On the Rigour of Some Misspecification Tests for Modelling Dynamic Relationships

For regression models alternative asymptotically equivalent misspecification tests may lead to conflicting inference in small samples. Effective misspecification tests should have correct significance levels irrespective of the true parameters and any redundant regressors in the model, and reasonable power against a wide class of alternative specifications. A simulation study of various tests for serial correlation and predictive failure in models with lagged dependent variables finds many tests defective in small samples. Only particular degrees of freedom adjustments to the test statistics yield improved small sample behaviour.

[1]  James Davidson,et al.  Econometric Modelling of the Aggregate Time-Series Relationship Between Consumers' Expenditure and Income in the United Kingdom , 1978 .

[2]  David F. Hendry,et al.  An Empirical Application and Monte Carlo Analysis of Tests of Dynamic Specification , 1980 .

[3]  The small sample bias of Durbin's tests for serial correlation: When one of the regressors is the lagged dependent variable and the null hypothesis is true , 1975 .

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

[5]  K. Mardia,et al.  Tables of the F- and related distributions with algorithms , 1978 .

[6]  James Davidson,et al.  Interpreting econometric evidence: The behaviour of consumers' expenditure in the UK☆ , 1981 .

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

[8]  L. Godfrey.  TESTING AGAINST GENERAL AUTOREGRESSIVE AND MOVING AVERAGE ERROR MODELS WHEN THE REGRESSORS INCLUDE LAGGED DEPENDENT VARIABLES , 1978 .

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

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

[11]  A. Wilson.  When is the Chow Test UMP , 1978 .

[12]  David F. Hendry,et al.  Serial Correlation as a Convenient Simplification, not a Nuisance: A Comment on a Study of the Demand for Money by the Bank of England. , 1978 .

[13]  D. A. Pierce.  Distribution of Residual Autocorrelations in the Regression Model with Autoregressive-Moving Average Errors , 1971 .

[14]  G. Box,et al.  On a measure of lack of fit in time series models , 1978 .

[15]  T. W. Anderson,et al.  An Introduction to Multivariate Statistical Analysis , 1959 .

[16]  N. Savin.  CONFLICT AMONG TESTING PROCEDURES IN A LINEAR REGRESSION MODEL WITH AUTOREGRESSIVE DISTURBANCES , 1976 .

[17]  N. Savin,et al.  Conflict among the Criteria Revisited: The W, LR and LM Tests , 1982 .

[18]  Andrew Harvey,et al.  The econometric analysis of time series , 1991 .

[19]  N. Davies,et al.  Significance levels of the Box-Pierce portmanteau statistic in finite samples , 1977 .

[20]  David F. Hendry,et al.  The behaviour of inconsistent instrumental variables estimators in dynamic systems with autocorrelated errors , 1979 .

[21]  Adrian Pagan,et al.  Diagnostic tests as residual analysis , 1983 .

[22]  Keith W. Hipel,et al.  Simulation procedures for Box‐Jenkins Models , 1978 .

[23]  G. Mizon.  Inferential Procedures in Nonlinear Models: An Application in a UK Industrial Cross Section Study of Factor Substitution and Returns to Scale , 1977 .

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

[25]  G. Box,et al.  Distribution of Residual Autocorrelations in Autoregressive-Integrated Moving Average Time Series Models , 1970 .

[26]  Trevor Breusch,et al.  Conflict among Criteria for Testing Hypotheses: Extensions and Comments , 1979 .

[27]  David F. Hendry,et al.  On the Formulation of Empirical-models in Dynamic Econometrics , 1982 .

[28]  D. Hendry,et al.  Maximum Likelihood Estimation of Difference Equations with Moving Average Errors: A Simulation Study , 1972 .