John Randal

A reinvestigation of robust scale estimation in finite samples

This paper reworks and expands on the results of existing simulation studies, investigating the performance of various robust estimators of scale for Tukeys three corner distributions. We focus attention on the popular biweight A-estimator, but also propose a new estimator based on the Students t-distribution, which attains an efficiency close to that of the A-estimator. We investigate the use of more efficient auxiliary location and scale estimators in two-pass estimators such as the A- and t-estimators, and find overall efficiency can be improved. Using much larger simulation sizes than previous studies, significant departures from existing efficiencies are obtained, and these lead to different recommendations for estimation.

Ethics and experiments in accounting

Purpose – This research aims to measure compliance in a tax experiment among students. The aim of the study is to investigate relationships between claimed behaviour in a questionnaire and actual behaviour in an experimental environment, together with different behaviours between males and females, and different age cohorts.Design/methodology/approach – A total of 630 undergraduate Commerce students at a New Zealand university completed a questionnaire on attitudes towards the tax system. The students subsequently participated in a simulation experiment requiring responses to hypothetical tax evasion decisions. Individual reward payments were contingent on the outcome of these tax evasion decisions. Questionnaire responses, which captured intended behaviour, were compared with actual behaviour in the experiment.Findings – The study finds more compliant behaviour among older students and students who have been at university longer. It also finds female students demonstrate more ethical responses in their b...

Non-parametric estimation of historical volatility

Evolving volatility is a dominant feature observed in most financial time series and a key parameter used in option pricing and many other financial risk analyses. A number of methods for non-parametric scale estimation are reviewed and assessed with regard to the stylized features of financial time series. A new non-parametric procedure for estimating historical volatility is proposed based on local maximum likelihood estimation for the t-distribution. The performance of this procedure is assessed using simulated and real price data and is found to be the best among estimators we consider. We propose that it replaces the moving variance historical volatility estimator.

Maximum likelihood estimation for Tukey's three corners

We use the EM algorithm to derive recursive expressions for maximum likelihood location and scale estimators for Tukeys corner distributions, in particular the one-wild. This now enables optimal estimation for the triefficiency criterion used to appraise robust estimators. The effect of improved estimation for the one-wild case is investigated. Simulations are conducted, both to illustrate the operation of the algorithm, and to reinvestigate the properties of three common location estimates. In particular, the scaling constant c=6 in the one-step biweight M-estimator used in procedures such as loess, is shown to be too small under the triefficiency criterion.

Dynamics of Political Risk Rating and Stock Market Volatility

In this paper we propose a framework for predicting market returns and volatility using changes in the countrys political risk. We identify the appropriate lag to calculate changes over, and show how the changes should be included in mean and volatility equations. The appropriate level of aggregation for the political risk variable is also examined. We analyse 47 emerging and 21 developed markets. We find political risk predictive power primarily for volatility, when looking at emerging markets. Our paper recommends use of three political risk components, which suitably capture important dimensions of the political environment.

Modelling Seasonality and Structural Breaks: Visitors to NZ and 9/11

We demonstrate the poor performance, with seasonal data, of existing methods for endogenously dating multiple structural breaks. Motivated by iterative nonparametric techniques, we present a new approach for estimating parametric structural break models that perform well. We suggest that iterative estimation methods are a simple but important feature of this approach when modelling seasonal data. The methodology is illustrated by simulation and then used for an analysis of monthly short-term visitor arrival time series to New Zealand, to assess the effect of the 9/11 terrorist attacks. While some historical events had a marked structural effect on trends in those arrivals, we show that 9/11 did not.