Luati, Alessandra and Proietti, Tommaso and Reale, Marco (2011): The Variance Profile.

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Abstract
The variance profile is defined as the power mean of the spectral density function of a stationary stochastic process. It is a continuous and nondecreasing function of the power parameter, p, which returns the minimum of the spectrum (p → −∞), the interpolation error variance (harmonic mean, p = −1), the prediction error variance (geometric mean, p = 0), the unconditional variance (arithmetic mean, p = 1) and the maximum of the spectrum (p → ∞). The variance profile provides a useful characterisation of a stochastic processes; we focus in particular on the class of fractionally integrated processes. Moreover, it enables a direct and immediate derivation of the SzegoKolmogorov formula and the interpolation error variance formula. The paper proposes a nonparametric estimator of the variance profile based on the power mean of the smoothed sample spectrum, and proves its consistency and its asymptotic normality. From the empirical standpoint, we propose and illustrate the use of the variance profile for estimating the long memory parameter in climatological and financial time series and for assessing structural change.
Item Type:  MPRA Paper 

Original Title:  The Variance Profile 
Language:  English 
Keywords:  Predictability; Interpolation; Nonparametric spectral estimation; Long memory. 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C13  Estimation: General C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C14  Semiparametric and Nonparametric Methods: General C  Mathematical and Quantitative Methods > C2  Single Equation Models ; Single Variables > C22  TimeSeries Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes 
Item ID:  30378 
Depositing User:  Tommaso Proietti 
Date Deposited:  24. Apr 2011 13:03 
Last Modified:  16. Feb 2013 00:31 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/30378 