Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaper › Journal article › Research › peer-review
Final published version, 490 KB, PDF document
Final published version
This paper introduces a class of generalized linear models with a Box–Cox link for the spectrum of a time series. The Box–Cox transformation of the spectral density is represented as a finite Fourier polynomial. Here, the coefficients of the polynomial, called generalized cepstral coefficients, provide a complete characterization of the properties of the random process. The link function depends on a power-transformation parameter, and can be expressed as an exponential model (logarithmic link), an autoregressive model (inverse link), or a moving average model (identity link). An advantage of this model class is the possibility of nesting alternative spectral estimation methods within the same likelihood-based framework. As a result, selecting a particular parametric spectrum is equivalent to estimating the transformation parameter. We also show that the generalized cepstral coefficients are a one-to-one function of the inverse partial autocorrelations of the process, which can be used to evaluate the mutual information between the past and the future of the process.
Original language | English |
---|---|
Journal | Statistica Sinica |
Volume | 29 |
Issue | 3 |
Pages (from-to) | 1561-1583 |
Number of pages | 23 |
ISSN | 1017-0405 |
DOIs | |
Publication status | Published - 2019 |
See relations at Aarhus University Citationformats
ID: 155494898