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Originally published in 2000, this volume was an early example of the application of differential geometry to econometrics.
This book deals with the omitted variable test for a multivariate time-series regression model. The empirical motivation is the homogeneity test for a consumer demand system. The consequences of using a dynamically misspecified omitted variable test are shown in detail. The analysis starts with the univariate t-test and is then extended to the multivariate regression system. The small sample performance of the dynamically correctly specified omitted variable test is analysed by simulation. Two classes of tests are considered: versions of the likelihood ratio test and the robust Wald test which is based on a heteroskedasticity and autocorrelation consistent variance-covariance estimator (HAC).
Abstract: "We consider a class of time series specification tests based on quadratic forms of weighted sums of residuals autocorrelations. Asymptotically distribution-free tests in the presence of estimated parameters are obtained by suitably transforming the weights, which can be optimally chosen to maximize the power function when testing in the direction of local alternatives. We discuss in detail an asymptotically optimal distribution-free alternative to the popular Box-Pierce when testing in the direction of AR or MA alternatives. The performance of the test with small samples is studied by means of a Monte Carlo experiment." [author's abstract]
The main problem in econometric modelling of time series is discovering sustainable and interpretable relationships between observed economic variables. The primary aim of this book is to develop an operational econometric approach which allows constructive modelling. Professor Hendry deals with methodological issues (model discovery, data mining, and progressive research strategies); with major tools for modelling (recursive methods, encompassing, super exogeneity, invariance tests); and with practical problems (collinearity, heteroscedasticity, and measurement errors). He also includes an extensive study of US money demand. The book is self-contained, with the technical background covered in appendices. It is thus suitable for first year graduate students, and includes solved examples and exercises to facilitate its use in teaching. About the Series Advanced Texts in Econometrics is a distinguished and rapidly expanding series in which leading econometricians assess recent developments in such areas as stochastic probability, panel and time series data analysis, modeling, and cointegration. In both hardback and affordable paperback, each volume explains the nature and applicability of a topic in greater depth than possible in introductory textbooks or single journal articles. Each definitive work is formatted to be as accessible and convenient for those who are not familiar with the detailed primary literature.