Finite Sample Significance Levels Research Articles

Robust Non-nested Testing for Ordinary Least Squares Regression when Some of the Regressors are Lagged Dependent Variables*

The problem of testing non-nested regression models that include lagged values of the dependent variable as regressors is discussed. It is argued that it is essential to test for error autocorrelation if ordinary least squares and the associated J and F tests are to be used. A heteroskedasticity–robust joint test against a combination of the artificial alternatives used for autocorrelation and non-nested hypothesis tests is proposed. Monte Carlo results indicate that implementing this joint test using a wild bootstrap method leads to a well-behaved procedure and gives better control of finite sample significance levels than asymptotic critical values.

Improvement of the quasi‐likelihood ratio test in ARMA models: some results for bootstrap methods

Abstract. Quasi‐likelihood ratio tests for autoregressive moving‐average (ARMA) models are examined. The ARMA models are stationary and invertible with white‐noise terms that are not restricted to be normally distributed. The white‐noise terms are instead subject to the weaker assumption that they are independently and identically distributed with an unspecified distribution. Bootstrap methods are used to improve control of the finite sample significance levels. The bootstrap is used in two ways: first, to approximate a Bartlett‐type correction; and second, to estimate the p‐value of the observed test statistic. Some simulation evidence is provided. The bootstrap p‐value test emerges as the best performer in terms of controlling significance levels.

The wild bootstrap and heteroskedasticity-robust tests for serial correlation in dynamic regression models

Conditional heteroskedasticity is a common feature of financial and macroeconomic time series data. When such heteroskedasticity is present, standard checks for serial correlation in dynamic regression models are inappropriate. In such circumstances, it is obviously important to have asymptotically valid tests that are reliable in finite samples. Monte Carlo evidence reported in this paper indicates that asymptotic critical values fail to give good control of finite sample significance levels of heteroskedasticity-robust versions of the standard Lagrange multiplier test, a Hausman-type check, and a new procedure. The application of computer-intensive methods to removing size distortion is, therefore, examined. It is found that a particularly simple form of the wild bootstrap leads to well-behaved tests. Some simulation evidence on power is also given.

Controlling the finite sample significance levels of heteroskedasticity-robust tests of several linear restrictions on regression coefficients

It is argued that the two approaches that have been suggested for improving the behaviour of heteroskedasticity-robust quasi- t tests must be combined to achieve reliability in the case of joint tests: neither is by itself sufficient.

Estimating the p-values of robust tests for the linear model

In this paper, we study the estimation of p-values for robust tests for the linear regression model. The asymptotic distribution of these tests has only been studied under the restrictive assumption of errors with known scale or symmetric distribution. Since these robust tests are based on robust regression estimates, Efron's bootstrap (1979) presents a number of problems. In particular, it is computationally very expensive, and it is not resistant to outliers in the data. In other words, the tails of the bootstrap distribution estimates obtained by re-sampling the data may be severely affected by outliers. We show how to adapt the Robust Bootstrap (Ann. Statist 30 (2002) 556; Bootstrapping MM-estimators for linear regression with fixed designs, http://mathstat.carleton.ca/~matias/pubs.html) to this problem. This method is very fast to compute, resistant to outliers in the data, and asymptotically correct under weak regularity assumptions. In this paper, we show that the Robust Bootstrap can be used to obtain asymptotically correct, computationally simple p-value estimates. A simulation study indicates that the tests whose p-values are estimated with the Robust Bootstrap have better finite sample significance levels than those obtained from the asymptotic theory based on the symmetry assumption. Although this paper is focussed on robust scores-type tests (in: Directions in Robust Statistics and Diagnostics, Part I, Springer, New York), our approach can be applied to other robust tests (for example, Wald- and dispersion-type also discussed in Markatou et al., 1991).

The robustness, reliabiligy and power of heteroskedasticity tests

Several tests for heteroskedasticity in linear regression models are examined. Asymptoticrobustness to heterokurticity, nonnormality and skewness is discussed. The finite sample eliability of asymptotically valid tests is investigated using Monte Carlo experiments. It is found that asymptotic critical values cannot, in general. be relied upon to give good agreement between nominal and actual finite sample significance levels. The use of the bootstrap overcomes this problem for general approaches that lead to asymptotically pivotal test statistics. Power comparisons are made for bootstrap tests and modified Glejser and Koenker tests are recommended.

Bootstrap-based critical values for tests of common factor restrictions

It is shown that the bootstrap can be very useful in controlling the finite sample significance levels of Wald tests of common factor restrictions, especially when the restrictions are in multiplicative form.

Some results on the finite sample significance levels of instrumental variable tests for non-nested models

Monte-Carlo estimates of the finite sample significance levels of a number of instrumental variable tests for non-nested models are provided. A simple generalization of the J-test performs better than other procedures.