Journal ArticleDOI
A Simple Test for Heteroscedasticity and Random Coefficient Variation.
Trevor Breusch,Adrian Pagan +1 more
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In this paper, a simple test for heteroscedastic disturbances in a linear regression model is developed using the framework of the Lagrangian multiplier test, and the criterion is given as a readily computed function of the OLS residuals.Abstract:
A simple test for heteroscedastic disturbances in a linear regression model is developed using the framework of the Lagrangian multiplier test. For a wide range of heteroscedastic and random coefficient specifications, the criterion is given as a readily computed function of the OLS residuals. Some finite sample evidence is presented to supplement the general asymptotic properties of Lagrangian multiplier tests.read more
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Journal ArticleDOI
Generalized autoregressive conditional heteroskedasticity
Tim Bollerslev,Tim Bollerslev +1 more
TL;DR: In this paper, a natural generalization of the ARCH (Autoregressive Conditional Heteroskedastic) process introduced in 1982 to allow for past conditional variances in the current conditional variance equation is proposed.
Journal ArticleDOI
A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle.
TL;DR: In this article, the parameters of an autoregression are viewed as the outcome of a discrete-state Markov process, and an algorithm for drawing such probabilistic inference in the form of a nonlinear iterative filter is presented.
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The Lagrange Multiplier Test and its Applications to Model Specification in Econometrics
Trevor Breusch,Adrian Pagan +1 more
TL;DR: The Lagrange multiplier (LM) statistic as mentioned in this paper is based on the maximum likelihood ratio (LR) procedure and is used to test the effect on the first order conditions for a maximum of the likelihood of imposing the hypothesis.
Journal ArticleDOI
Quasi-maximum likelihood estimation and inference in dynamic models with time-varying covariances
TL;DR: In this paper, the authors study the properties of the quasi-maximum likelihood estimator and related test statistics in dynamic models that jointly parameterize conditional means and conditional covariances, when a normal log-likelihood is maximized but the assumption of normality is violated.
Journal ArticleDOI
Efficient tests for normality, homoscedasticity and serial independence of regression residuals
Carlos M. Jarque,Anil K. Bera +1 more
TL;DR: In this paper, the Lagrange multiplier procedure is used to derive efficient joint tests for residual normality, homoscedasticity and serial independence, which are simple to compute and asymptotically distributed as χ2.
References
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Book
Linear statistical inference and its applications
TL;DR: Algebra of Vectors and Matrices, Probability Theory, Tools and Techniques, and Continuous Probability Models.
Journal ArticleDOI
Computing the distribution of quadratic forms in normal variables
TL;DR: In this paper, exact and approximate methods for computing the distribution of quadratic forms in normal variables are given for a given value x, around the probability P{Q > x}.
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Testing for Serial Correlation in Least-Squares Regression When Some of the Regressors are Lagged Dependent Variables
TL;DR: In this paper, it is shown that the asymptotic distribution of the serial correlation coefficient calculated from the least-squares residuals differs from that of the true disturbances in a regression model where some of the regressors are lagged dependent variables.
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On the Distribution of the Likelihood Ratio
TL;DR: In this paper, the asymptotic distribution of the likelihood ratio λ is examined when the value of the parameter is a boundary point of both the set of points corresponding to the hypothesis and the set corresponding to an alternative.