Consistency tests for heteroskedastic and risk models

  • Adrian R. Pagan University of Rochester
  • Hernán Sabau Operadora de Bolsa
Keywords: consistency tests, Engle, Lilie and Robins model


This paper considers a class of consistency tests for the specification of heteroskedastic and risk models. The tests are related to other procedures such as the conditional moment tests of Newey and Tauchen, Hausman's tests, White's tests, the variable addition Lagrange multiplier tests of Engle and Pagan, and the residual analysis of Pagan and Hall. The power of the consistency tests in the presence of local departures is analyzed and the risk premia model of Engle, Lilien and Robins is re-assessed.


Amemiya, T. (1973). "Regression Analysis when the Variance of the Dependent Variable is Proportional to the Square of its Expectation", Journal of the American Statistical Association, vol. 68, pp. 928-934.

Bollerslev, T. (1986). "Generalized Autoregressive Conditional Heteroscedasticity", Journal of Econometrics, vol. 31, pp. 307-327.

Breusch, and L. G. Godfrey (1986). "Data Transformation Tests", The Economic Journal, vol. 96, pp. 47-58.

Breusch, L. G. Godfrey, T. S., and A. R. Pagan (1980). "The Lagrange Multiplier Test and its Applications to Model Specification in Econometrics", Review of Economic Studies, vol. 47, pp. 239-253.

Carroll, R. J. (1982). "Adapting for Heteroscedasticity in Linear Models", Annals of Statistics, vol. 10, pp. 1224-1233.

Carroll, R. J., and D. Ruppert (1982). "A Comparison between Maximum Likelihood and Generalized Least Squares in a Heteroscedastic Linear Model", Journal of the American Statistical Association, vol. 77, pp. 878-882.

Davidson, R., and J. G. MacKinnon (1984). "Model Specification Tests Based on Artificial Linear Regressions", International Economic Review, vol. 25, pp. 485-502.

Domowitz, l., and C. S. Hakkio (1985). "Conditional Variance and the Risk Premium in the Foreign Exchange Market", Journal of International Economics, vol. 19, pp. 47-66.

Domowitz, l., C. S. Hakkio, and H. White (1982). "Misspecified Models With Dependent Observations", Journal of Econometrics, vol. 20, pp. 35-58.

Engle, R. F. (1982a). "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation", Econometrica, vol. 50, pp. 987-1007.

Engle, R. F. (1982b). "A General Approach to Lagrange Multiplier Model biagnostics", Journal of Econometrics, vol. 20, pp. 83-104.

Engle, R. F. (1983). "Estimates of the Variance of U.S. Inflation Based upon the ARCH Model", Journal of Money, Credit, and Banking, vol. 15, pp. 286-301.

Engle, R. F. (1984). "Wald, Likelihood Ratio, and Lagrange Multiplier Tests in Econometrics", in Z. Griliches and M. D. Intrilligator (eds.), Handbook of Econometrics, vol. 2, Elsevier Science Publishers.

Engle, R. F. and T. Bollerslev (1986). "Modelling the Persistence of Conditional Variances", Econometric Reviews, vol. 5, pp. 1-50.

Engle, R. F., D. F. Hendry, and J. F. Richard (1983). "Exogeneity", Econometrica, vol. 51, pp. 277-304.

Engle, R. F., D. M. Lilien, and R. P. Robins (1987). "Estimating Time Varying Risk Premia in the Term Structure: The ARCH-M Model", Econometrica, vol. 55, pp. 391-407.

Geweke, J. (1986). "Comment", Econometric Reviews, vol. 5, pp. 57-61.

Hansen, L. P. (1982). "Large Sample Properties of Generalized Method of Moments Estimators", Econometrica, vol. 50, pp. 1029-1054.

Hausman, J. A. (1978). "Specification Tests in Econometrics", Econometrica, vol. 46, pp. 1251-1271.

Hausman, J. A., Z. Griliches and B. H. Holland (1984). "Econometric Models for Count Data with an Application to the Patents R and D Relationship", Econometrica, vol. 52, pp. 909-938.

Jennrich, R. I. (1969). "Asymptotic Properties of Non-Unear Least Squares Estimators", Annals of Mathematical Statistics, vol. 40, pp. 633-643.

Kraft, D. F., and R. F. Engle (1982). "Autoregressive Conditional Heteroscedasticity in Multiple Time Series Models", UCSD Discussion Paper, pp. 82-23.

Newey, W. D. (1985a). "Maximum Likelihood Specification Testing and Conditional Moments", Econometrica, vol. 53, pp. 1047-1070.

Newey, W. D. (1985b). "Generalized Method of Moments Specification Testing", Journal of Econometrics, vol. 29, pp. 229-256.

Newey, W. D. (1986)."Efficient Estimation of Models with Conditional Moment Restrictions", MIT, manuscript.

Pagan, A. R. (1984a). "Model Evaluation by Variable Addition", in D. F. Hendry and K. F. Wallis (eds.), Econometrics and Quantitative Economics, Basil Blackwell.

Pagan, A. R. (1984b). "Econometric Issues in the Analysis of Regressions with Generated Regressors", International Economic Review, vol. 25, pp. 221-247.

Pagan, A. R., and A. D. Hall (1983). "Diagnostic Tests as Residual Analysis", Econometric Reviews, vol. 2, pp. 159-218.

Pagan, A. R., and H. C. Sabau (1991). "On the Inconsistency of the MLE in Certain Heteroskedastic Regression Models", Estudios Económicos, vol. 6, pp. 159-172.

Pagan, A. R., and A. Ullah (1987). "The Econometric Analysis of Models with Risk Terms", University of Rochester, manuscript.

Ramsey, J. B. (1969). "Tests for Specification Errors in Classical Linear Least-Squares Regression Analysis", Journal of the Royal Statistical Society, Series B, vol. 31, pp. 350-371.

Robinson, P. M. (1987). "Asymptotically Efficient Estimation in the Presence of Heteroscedasticity of Unknown Form", Econometrica, vol. 55, pp. 875-891.

Sabau, H. C. (1987a). "The Structure of the Maximum Likelihood Estimator in Heteroskedastic Normal Conditional Models", ANU, manuscript.

Sabau, H. C. (1987b). "Testing Normality in Heteroskedastic Models", ANU, manuscript.

Tauchen, G. (1985). "Diagnostic Testing and Evaluation of Maximum Likelihood Models", Journal of Econometrics, vol. 30, pp. 415-443.

Weiss, A. A. (1984). "ARMA Model with ARCH Errors", Journal of Time Series Analysis, vol. 5, pp. 129-143.

White, H. (1980). "Using Least Squares to Approximate Unknown Regression Functions", International Economic Review, vol. 21, pp. 149-170.

How to Cite
R. PaganA., & SabauH. (1992). Consistency tests for heteroskedastic and risk models. Estudios Económicos, 7(1), 3-30.
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