A Note on Whittle's Likelihood

Contreras‐Cristán, Alberto; Gutiérrez‐Peña, Eduardo; Walker, Stephen G.

doi:10.1080/03610910600880203

Cited by 31 publications

(28 citation statements)

References 16 publications

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“…This is sometimes known as the Whittle likelihood method, after Whittle (1953) and Whittle (1957), and has been discussed in detail elsewhere (e.g. Hannan 1973; Pawitan & O'Sullivan 1994; Fan & Zhang 2004; Contreras‐Cristán, Gutiérrez‐Peña & Walker 2006). Here, we use the notation D ( I , θ ) for consistency with Gelman et al (2004, section 6.7) where it is used as the deviance , a generalization of the common weighted square deviation (or chi square) statistic.…”

Section: Periodogram Analysis Via the Likelihood Functionmentioning

confidence: 99%

A Bayesian test for periodic signals in red noise

Vaughan¹

2009

Monthly Notices of the Royal Astronomical Society

177

219

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Many astrophysical sources, especially compact accreting sources, show strong, random brightness fluctuations with broad power spectra in addition to periodic or quasi-periodic oscillations (QPOs) that have narrower spectra. The random nature of the dominant source of variance greatly complicates the process of searching for possible weak periodic signals. We have addressed this problem using the tools of Bayesian statistics; in particular using Markov chain Monte Carlo techniques to approximate the posterior distribution of model parameters, and posterior predictive model checking to assess model fits and search for periodogram outliers that may represent periodic signals. The methods developed are applied to two example datasets, both long XMM-Newton observations of highly variable Seyfert 1 galaxies: RE J1034+396 and Mrk 766. In both cases a bend (or break) in the power spectrum is evident. In the case of RE J1034+396 the previously reported QPO is found but with somewhat weaker statistical significance than reported in previous analyses. The difference is due partly to the improved continuum modelling, better treatment of nuisance parameters, and partly to different data selection methods.Comment: 15 pages, 6 figures. Accepted for publication in MNRA

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Section: Periodogram Analysis Via the Likelihood Functionmentioning

confidence: 99%

A Bayesian test for periodic signals in red noise

Vaughan¹

2009

Monthly Notices of the Royal Astronomical Society

177

219

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“…However, when working with processes for which an exact likelihood is hard to compute or is not analytically tractable but where the second-order spectral density is easy to compute, Whittle estimation remains a useful addition to the time-series analyst's toolkit. Indeed, over the last decade or so, there has been a resurgence of interest in the methodology, when using non-standard models in application areas such as hydrology (Montanari and Toth, 2007), biomedicine (Krafty and Hall, 2013) and oceanography (Sykulski et al, 2015), although it is becoming accepted that the resulting estimators can be inefficient in non-Gaussian settings (Contreras-Cristán et al, 2006).…”

Section: Introductionmentioning

confidence: 99%

Inference with the Whittle Likelihood: A Tractable Approach Using Estimating Functions

Jesus

Chandler

2016

Journal Time Series Analysis

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The theoretical properties of the Whittle likelihood have been studied extensively for many different types of process. In applications however, the utility of the approach is limited by the fact that the asymptotic sampling distribution of the estimator typically depends on third‐order and fourth‐order properties of the process that may be difficult to obtain. In this article, we show how the methodology can be embedded in the standard framework of estimating functions, which allows the asymptotic distribution to be estimated empirically without calculating higher‐order spectra. We also demonstrate that some aspects of the inference, such as the calculation of confidence regions for the entire parameter vector, can be inaccurate but that a small adjustment, designed for application in situations where a mis‐specified likelihood is used for inference, can lead to marked improvements.

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“…The Whittle estimator has recently been applied to rainfall-runoff models by Montanari and Toth (2007)." ... "However, as shown by Contreras-Cristán et al (2006), it can produce unreliable estimates for nonGaussian processes or show an important loss of efficiency if the autocorrelation of the process is high." Hence the most important drawback of Fourier analysis is that timing aspects of the original series are not retained.…”

Section: Dominant Mode Analysismentioning

confidence: 99%

Series distance – an intuitive metric to quantify hydrograph similarity in terms of occurrence, amplitude and timing of hydrological events

Ehret

Zehe

2011

Hydrol. Earth Syst. Sci.

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Abstract. Applying metrics to quantify the similarity or dissimilarity of hydrographs is a central task in hydrological modelling, used both in model calibration and the evaluation of simulations or forecasts. Motivated by the shortcomings of standard objective metrics such as the Root Mean Square Error (RMSE) or the Mean Absolute Peak Time Error (MAPTE) and the advantages of visual inspection as a powerful tool for simultaneous, case-specific and multi-criteria (yet subjective) evaluation, we propose a new objective metric termed Series Distance, which is in close accordance with visual evaluation. The Series Distance quantifies the similarity of two hydrographs neither in a time-aggregated nor in a point-by-point manner, but on the scale of hydrological events. It consists of three parts, namely a Threat Score which evaluates overall agreement of event occurrence, and the overall distance of matching observed and simulated events with respect to amplitude and timing. The novelty of the latter two is the way in which matching point pairs on the observed and simulated hydrographs are identified: not by equality in time (as is the case with the RMSE), but by the same relative position in matching segments (rise or recession) of the event, indicating the same underlying hydrological process. Thus, amplitude and timing errors are calculated simultaneously but separately, from point pairs that also match visually, considering complete events rather than only individual points (as is the case with MAPTE). Relative weights can freely be assigned to each component of the Series Distance, which allows (subjective) customization of the metric to various fields of application, but in a traceable way. Each of the three components of the Series DistanceCorrespondence to: U. Ehret (uwe.ehret@kit.edu) can be used in an aggregated or non-aggregated way, which makes the Series Distance a suitable tool for differentiated, process-based model diagnostics.After discussing the applicability of established time series metrics for hydrographs, we present the Series Distance theory, discuss its properties and compare it to those of standard metrics used in Hydrology, both at the example of simple, artificial hydrographs and an ensemble of realistic forecasts. The results suggest that the Series Distance quantifies the degree of similarity of two hydrographs in a way comparable to visual inspection, but in an objective, reproducible way.

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A Note on Whittle's Likelihood

Cited by 31 publications

References 16 publications

A Bayesian test for periodic signals in red noise

A Bayesian test for periodic signals in red noise

Inference with the Whittle Likelihood: A Tractable Approach Using Estimating Functions

Series distance – an intuitive metric to quantify hydrograph similarity in terms of occurrence, amplitude and timing of hydrological events

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