Thesis (PhD (Statistics and Actuarial Science))--University of Stellenbosch, 2011.

A local linear estimator of generalized impulse response (GIR) functions for nonlinear conditional heteroskedastic autoregressive processes is derived and shown to be asymptotically normal. A plug-in bandwidth is obtained that minimizes the asymptotical mean squared error of the GIR estimator. A...

Applied researchers often need to estimate confidence intervals for functions of parameters, such as the effects of counterfactual policy changes. If the function is continuously differentiable and has non-zero and bounded derivatives, then they can use the delta method. However, if the function...

According to the Purchasing Power Parity {(PPP)} theory, real exchange rate fluctuations are mainly caused by transitory shocks. The theory fits well one empirical feature of the data, namely the short-run volatility of real exchange rates, but also implies that shocks should die away in one to...

ENGLISH ABSTRACT: The aim of this study is to obtain estimates and confidence intervals for welfareindices under complex sampling. It begins by looking at sampling in general withspecific focus on complex sampling and weighting. For the estimation of the welfareindices, two resampling...

We use past forecast errors to construct confidence intervals around Australian Government Budget forecasts of key economic and fiscal variables. These confidence intervals provide an indication of the extent of uncertainty around the point estimate forecasts presented in the Budget.

We consider the problem of constructing honest confidence intervals (CIs) for a scalar parameter of interest, such as the regression discontinuity parameter, in nonparametric regression based on kernel or local polynomial estimators. To ensure that our CIs are honest, we use critical values that...

The quality of the asymptotic normality of realized volatility can be poor if sampling does not occur at very high frequencies. In this article we consider an alternative approximation to the finite sample distribution of realized volatility based on Edgeworth expansions. In particular, we show...

The current research examines the capacity of the Edgeworth-Sargan density on forecasting market crashes. Focusing on the 1987 stock market crash the performance of this distribution is compared to the Student’s t concluding that the latter overestimates the risk. In contrast, and due to its...

The classic conditional test for checking that the difference between two independent proportions is not null may not be appropriate in many circumstances. Dunnett & Gent (1977) showed that in clinical trials, in studies of drugs, etc, the aim is to prove the practical equality (equivalence) of...