Catherine Forbes

Bayesian analysis of the stochastic conditional duration model

A Bayesian Markov chain Monte Carlo methodology is developed for estimating the stochastic conditional duration model. The conditional mean of durations between trades is modelled as a latent stochastic process, with the conditional distribution of durations having positive support. Regressors are included in the model for the latent process in order to allow additional variables to impact on durations. The sampling scheme employed is a hybrid of the Gibbs and Metropolis-Hastings algorithms, with the latent vector sampled in blocks. Candidate draws for the latent process are generated by applying a Kalman filtering and smoothing algorithm to a linear Gaussian approximation of the non-Gaussian state space representation of the model. Monte Carlo sampling experiments demonstrate that the Bayesian method performs better overall than an alternative quasi-maximum likelihood approach. The methodology is illustrated using Australian intraday stock market data, with Bayes factors used to discriminate between different distributional assumptions for durations.

Parameterisation and efficient MCMC estimation of non-Gaussian state space models

The impact of parameterisation on the simulation efficiency of Bayesian Markov chain Monte Carlo (MCMC) algorithms for two non-Gaussian state space models is examined. Specifically, focus is given to particular forms of the stochastic conditional duration (SCD) model and the stochastic volatility (SV) model, with four alternative parameterisations of each model considered. A controlled experiment using simulated data reveals that relationships exist between the simulation efficiency of the MCMC sampler, the magnitudes of the population parameters and the particular parameterisation of the state space model. Results of an empirical analysis of two separate transaction data sets for the SCD model, as well as equity and exchange rate data sets for the SV model, are also reported. Both the simulation and empirical results reveal that substantial gains in simulation efficiency can be obtained from simple reparameterisations of both types of non-Gaussian state space models.

Inference for a Class of Stochastic Volatility Models Using Option and Spot Prices: Application of a Bivariate Kalman Filter

In this paper Bayesian methods are applied to a stochastic volatility model using both the prices of the asset and the prices of options written on the asset. Posterior densities for all model parameters, latent volatilities and the market price of volatility risk are produced via a Markov Chain Monte Carlo (MCMC) sampling algorithm. Candidate draws for the unobserved volatilities are obtained in blocks by applying the Kalman filter and simulation smoother to a linearization of a nonlinear state space representation of the model. Crucially, information from both the spot and option prices affects the draws via the specification of a bivariate measurement equation, with implied Black–Scholes volatilities used to proxy observed option prices in the candidate model. Alternative models nested within the Heston (1993) framework are ranked via posterior odds ratios, as well as via fit, predictive and hedging performance. The method is illustrated using Australian News Corporation spot and option price data.

Measuring the cost of leaving care in Victoria

On any given night in Victoria, around 4,000 children and young people live under the care and protection of the State. For many young people, this care extends over a long period of time, sometimes until their 18th birthday. It is well documented that young people leaving State care often lack the social and economic resources to assist them in making the transition into independent living. As a consequence, the long-term life outcomes from this group are frequently very poor. A recent report from The Centre for Excellence in Child and Family Welfare in partnership with Monash University estimated that, for a typical cohort of 450 young people who leave care in Victoria each year, the direct cost to the State resulting from these poor outcomes is

Systemic risk in the European sovereign and banking system

332.5 million. The estimated average outcomes of the leaving care population are based on a recent survey involving sixty young people who had spent at least two years in care as teenagers. This paper provides an overview of the economic methodology used to estimate this cost, and provides discussion of the motivation for measuring outcomes in terms of costs to the State.

Reconstructing the Kalman Filter for Stationary and Non Stationary Time Series

We investigate the systemic risk of the European sovereign and banking system during 2008–2013. We utilize a conditional measure of systemic risk that reflects market perceptions and can be intuitively interpreted as an entity’s conditional joint probability of default, given the hypothetical default of other entities. The measure of systemic risk is applicable to high dimensions and not only incorporates individual default risk characteristics but also captures the underlying interdependent relations between sovereigns and banks in a multivariate setting. In empirical applications, our results reveal significant time variation in systemic risk spillover effects for the sovereign and banking system. We find that systemic risk is mainly driven by risk premiums coupled with a steady increase in physical default risk.

Statistical Distributions

A Kalman filter for application to stationary or non-stationary time series is proposed. A major feature is a new initialisation method to accommodate non-stationary time series. The filter works on time series with missing values at any point of time including the initialisation phase. It can also be used where a state space model does not satisfy the traditional observability condition, a situation that can arise with seasonal time series.Another feature of the paper is that the Kalman filter is described in terms of the augmented moments of the state vectors, these being an aggregate of means, variances, covariances and other pertinent information. By doing this, the Kalman filter is specified without direct recourse to those relatively complex formulae for calculating associated means and variances found in traditional expositions.A computer implementation of the Kalman filter is also described where the augmented moments are treated as an object; the operations of addition and multiplication are overloaded to work on instances of this object; and a form of statistical conditioning is implemented as an operator.