Cas G. Troskie

The Distribution of Stock Returns When the Market Is Up

Abstract For some investments, the relation between stock returns and the market proxy is conventionally described by a linear regression model with the normality assumption. This paper derives the distribution of stock returns for a security in an upgrade (or downgrade) market with the assumption that the log stock returns of the market proxy follow a mixture of normal distributions. We discuss MLE and the method of moment estimation for parameters involved in the model. An analysis of stock data in Johannesburg Stock Exchange is included to illustrate the model. This note explains the phenomenon in financial analysis regarding the shape of the distribution of long-run stock returns limited on an upgrade or downgrade market index.

Ridge Regression – A Simulation Study

In this article we assess the suitability of two new ridge estimators by means of a simulation study. We compare these estimators with well-known ridge estimators. We also make direct comparisons between the ordinary least squares (OLS) estimator and the ridge estimators by using ratio of the average total mean square error of the OLS estimator and the ridge estimators. We find that the new estimators perform well under certain conditions.

Parameter changes in the multiple regression model with autocorrelated errors : Bayesian analysis

The Bayesian analysis of the multiple regression model with autocorrelated errors is modified to account for a shift in the parameters. The approach of Salazar, Broemeling and Chi (1981) is considered and modified. The emphasis is on the predictive density of a future observation.

Regression and ICOMP—A Simulation Study

A regression simulation study investigates the behaviour of ICOMP, AIC, and BIC under various collinearity-, sample size-, and residual variance-levels. When the variation in the design matrix is large, as the collinearity levels in the design matrix increased, the agreement percentages for all of the information criteria decreased monotonically and that ICOMP agreed with the Kullback Leibler model more often. As the residual variance increases, the agreement percentages of all of the information criteria decreases. However, as the sample size increased the agreement percentages of all information criteria increased. When the variation in the design matrix is low and the collinearity is low, as the residual variance increases, the agreement percentages for all of the information criteria decreases monotonically such that ICOMP agreed more often with Kullback Leibler model than both AIC and BIC.

Detection of outliers and influential observations in regression analysis using stochastic prior information

When stochastic prior information is available there can be a considerable improvement in the estimation of β in the usual model Y = Xβ + e . Test statistics and diagnostics are developed to test for outliers and to detect influential observations when the residuals are analysed after these residuals have been computed using stochastic prior information. Applications to Ridge? Generalized Ridge and Stein type estimators and some examples are given.

Q plots, a graphical aid for regression analysis

Plots are presented which are based on the singular value decomposition of the augmented data matrix in regression. In general, these plots assist in identifying discrepant observations, and in conjunction with associated diagnostics they are useful for identifying influential observations.

Time Series and Model Selection

In this article, we investigate the behavior of Bozdogans Information criterion (ICOMP) and other information criteria in a time series context. The study entails simulating stationary autoregressive moving average models 1,000 times and then fitting different time series models to the simulated series. Different series will be considered by changing the size of the residual variance as well as the sample size of the time series. It was found that under certain conditions ICOMP selects the correct time series model most often, although it is suggested that no single information criteria should be used independently of other information criteria.

On the compatibility of sample and prior information in the mixed regression model

The mixed regression estimator involves combining prior information with the sample data, for which there is a standard test for their compatibility. We show that this test is equivalent to a test for outliers applied to the observations corresponding to the prior information. For a single outlier, this test statistic can be used to obtain a robust regression estimator.

Identification of outlying and influential data with biased estimation : A simulation study

An important aspect of multiple regression analysis is the identification of out-lying and influential data. There are a number of diagnostic measures and graphical methods available to assist in this identification problem. However, no recommen-dations exist for the use of these diagnostic measures with biased estimators, in par-ticular for those estimators designed to overcome the problem of multicollinearity. We have carried out a simulation study with the ridge regression and the fractional rank estimators to investigate the use of standard cutoffs for some of these diagnos-tic measures. The results indicate that no cutoff can be adopted as standard and the diagnostic values must be interpreted with caution.