The Variance Profile
AbstractThe variance profile is defined as the power mean of the spectral density function of a stationary stochastic process. It is a continuous and non-decreasing 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 Szego-Kolmogorov formula and the interpolation error variance formula. The paper proposes a non-parametric 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.
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Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 30378.
Date of creation: 19 Apr 2011
Date of revision:
Predictability; Interpolation; Non-parametric spectral estimation; Long memory.;
Other versions of this item:
- C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
- C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-04-30 (All new papers)
- NEP-ECM-2011-04-30 (Econometrics)
- NEP-ORE-2011-04-30 (Operations Research)
- NEP-RMG-2011-04-30 (Risk Management)
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- Francis X. Diebold & Lutz Kilian, 2001.
"Measuring predictability: theory and macroeconomic applications,"
Journal of Applied Econometrics,
John Wiley & Sons, Ltd., vol. 16(6), pages 657-669.
- Francis X. Diebold & Lutz Kilian, 1997. "Measuring predictability: theory and macroeconomic applications," Working Papers 97-23, Federal Reserve Bank of Philadelphia.
- Diebold, Francis X & Kilian, Lutz, 2000. "Measuring Predictability: Theory And Macroeconomic Applications," CEPR Discussion Papers 2424, C.E.P.R. Discussion Papers.
- Francis X. Diebold & Lutz Kilian, 1998. "Measuring Predictability: Theory and Macroeconomic Applications," Working Papers 98-16, New York University, Leonard N. Stern School of Business, Department of Economics.
- Francis X. Diebold & Lutz Kilian, 1997. "Measuring Predictability: Theory and Macroeconomic Applications," NBER Technical Working Papers 0213, National Bureau of Economic Research, Inc.
- Luati, Alessandra & Proietti, Tommaso, 2009.
"Hyper-spherical and Elliptical Stochastic Cycles,"
15169, University Library of Munich, Germany.
- Hannan, E J & Terrell, R D & Tuckwell, N E, 1970. "The Seasonal Adjustment of Economic Time Series," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 11(1), pages 24-52, February.
- Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
- Nidhan Choudhuri & Subhashis Ghosal & Anindya Roy, 2004. "Bayesian Estimation of the Spectral Density of a Time Series," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 1050-1059, December.
- James H. Stock & Mark W. Watson, 2003.
"Has the Business Cycle Changed and Why?,"
in: NBER Macroeconomics Annual 2002, Volume 17, pages 159-230
National Bureau of Economic Research, Inc.
- Kasahara, Yukio & Pourahmadi, Mohsen & Inoue, Akihiko, 2009. "Duals of random vectors and processes with applications to prediction problems with missing values," Statistics & Probability Letters, Elsevier, vol. 79(14), pages 1637-1646, July.
- Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
- Tommaso Proietti & Alessandra Luati, 2013.
"The Exponential Model for the Spectrum of a Time Series: Extensions and Applications,"
CEIS Research Paper
272, Tor Vergata University, CEIS, revised 19 Apr 2013.
- Proietti, Tommaso & Luati, Alessandra, 2013. "The Exponential Model for the Spectrum of a Time Series: Extensions and Applications," MPRA Paper 45280, University Library of Munich, Germany.
- Tommaso Proietti & Alessandra Luati, 2013. "The Exponential Model for the Spectrum of a Time Series: Extensions and Applications," CREATES Research Papers 2013-34, School of Economics and Management, University of Aarhus.
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