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Pseudo-maximum likelihood estimators in linear regression models with fractional time series. (English) Zbl 1477.62246

Summary: 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) \[ y_t=x_t^T\beta +\varepsilon_t,\quad t=1,2,\dots ,n, \] where \[ \varepsilon_t=\Delta^{-\delta }g(L;\varphi )\eta_t \] with parameters \(0\leq \delta \leq 1,\varphi,\beta,\sigma^2\) and \(\eta_t\) i.i.d. with zero mean and variance \(\sigma^2\). Firstly, the pseudo-maximum likelihood (ML) estimators of \(\varphi,\beta,\sigma^2\) 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.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62J05 Linear regression; mixed models
62F12 Asymptotic properties of parametric estimators

Software:

longmemo
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Full Text: DOI

References:

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