The Exponential Model for the Spectrum of a Time Series: Extensions and Applications
AbstractThe exponential model for the spectrum of a time series and its fractional extensions are based on the Fourier series expansion of the logarithm of the spectral density. The coefficients of the expansion form the cepstrum of the time series. After deriving the cepstrum of important classes of time series processes, also featuring long memory, we discuss likelihood inferences based on the periodogram, for which the estimation of the cepstrum yields a generalized linear model for exponential data with logarithmic link, focusing on the issue of separating the contribution of the long memory component to the log-spectrum. We then propose two extensions. The first deals with replacing the logarithmic link with a more general Box-Cox link, which encompasses also the identity and the inverse links: this enables nesting alternative spectral estimation methods (autoregressive, exponential, etc.) under the same likelihood-based framework. Secondly, we propose a gradient boosting algorithm for the estimation of the log-spectrum and illustrate its potential for distilling the long memory component of the log-spectrum.
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Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 45280.
Date of creation: 19 Mar 2013
Date of revision:
Frequency Domain Methods; Generalized linear models; Long Memory; Boosting.;
Other versions of this item:
- 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.
- 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.
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
- C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
This paper has been announced in the following NEP Reports:
- NEP-ALL-2013-03-23 (All new papers)
- NEP-ETS-2013-03-23 (Econometric Time Series)
- NEP-ORE-2013-03-23 (Operations Research)
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