The Large-Sample Distribution of the Likelihood Ratio for Testing Composite Hypotheses

Wilks, S. S.

doi:10.1214/aoms/1177732360

Cited by 2,817 publications

(1,932 citation statements)

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“…As a likelihood ratio test, standard large-sample theory (Wilks, 1938;Wald, 1943) applies to the time-domain Gcausality estimator in both the conditional and unconditional cases. If dim(X) = n x , dim(Y) = n y and dim(Z) = n z (with n x +n y +n z = n) then the difference in the number of parameters between the full model (20) and the nested reduced model (21) is just d ≡ pn x n y .…”

Section: Statistical Inferencementioning

confidence: 99%

The MVGC multivariate Granger causality toolbox: A new approach to Granger-causal inference

Barnett

Seth

2014

Journal of Neuroscience Methods

854

874

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Background: Wiener-Granger causality ("G-causality") is a statistical notion of causality applicable to time series data, whereby cause precedes, and helps predict, effect. It is defined in both time and frequency domains, and allows for the conditioning out of common causal influences. Originally developed in the context of econometric theory, it has since achieved broad application in the neurosciences and beyond. Prediction in the G-causality formalism is based on VAR (Vector AutoRegressive) modelling.New Method: The MVGC Matlab c Toolbox approach to G-causal inference is based on multiple equivalent representations of a VAR model by (i) regression parameters, (ii) the autocovariance sequence and (iii) the cross-power spectral density of the underlying process. It features a variety of algorithms for moving between these representations, enabling selection of the most suitable algorithms with regard to computational efficiency and numerical accuracy.Results: In this paper we explain the theoretical basis, computational strategy and application to empirical G-causal inference of the MVGC Toolbox. We also show via numerical simulations the advantages of our Toolbox over previous methods in terms of computational accuracy and statistical inference. Comparison with Existing Method(s):The standard method of computing G-causality involves estimation of parameters for both a full and a nested (reduced) VAR model. The MVGC approach, by contrast, avoids explicit estimation of the reduced model, thus eliminating a source of estimation error and improving statistical power, and in addition facilitates fast and accurate estimation of the computationally awkward case of conditional G-causality in the frequency domain. Conclusions:The MVGC Toolbox implements a flexible, powerful and efficient approach to G-causal inference.

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Section: Statistical Inferencementioning

confidence: 99%

The MVGC multivariate Granger causality toolbox: A new approach to Granger-causal inference

Barnett

Seth

2014

Journal of Neuroscience Methods

854

874

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“…Right: details of the secondary pipeline described in the Appendix: each ROI (marked by a solid blue circle) of radius 10°is centered on b 0 =  and separated from its neighbors (orange circles) by 5°in Galactic longitude. obtained from Wilks's theorem (Wilks 1938). In the null hypothesis, TS follows a 2 c distribution with n degrees of freedom, where n is the number of additional parameters in the model.…”

Section: Localization and Extensionmentioning

confidence: 99%

Search for Extended Sources in the Galactic Plane Using Six Years of Fermi-Large Area Telescope Pass 8 Data above 10 GeV

Ackermann

Ajello

Baldini

et al. 2017

ApJ

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The spatial extension of a γ-ray source is an essential ingredient to determine its spectral properties, as well as its potential multiwavelength counterpart. The capability to spatially resolve γ-ray sources is greatly improved by the newly delivered Fermi-Large Area Telescope (LAT) Pass 8 event-level analysis, which provides a greater acceptance and an improved point-spread function, two crucial factors for the detection of extended sources. Here, we present a complete search for extended sources located within 7°from the Galactic plane, using 6 yr of Fermi-LAT data above 10 GeV. We find 46 extended sources and provide their morphological and spectral characteristics. This constitutes the first catalog of hard Fermi-LAT extended sources, named the Fermi Galactic Extended Source Catalog, which allows a thorough study of the properties of the Galactic plane in the sub-TeV domain.

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“…For example, even in the synthetic cases discussed here, we find that residual analysis is usually unable to reject the false model in the sub-critical regime, especially far from criticality (n < 0.7). Nested statistical tests [36] are not applicable here, since none of the models (6)- (8) can be embedded into another one. We find that the Akaike information criterion [37] can successfully select the correct model in our synthetic cases.…”

Section: Effect Of the Regularization Part Of Power Law Kernelsmentioning

confidence: 99%

Apparent criticality and calibration issues in the Hawkes self-excited point process model: application to high-frequency financial data

Filimonov

Sornette

2015

Quantitative Finance

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We present a careful analysis of possible issues on the application of the self-excited Hawkes process to high-frequency financial data. We carefully analyze a set of effects leading to significant biases in the estimation of the "criticality index" n that quantifies the degree of endogeneity of how much past events trigger future events. We report the following model biases: (i) evidence of strong upward biases on the estimation of n when using power law memory kernels in the presence of outliers, (ii) strong effects on n resulting from the form of the regularization part of the power law kernel, (iii) strong edge effects on the estimated n when using power law kernels, and (iv) the need for an exhaustive search of the absolute maximum of the log-likelihood function due to its complicated shape. Moreover, we demonstrate that the calibration of the Hawkes process on mixtures of pure Poisson process with changes of regime leads to completely spurious apparent critical values for the branching ratio (n ≃ 1) while the true value is actually n = 0. More generally, regime shifts on the parameters of the Hawkes model and/or on the generating process itself are shown to systematically lead to a significant upward bias in the estimation of the branching ratio. We demonstrate the importance of the preparation of the high-frequency financial data, in particular: (a) the impact of overnight trading in the analysis of long-term trends, (b) intraday seasonality and detrending of the data and (c) vulnerability of the analysis to day-to-day non-stationarity and regime shifts. Special care is given to the decrease of quality of the timestamps of tick data due to latency and grouping of messages to packets by the stock exchange. Altogether, our careful exploration of the caveats of the calibration of the Hawkes process stresses the need for considering all the above issues before any conclusion can be sustained. In this respect, because the above effects are plaguing their analyses, the claim by Hardiman, Bercot and Bouchaud (2013) that financial market have been continuously functioning at or close to criticality (n ≃ 1) cannot be supported. In contrast, our previous results on E-mini S&P 500 Futures Contracts and on major commodity future contracts are upheld.

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The Large-Sample Distribution of the Likelihood Ratio for Testing Composite Hypotheses

Cited by 2,817 publications

References 0 publications

The MVGC multivariate Granger causality toolbox: A new approach to Granger-causal inference

The MVGC multivariate Granger causality toolbox: A new approach to Granger-causal inference

Search for Extended Sources in the Galactic Plane Using Six Years of Fermi-Large Area Telescope Pass 8 Data above 10 GeV

Apparent criticality and calibration issues in the Hawkes self-excited point process model: application to high-frequency financial data

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