Distribution-Free Bounds for Serial Correlation Coefficients in Heteroskedastic Symmetric Time Series

We consider the problem of testing whether the observations X1, ..., Xn of a time series are independent with unspecified (possibly nonidentical) distributions symmetric about a common known median. Various bounds on the distributions of serial correlation coefficients are proposed: exponential bounds, Eaton-type bounds, Chebyshev bounds and Berry-Esséen-Zolotarev bounds. The bounds are exact in finite samples, distribution-free and easy to compute. The performance of the bounds is evaluated and compared with traditional serial dependence tests in a simulation experiment. The procedures proposed are applied to U.S. data on interest rates (commercial paper rate).

Exact Nonparametric Two-Sample Homogeneity Tests for Possibly Discrete Distributions.

In this paper, we study several tests for the equality of two unknown distributions. Two are based on empirical distribution functions, three others on nonparametric probability density estimates, and the last ones on differences between sample moments. We suggest controlling the size of such tests (under nonparametric assumptions) by using permutational versions of the tests jointly with the method of Monte Carlo tests properly adjusted to deal with discrete distributions. We also propose a combined test procedure, whose level is again perfectly controlled through the Monte Carlo test technique and has better power properties than the individual tests that are combined. Finally, in a simulation experiment, we show that the technique suggested provides perfect control of test size and that the new tests proposed can yield sizeable power improvements.

Les entrées de capitaux et la maladie hollandaise dans les pays de l'UEMOA : un test empirique.

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Predictors of PSA test and Mammography use in the Canadian population.

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Un test de circulation pour mesurer la réversibilité temporelle de la volatilité.

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The Seemingly Unrelated Dynamic Cointegration Regression Model and Testing for Purching Power Parity.

This paper studies seemingly unrelated linear models with integrated regressors and stationary errors. By adding leads and lags of the first differences of the regressors and estimating this augmented dynamic regression model by feasible generalized least squares using the long-run covariance matrix, we obtain an efficient estimator of the cointegrating vector that has a limiting mixed normal distribution. Simulation results suggest that this new estimator compares favorably with others already proposed in the literature. We apply these new estimators to the testing of purchasing power parity (PPP) among the G-7 countries. The test based on the efficient estimates rejects the PPP hypothesis for most countries.

Simulation-Based Finite-Sample Tests for Heteroskedasticity and ARCH Effects.

A wide range of tests for heteroskedasticity have been proposed in the econometric and statistics literature. Although a few exact homoskedasticity tests are available, the commonly employed procedures are quite generally based on asymptotic approximations which may not provide good size control in finite samples. There has been a number of recent studies that seek to improve the reliability of common heteroskedasticity tests using Edgeworth, Bartlett, jackknife and bootstrap methods. Yet the latter remain approximate. In this paper, we describe a solution to the problem of controlling the size of homoskedasticity tests in linear regression contexts. We study procedures based on the standard test statistics [e.g., the Goldfeld-Quandt, Glejser, Bartlett, Cochran, Hartley, Breusch-Pagan-Godfrey, White and Szroeter criteria] as well as tests for autoregressive conditional heteroskedasticity (ARCH-type models). We also suggest several extensions of the existing procedures (sup-type of combined test statistics) to allow for unknown breakpoints in the error variance. We exploit the technique of Monte Carlo tests to obtain provably exact p-values, for both the standard and the new tests suggested. We show that the MC test procedure conveniently solves the intractable null distribution problem, in particular those raised by the sup-type and combined test statistics as well as (when relevant) unidentified nuisance parameter problems under the null hypothesis. The method proposed works in exactly the same way with both Gaussian and non-Gaussian disturbance distributions [such as heavy-tailed or stable distributions]. The performance of the procedures is examined by simulation. The Monte Carlo experiments conducted focus on : (1) ARCH, GARCH, and ARCH-in-mean alternatives; (2) the case where the variance increases monotonically with : (i) one exogenous variable, and (ii) the mean of the dependent variable; (3) grouped heteroskedasticity; (4) breaks in variance at unknown points. We find that the proposed tests achieve perfect size control and have good power.