | Zbl

[6] George E. P. Box; Gwilym M. Jenkins Time series analysis: Forecasting and control, Holden-Day Series in Time Series Analysis, Holden Day, 1970 | Zbl

[7] Chung Ching-fan Sample means, sample autocovariances, and linear regression of stationary multivariate long memory processe, Econom. Theory, Volume 18 (2002) no. 1, pp. 51-78 | DOI | MR | Zbl

[8] E. G. Gladyshev Periodically correlated random sequences, Sov. Math., Dokl., Volume 2 (1961), pp. 385-388 | MR | Zbl

[9] Sat. N. Gupta Estimation in long memory time series models, Commun. Stat., Theory Methods, Volume 21 (1992) no. 5, pp. 1327-1338 | DOI | MR | Zbl

[10] Ouagnina Hili On the estimation of nonlinear time series models, Stochastics Stochastics Rep., Volume 52 (1995) no. 3-4, pp. 207-226 | DOI | MR | Zbl

[11] Jonathan R. M. Hosking Fractional differencing, Biometrika, Volume 68 (1981) no. 1, pp. 165-176 | DOI | MR | Zbl

[12] Amadou Kamagaté; Ouagnina Hili Estimation par le minimum de distance de Hellinger d’un processus ARFIMA, C. R. Acad. Sci. Paris, Volume 350 (2012) no. 13-14, pp. 721-725 | DOI | MR | Zbl

[13] Amadou Kamagaté; Ouagnina Hili The quasi maximum likelihood approach to statistical inference on a nonstationary multivariate ARFIMA process, Random Oper. Stoch. Equ., Volume 21 (2013) no. 3, pp. 305-320 | DOI | MR | Zbl

[14] Hwi-Young Lee; Hyoung-Jin Park; Hyoung-Moon Kim A clarification of the Cauchy distribution, Commun. Stat. Appl. Methods, Volume 21 (2014) no. 2, pp. 183-191 | DOI | Zbl

[15] Laura Mayoral Minimum distance estimation of stationary and non-stationary ARFIMA processes, The Econometrics Journal, Volume 10 (2007) no. 1, pp. 124-148 | DOI | MR | Zbl

[16] Kévin S. Mbeke; Ouagnina Hili Estimation of a stationary multivariate ARFIMA process, Afr. Stat., Volume 13 (2018) no. 3, pp. 1717-1732 | DOI | MR | Zbl

[17] H. Joseph Newton Using periodic autoregressions for multiple spectral estimation, Technometrics, Volume 24 (1982) no. 2, pp. 109-116 | DOI | MR | Zbl

[18] Mitsuhiro Odaki On the invertibility of fractionally differenced ARIMA processes, Biometrika, Volume 80 (1993) no. 3, pp. 703-709 | DOI | MR | Zbl

[19] Marcello Pagano On periodic and multiple autoregressions, Ann. Stat., Volume 6 (1978) no. 6, pp. 1310-1317 | MR | Zbl

[20] B. L. S. Prakasa Rao Nonparametric functional estimation, Probability and Mathematical Statistics, Academic Press Inc., 1983 | Zbl

[21] Fallaw Sowell Maximum likelihood estimation of stationary univariate fractionally integrated time series models, J. Econom., Volume 53 (1992) no. 1-3, pp. 165-188 | DOI | MR

[22] Brent M. Troutman Some results in periodic autoregression, Biometrika, Volume 66 (1979) no. 2, pp. 219-228 | DOI | MR | Zbl

[23] Aldo V. Vecchia Periodic autoregressive-moving average (PARMA) modeling with application to water resources, Journal of the American Water Resources Association, Volume 21 (1985) no. 5, p. 721-30 | DOI

[24] Wei Biao Wu; Jan Mielniczuk Kernel density estimation for linear process, Ann. Stat., Volume 30 (2002) no. 5, pp. 1441-1459 | Zbl

[25] Yoshihiro Yajima On estimation of long-memory time series models, Aust. J. Stat., Volume 27 (1985) no. 3, pp. 303-320 | DOI | MR | Zbl

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