Diagnostic tests as residual analysis

TLDR

Residual analysis is widely used by applied workers to assess model adequacy, yet formal adequacy tests are often derived from likelihood theory via Lagrange multipliers. This paper aims to derive formal adequacy test statistics by concentrating on the distribution of residuals. The authors develop a framework that derives tests from residual distributions and facilitates exploration of independence and robustness within diagnostic testing. They show that most existing tests can be derived from elementary specification principles and that the alternative approach clarifies difficulties and offers solutions, such as improved heteroscedasticity testing in simultaneous equations. Keywords: Diagnostic Tests, Residual Analysis, Lagrange Multiplier, Heteroscedasticity, Autocorrelation, Functional Form Specification, Normality, Independence, Diagnostic Tests in Simultaneous Equations.

Abstract

Abstract Many applied workers are strongly oriented to residual analysis for assessing model adequacy. Formal test statistics of adequacy however are frequently derived from likelihood theory, particularly through Lagrange Multipliers. In contraGt, the present paper derives the formal statistics by concentrating Upon the distribution of residuals. It is shown that most existing tests can be derived in this way from a few elementary principles of specification analysis. One advantage of this alternative methodology is that it highlights some difficulties in existing approaches and simultaneously indicates a resolution of them; a good example being testing for heteroscedasticity in simultaneous equations. Other issues such as independence and robustness of diagnostic tests are also easily explored within the proposed framework. Keywords: Diagnostic TestsReeidual AnalysisLagraange Multipliera TestsHeteraoscedasticityAutocorraelationFunctional FormSpecification ErrorNormalalityIndependence Of Diagnostic TestsDiagnostic Tests In Simultaneous Equations