Diagnostic tests as residual analysis

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.

[1]  J. Sargan.  THE ESTIMATION OF ECONOMIC RELATIONSHIPS USING INSTRUMENTAL VARIABLES , 1958 .

[2]  G. Chow.  Tests of equality between sets of coefficients in two linear regressions (econometrics voi 28 , 1960 .

[3]  A. Zellner.  An Efficient Method of Estimating Seemingly Unrelated Regressions and Tests for Aggregation Bias , 1962 .

[4]  Calyampudi Radhakrishna Rao,et al.  Linear Statistical Inference and its Applications , 1967 .

[5]  J. B. Ramsey,et al.  Tests for Specification Errors in Classical Linear Least‐Squares Regression Analysis , 1969 .

[6]  P. A. P. Moran,et al.  On asymptotically optimal tests of composite hypotheses , 1970 .

[7]  James Durbin,et al.  Testing for Serial Correlation in Least-Squares Regression When Some of the Regressors are Lagged Dependent Variables , 1970 .

[8]  D. F. Andrews,et al.  Significance tests based on residuals , 1971 .

[9]  Kenneth F. Wallis,et al.  Testing for Fourth Order Autocorrelation in Qtrly Regression Equations , 1972 .

[10]  Richard E. Quandt,et al.  Nonlinear methods in econometrics , 1973 .

[11]  Harry H. Kelejian,et al.  Introduction to Econometrics: Principles and Applications , 1974 .

[12]  Harry H. Kelejian,et al.  Random Parameters in a Simultaneous Equation Framework: Identification and Estimation , 1974 .

[13]  D. Hendry.  The structure of simultaneous equations estimators , 1976 .

[14]  P. Loeb.  Specificaton Error Tests and Investment Functions , 1976 .

[15]  L. Godfrey,et al.  Testing for Serial Correlation in Dynamic Simultaneous Equation Models , 1976 .

[16]  Takeshi Amemiya,et al.  A note on a heteroscedastic model , 1977 .

[17]  T. W. Epps,et al.  The Robustness of Some Standard Tests for Autocorrelation and Heteroskedasticity When Both Problems Are Present , 1977 .

[18]  P. Robinson,et al.  The estimation of a nonlinear moving average model , 1977 .

[19]  R. Davies.  Hypothesis testing when a nuisance parameter is present only under the alternative , 1977 .

[20]  L. Godfrey,et al.  REGRESSION EQUATIONS WHEN THE REGRESSORS INCLUDE LAGGED DEPENDENT VARIABLES , 1978 .

[21]  J. Szroeter.  A Class of Parametric Tests for Heteroscedasticity in Linear Econometric Models X1-ab , 1978 .

[22]  Leslie Godfrey,et al.  Testing for multiplicative heteroskedasticity , 1978 .

[23]  Lynn Roy LaMotte,et al.  An Exact Test for the Presence of Random Walk Coefficients in a Linear Regression Model , 1978 .

[24]  T. Breusch.  TESTING FOR AUTOCORRELATION IN DYNAMIC LINEAR MODELS , 1978 .

[25]  L. Godfrey.  A Note on the Use of Durbin's h Test When the Equation is Estimated by Instrumental Variables , 1978 .

[26]  C. Granger,et al.  An introduction to bilinear time series models , 1979 .

[27]  R. Koenker,et al.  Asymptotic Theory of Least Absolute Error Regression , 1978 .

[28]  R. Farebrother.  A Grouping Test for Misspecification , 1979 .

[29]  T. Breurch,et al.  A simple test for heteroscedasticity and random coefficient variation (econometrica vol 47 , 1979 .

[30]  David F. Hendry,et al.  Econometrics-Alchemy or Science? , 1980 .

[31]  Glenn M. MacDonald,et al.  Some Large-Sample Tests for Nonnormality in the Linear Regression Model , 1980 .

[32]  P. Hall,et al.  Martingale Limit Theory and Its Application , 1980 .

[33]  Adrian Pagan,et al.  The Lagrange Multiplier Test and its Applications to Model Specification in Econometrics , 1980 .

[34]  K. Mardia.  9 Tests of unvariate and multivariate normality , 1980 .

[35]  H. White.  A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity , 1980 .

[36]  M. Wickens,et al.  Testing Linear and Log-Linear Regressions for Functional Form , 1981 .

[37]  Roger Koenker,et al.  A note on studentizing a test for heteroscedasticity , 1981 .

[38]  Testing for heteroscedasticity in simultaneous equation models , 1981 .

[39]  R. Koenker.  Robust methods in econometrics , 1981 .

[40]  L. Godfrey.  ON THE INVARIANCE OF THE LAGRANGE MULTIPLIER TEST WITH RESPECT TO CERTAIN CHANGES IN THE ALTERNATIVE HYPOTHESIS , 1981 .

[41]  C. Jarque,et al.  An efficient large-sample test for normality of observations and regression residuals , 1981 .

[42]  C. Gouriéroux,et al.  Likelihood Ratio Test, Wald Test, and Kuhn-Tucker Test in Linear Models with Inequality Constraints on the Regression Parameters , 1982 .

[43]  Jerry G. Thursby.  Misspecification, Heteroscedasticity, and the Chow and Goldfeld-Quandt Tests , 1982 .

[44]  H. White,et al.  Misspecified models with dependent observations , 1982 .

[45]  R. Engle.  Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation , 1982 .

[46]  H. White.  Maximum Likelihood Estimation of Misspecified Models , 1982 .

[47]  Anil K. Bera,et al.  Model specification tests: A simultaneous approach☆ , 1982 .

[48]  H. Kelejian.  An extension of a standard test for heteroskedasticity to a systems framework , 1982 .

[49]  G. William Schwert,et al.  Differencing as a Test of Specification , 1982 .

[50]  M. McAleer,et al.  Testing Separate Regression Models Subject to Specification Error , 1982 .

[51]  R. Engle.  A general approach to lagrange multiplier model diagnostics , 1982 .

[52]  M. Pesaran.  A Critique of the Proposed Tests of the Natural Rate-Rational Expectations Hypothesis , 1982 .

[53]  Adrian Pagan,et al.  Assessing the variability of inflation , 1983 .

[54]  The econometric approach to business-cycle analysis reconsidered , 1984 .