## Offline and online weighted least squares estimation of nonstationary power ARCH processes.(English)Zbl 1219.62131

Summary: This paper proposes two estimation methods based on a weighted least squares criterion for non-(strictly) stationary power ARCH models. The weights are the squared volatilities evaluated at a known value in the parameter space. The first method is adapted for fixed sample size data while the second one allows for online data available in real time. It will be shown that these methods provide consistent and asymptotically Gaussian estimates having asymptotic variance equal to that of the quasi-maximum likelihood estimate (QMLE) regardless of the value of the weighting parameter. Finite-sample performances of the proposed WLS estimates are shown via a simulation study for various sub-classes of power ARCH models.

### MSC:

 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 62F12 Asymptotic properties of parametric estimators 65C60 Computational problems in statistics (MSC2010)
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### References:

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