Generalised Linear Cepstral Models for the Spectrum of a Time Series

Tommaso Proietti, Alessandra Luati
2019 Statistica sinica  
The exponential model for the spectrum of a time series is based on the Fourier series expansion of the logarithm of the spectral density. The coefficients of the expansion are the cepstral coefficients and their collection is the cepstrum of the time series. Approximate likelihood inference based on the periodogram leads to a generalised linear model for asymptotically independent exponential data with logarithmic link. The paper introduces the class of generalised linear cepstral models with
more » ... pstral models with Box-Cox link, which is based on the truncated Fourier series expansion of the Box-Cox transformation of the spectral density; the coefficients of the expansions can be termed generalised cepstral coefficients and are related to the generalised autocovariances of the series. The link function depends on a power transformation parameter, and encompasses the exponential model. Other important special cases are the inverse link (which leads to modelling the inverse spectrum), and the identity link. One of the merits of this model class is the possibility of nesting alternative spectral estimation methods (autoregressive, exponential, etc.) under the same likelihood-based framework.
doi:10.5705/ss.202017.0322 fatcat:vflicagwjjdsrjkab4v7q2umzq