Proietti, Tommaso and Luati, Alessandra (2013): The Exponential Model for the Spectrum of a Time Series: Extensions and Applications.

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Abstract
The 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 logspectrum. We then propose two extensions. The first deals with replacing the logarithmic link with a more general BoxCox link, which encompasses also the identity and the inverse links: this enables nesting alternative spectral estimation methods (autoregressive, exponential, etc.) under the same likelihoodbased framework. Secondly, we propose a gradient boosting algorithm for the estimation of the logspectrum and illustrate its potential for distilling the long memory component of the logspectrum.
Item Type:  MPRA Paper 

Original Title:  The Exponential Model for the Spectrum of a Time Series: Extensions and Applications 
Language:  English 
Keywords:  Frequency Domain Methods; Generalized linear models; Long Memory; Boosting. 
Subjects:  C  Mathematical and Quantitative Methods > C2  Single Equation Models ; Single Variables > C22  TimeSeries Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes C  Mathematical and Quantitative Methods > C5  Econometric Modeling > C52  Model Evaluation, Validation, and Selection 
Item ID:  45280 
Depositing User:  Tommaso Proietti 
Date Deposited:  20. Mar 2013 18:06 
Last Modified:  20. Mar 2013 18:06 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/45280 