Guorui Bian

Time Series Models in Non‐Normal Situations: Symmetric Innovations

We consider AR(q) models in time series with non‐normal innovations represented by a member of a wide family of symmetric distributions (Students t). Since the ML (maximum likelihood) estimators are intractable, we derive the MML (modified maximum likelihood) estimators of the parameters and show that they are remarkably efficient. We use these estimators for hypothesis testing, and show that the resulting tests are robust and powerful.

Estimating parameters in autoregressive models in non-normal situations: symmetric innovations

The estimation of coe±cients in a simple regression model with autocorrelated errors is considered. The underlying distribution is assumed to be symmetric, one of Students t family for illustration. Closed form estimators are obtained and shown to be remarkably e±cient and robust. Skew distributions will be considered in a future paper.

Time series models with asymmetric innovations

We consider AR(q) models in time series with asymmetric innovations represented by two families ofdistributions: (i) gamma with support IR : (0, ∞), and (ii) generalized logistic with support IR:(-∞,∞). Since the ML (maximum likelihood) estimators are intractable, we derive the MML (modified maximum likelihood) estimators of the parameters and show that they are remarkably efficient besides being easy to compute. We investigate the efficiency properties of the classical LS (least squares) estimators. Their efficiencies relative to the proposed MML estimators are very low.

Bayesian Inference Based on Robust Priors and MML Estimators: Part I, Symmetric Location-Scale Distributions

Motivated by the attractive features of robust priors and the MML estimators, we develop Bayesian estimators for the location parameter of a family which represents a very wide class of symmetric location-scale distributions ranging from Cauchy to normal distributions. We show that the new estimators are clearly superior to those obtained earlier by other authors. The proposed method can also be extended to asymmetric location-scale distributions. That will form Part II of this work.

ROBUST ESTIMATION IN CAPITAL ASSET PRICING MODEL

Bian and Dickey (1996) developed a robust Bayesian estimator for the vector of regression coecients 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 at-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 at-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 nd that the robust Bayesian estimate is uniformly more ecient than the least squares estimate in terms of the relative eciency of one-step ahead forecast mean square error, especially for small samples.

ROBUST ESTIMATION AND FORECASTING OF THE CAPITAL ASSET PRICING MODEL

In this paper, we develop a modified maximum likelihood (MML) estimator for the multiple linear regression model with underlying student t distribution. We obtain the closed form of the estimators, derive the asymptotic properties, and demonstrate that the MML estimator is more appropriate for estimating the parameters of the Capital Asset Pricing Model (CAPM) by comparing its performance with least squares estimators (LSE) on the monthly returns of US portfolios. The empirical results reveal that the MML estimators are more efficient than LSE in terms of the relative efficiency of one-step-ahead forecast mean square error in small samples.

Original article: A trinomial test for paired data when there are many ties

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 diRerences between observations, thereby increasing the use of sample information. Simulations demonstrate the power superiority of the proposed trinomial test statis- tic 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.

Robust Estimation and Forecasting of the Capital Asset Pricing Model

In this paper, we develop a modified maximum likelihood (MML) estimator for the multiple linear regression model with underlying student t distribution. We obtain the closed form of the estimators, derive the asymptotic properties, and demonstrate that the MML estimator is more appropriate for estimating the parameters of the Capital Asset Pricing Model by comparing its performance with least squares estimators (LSE) on the monthly returns of US portfolios. The empirical results reveal that the MML estimators are more efficient than LSE in terms of the relative efficiency of one-step-ahead forecast mean square error in small samples.