The Variance Profile

• 成果类型: Article
• 署名作者: Luati, Alessandra; Proietti, Tommaso; Reale, Marco
• 署名单位: University of Bologna; University of Sydney; University of Rome Tor Vergata; University of Canterbury
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2012.682832
• 发表日期: 2012
• 页码: 607-621
• 关键词: time-series; interpolation error; innovation variance; ma(1) disturbances; prediction error; moving average; testing ar(1); models; fit

摘要

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 -> infinity), 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 -> infinity). The variance profile provides a useful characterization of a stochastic process; we focus in particular on the class of fractionally integrated processes. Moreover, it enables a direct and immediate derivation of the Szego-Kolmogorov formula and the interpolation error variance formula. The article 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.