Exact tests and confidence sets in linear regressions with autocorrelated errors

This Paper Proposes a General Method to Build Exact Tests and Confidence Sets in Linear Regressions with First-Order Autoregressive Gaussian Disturbances. Because of a Nuisance Parameter Problem, We Argue That Generalized Bounds Tests and Conservative Confidence Sets Provide Natural Inference Procedures in Such a Context. Given an Exact Confidence Set for the Autocorrelation Coefficient, We Describe How to Obtain a Simular Simultaneous Confidence Set for the Autocorrelation Coefficient and Any Sub-Vector of Regression Coefficients. Conservative Confidence Sets for the Regression Coefficients Are Then Deduced by a Projection Method. for Any Hypothesis Which Specifies Jointly the Value of the Autocorrelation Coefficient and Any Set of Linear Restrictions on the Regression Coefficients, We Get Exeact Similar Tests. for Testing Bounds-Type Procedures. Exact Confidence Sets for the Autocorrelation Coefficient Are Built by "Inverting" Autocorrelatin Tests. the Method Is Illustrated with a Money Demand Equation.

[1]  Bridger M. Mitchell,et al.  Estimating the Autocorrelated Error Model with Trended Data: Further Results, , 1980 .

[2]  R. C. Geary,et al.  A General Expression for the Moments of Certain Symmetrical Functions of Normal Samples , 1933 .

[3]  Arnold Zellner,et al.  An Introduction to Bayesian Inference in Econometrics. , 1974 .

[4]  Alok Bhargava,et al.  Testing Residuals from Least Squares Regression for Being Generated by the Gaussian Random Walk , 1983 .

[5]  M. King.  The alternative Durbin-Watson test: An assessment of Durbin and Watson's choice of test statistic , 1981 .

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

[7]  H. Theil,et al.  Testing the Independence of Regression Disturbances , 1961 .

[8]  Takeaki Kariya,et al.  Robust Tests for Spherical Symmetry , 1977 .

[9]  Peter Schmidt,et al.  The Theory and Practice of Econometrics , 1985 .

[10]  E. Hannan.  EXACT TESTS FOR SERIAL CORRELATION , 1955 .

[11]  N. Savin,et al.  Testing for Unit Roots: 2 , 1984 .

[12]  J. Neumann.  Distribution of the Ratio of the Mean Square Successive Difference to the Variance , 1941 .

[13]  J. Durbin,et al.  Testing for serial correlation in least squares regression. II. , 1950, Biometrika.

[14]  Linear regression with correlated errors: bounds on coefficient estimates and t-values , 1987 .

[15]  J. Imhof.  Computing the distribution of quadratic forms in normal variables , 1961 .

[16]  Maxwell L. King,et al.  CRITICAL VALUE APPROXIMATIONS FOR TESTS OF LINEAR REGRESSION DISTURBANCES , 1985 .

[17]  N. Savin.  MULTIPLE HYPOTHESIS TESTING , 1984 .

[18]  Maxwell L. King,et al.  Joint one-sided tests of linear regression coefficients , 1986 .

[19]  F. C. Palm,et al.  Significance tests and spurious correlation in regression models with autocorrelated errors , 1983 .

[20]  E. Lehmann.  Testing Statistical Hypotheses , 1960 .

[21]  R. Davies.  The distribution of a linear combination of 2 random variables , 1980 .

[22]  H. Scheffé.  The Analysis of Variance , 1960 .

[23]  T. W. Anderson.  On the theory of testing serial correlation , 1948 .

[24]  Tjalling C. Koopmans,et al.  Serial Correlation and Quadratic Forms in Normal Variables , 1942 .

[25]  W. Griffiths,et al.  The properties of some covariance matrix estimators in linear models with AR(1) errors , 1984 .

[26]  J. Sargan,et al.  On the theory and application of the general linear model , 1970 .

[27]  H. Theil.  Principles of econometrics , 1971 .

[28]  G. S. Watson,et al.  SERIAL CORRELATION IN REGRESSION ANALYSIS. I , 1955 .

[29]  A. Zellner.  An Introduction to Bayesian Inference in Econometrics , 1971 .

[30]  E. J. G. Pitman,et al.  The “closest” estimates of statistical parameters , 1937, Mathematical Proceedings of the Cambridge Philosophical Society.

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

[32]  I. I. Berenblut,et al.  A New Test for Autocorrelated Errors in the Linear Regression Model , 1973 .

[33]  Kenneth J. White,et al.  THE DURBIN-WATSON TEST FOR SERIAL CORRELATION WITH EXTREME SAMPLE SIZES OR MANY REGRESSORS' , 1977 .

[34]  Alok Bhargava,et al.  On the Theory of Testing for Unit Roots in Observed Time Series , 1986 .

[35]  A. Ullah,et al.  On Robustness of Tests of Linear Restrictions in Regression Models with Elliptical Error Distributions , 1987 .

[36]  Kaname Akamatsu,et al.  NONEQUIVALENT EXCHANGE IN INTERNATIONAL TRADE , 1983 .

[37]  G. Judge,et al.  The Theory and Practice of Econometrics , 1981 .

[38]  Thomas J. Rothenberg,et al.  APPROXIMATE NORMALITY OF GENERALIZED LEAST SQUARES ESTIMATES , 1984 .

[39]  James G. MacKinnon,et al.  A MAXIMUM LIKELIHOOD PROCEDURE FOR REGRESSION WITH AUTOCORRELATED ERRORS , 1978 .

[40]  Hrishikesh D. Vinod,et al.  Recent Advances in Regression Methods. , 1983 .

[41]  K. R. Kadiyala.  Testing for the Independence of Regression Disturbances , 1970 .

[42]  N. Savin,et al.  Testing the autoregressive parameter with the t statistic , 1985 .

[43]  Rupert G. Miller.  Simultaneous Statistical Inference , 1966 .