Working Papers 1998 – Abstracts

10/98
A general volatility framework and the generalised historical volatility estimator
Bernard Bollen and Brett Inder

This study proposes a new approach to the estimation of the time series properties of daily volatility in financial markets. The estimation technique is a two stage procedure which initially estimates the volatility of any particular trading day from intraday data. This procedure is implemented over a number of trading days to produce a series of daily volatility estimates. A general volatility framework is also developed and the series of daily volatility estimates can be put into this framework to estimate the time series properties of daily volatility. Furthermore, with this new approach it is shown that the time series properties of daily volatility can be modelled in a wide range of functional forms, including those functional forms which capture asymmetric information effects.

11/98
Comparisons of estimators and tests based on modified likelihood and message length functions.
Mizan R. Laskar and Maxwell L. King

The presence of nuisance parameters causes unwanted complications in statistical and econometric inference procedures. A number of modified likelihood and message length functions have been developed for better handling of nuisance parameters but they are not equally efficient. In this paper, we empirically compare different modified likelihood and message length functions in the context of estimation and testing of parameters from linear regression disturbances that follow either first-order moving average or first-order autoregressive error processes. The results show that estimators based on the conditional profile likelihood and tests based on the marginal likelihood are best. If there is a minor identification problem, the sizes of the likelihood ratio and Wald tests based on simple message length functions are best. The true sizes of the Lagrange multiplier tests based on message length functions are rather poor because the score functions of message length functions are biased.

12/98
Residual diagnostic plots for checking for model mis-specification in time series regression
Richard Fraccaro, Rob Hyndman and Alan Veevers.

This paper considers residuals for time series regression. Despite much literature on visual diagnostics for uncorrelated data, there is little on the autocorrelated case. In order to examine various aspects of the fitted time series regression model, three residuals are considered. The fitted regression model can be checked using orthogonal residuals; the time series error model can be analysed using marginal residuals; and the white noise error component can be tested using conditional residuals. When used together, these residuals allow identification of outliers, model mis-specification and mean shifts. Due to the sensitivity of conditional residuals to model mis-specification, it is suggested that the orthogonal and marginal residuals be examined first.

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