We consider AR(q) models in time series with non-normal innovations represented by a member of a wide family of symmetric distributions (Student's t).Since the ML (maximum likelihood) estimators are intractable, we derive the MML (modi®ed maximum likelihood) estimators of the parameters and show that they are remarkably ef®cient. We use these estimators for hypothesis testing, and show that the resulting tests are robust and powerful.
Abstract. Bian and Dickey (1996) developed a robust Bayesian estimator for the vector of regression coefficients using a Cauchy-type g-prior. This estimator is an adaptive weighted average of the least squares estimator and the prior location, and is of great robustness with respect to flat-tailed sample distribution. In this paper, we introduce the robust Bayesian estimator to the estimation of the Capital Asset Pricing Model (CAPM) in which the distribution of the error component is well-known to be flat-tailed. To support our proposal, we apply both the robust Bayesian estimator and the least squares estimator in the simulation of the CAPM and in the analysis of the CAPM for US annual and monthly stock returns. Our simulation results show that the Bayesian estimator is robust and superior to the least squares estimator when the CAPM is contaminated by large normal and/or non-normal disturbances, especially by Cauchy disturbances. In our empirical study, we find that the robust Bayesian estimate is uniformly more efficient than the least squares estimate in terms of the relative efficiency of one-step ahead forecast mean square error, especially for small samples.
This paper develops a new test, the trinomial test, for pairwise ordinal data samples to improve the power of the sign test by modifying its treatment of zero differences between observations, thereby increasing the use of sample information. Simulations demonstrate the power superiority of the proposed trinomial test statistic over the sign test in small samples in the presence of tie observations. We also show that the proposed trinomial test has substantially higher power than the sign test in large samples and also in the presence of tie observations, as the sign test ignores information from observations resulting in ties.
The estimation of coefficients in a simple regression model with autocorrelated errors is considered. The underlying distribution is assumed t o be symmetric, one of Student's t family for illustration. Closed form estimators are obtained and shown to be remarkably efficient and robust. Skew distributions will be considered in a future paper.
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