Pseudo-maximum likelihood estimators in linear regression models with fractional time series

Hongchang Hu (), Weifu Hu and Xinxin Yu
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Hongchang Hu: Hubei Normal University
Weifu Hu: Hubei Normal University
Xinxin Yu: Hubei Normal University

Statistical Papers, 2021, vol. 62, issue 2, No 4, 639-659

Abstract: Abstract Fractal time series and linear regression models are known to play an important role in many scientific disciplines and applied fields. Although there have been enormous development after their appearance, nobody investigates them together. The paper studies a linear regression model (or trending fractional time series model) $$\begin{aligned} y_t=x_t^T\beta +\varepsilon _t,t=1,2,\ldots ,n, \end{aligned}$$ y t = x t T β + ε t , t = 1 , 2 , … , n , where $$\begin{aligned} \varepsilon _t=\Delta ^{-\delta }g(L;\varphi )\eta _t \end{aligned}$$ ε t = Δ - δ g ( L ; φ ) η t with parameters $$0\le \delta \le 1,\varphi ,\beta ,\sigma ^2$$ 0 ≤ δ ≤ 1 , φ , β , σ 2 and $$\eta _t$$ η t i.i.d. with zero mean and variance $$\sigma ^2$$ σ 2 . Firstly, the pseudo-maximum likelihood (ML) estimators of $$\varphi ,\beta ,\sigma ^2$$ φ , β , σ 2 are given. Secondly, under general conditions, the asymptotic properties of the ML estimators are investigated. Lastly, the validity of method is illuminated by a real example.

Keywords: Linear regression model; Maximum likelihood estimator; Fractional time series; Asymptotic property; 62J05; 62M10 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s00362-019-01091-1

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