Critical Value Approximations for Tests of Linear Regression Disturbances

Abstract

summary Two important classes of tests for non‐spherical disturbances in the linear regression model involve test statistics whose null distributions and hence critical values depend on the regressors. This paper investigates the accuracy of the normal, two moment beta and four moment beta approximations to the critical values of such tests. An empirical experiment aimed at evaluating the accuracy of the approximations for a variety of tests against autocorrelation and heteroscedasticity is conducted. Overall the approximations are found to provide reasonably accurate critical values with skewness being a factor determining the degree of accuracy.

Time Stationarity of Systematic Risk: Some Australian Evidence

“…This information can be used to approximate the distribution of our test statistic with one selected from Burr's family of distributions. This approach is described in detail in Evans and Fry (1990). In this case, the particular Burr distributions used are the Type XI1 and its 'reciprocal' Type 111.…”

“…See Evans and Fry (1990) on how to compute the c and k values. Alternatively, Burr (1973) produced tables of c and k for various values of skewness and kurtosis of the distribution of interest.…”

Econometrics

“…Using the results on moments of quadratic forms in regression residuals, see for e.g.,Evans and King (1985), we get They suggest an alternative Standardized Lagrange Multiplier (SLM) test whose asymptotic critical values are generally closer to the exact critical values than those of the LM test.…”

Testing for Block Effects in Regression Models Based on Survey Data

“…The form of the test statistic means that exact critical values and powers can be calculated by using methods similar to those proposed by Koerts and Abrahamse (1969) for the Durbin-Watson test. Furthermore, the methods outlined and analyzed by Evans and King (1985) can be used to obtain good approximate critical values. As…”