Gael M. Martin

US deficit sustainability: a new approach based on multiple endogenous breaks

Recent empirical work has questioned the consistency of US fiscal policy with an intertemporal budget constraint. Empirical results have tended to indicate that the deficit process has undergone at least one structural shift during recent decades, with the deficit becoming either unsustainable or sustainable in only a weak sense in the post-shift period. In this paper, we re-examine sustainability using a new approach, based on a cointegration model with multiple endogenous breaks. A Bayesian methodology is applied, incorporating Markov chain Monte Carlo simulators. In contrast to previous analyses, we find evidence of a sustainable deficit process over the 1947-1992 period, despite the occurrence of breaks during the 1970s and 1980s. Copyright

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.

Simulation-based Bayesian estimation of an affine term structure model

A Bayesian simulation-based method is developed for estimating a class of interest rate models known as affine term structure (ATS) models. The technique is based on a Markov chain Monte Carlo algorithm, with the discrete observations on yields augmented by additional higher frequency latent data. The introduction of augmented yield data reduces the bias associated with estimating a continuous time process using an approximate discrete time model. The technique is demonstrated using a single-factor term structure model that possesses closed-form solutions for the transition densities. Numerical application of the method is demonstrated using simulated data. The results show that increasing the degree of augmentation in the yield curve does, overall, produce estimates that more closely reflect those based on the use of the exact transition functions. However, the results also indicate that the benefits of increasing the degree of augmentation may, to some extent, be offset by the increased uncertainty in estimation associated with the introduction of additional highly correlated latent yields.

The distribution of exchange rate returns and the pricing of currency options

An empirical model of the distribution of exchange rate returns based on a combination of the generalized Student t distribution and conditional variance specifications, is formulated and estimated for four daily bilateral exchange rates over the period 1984 to 1991. The empirical results show that the stylized characteristics of exchange rate returns such as volatility clustering, leptokurtosis and skewness, are consistently captured by this model, in contrast with other model specifications based on more restrictive distributional assumptions. Implications of the analysis are also investigated for the pricing of currency options, including comparisons with Black–Scholes prices.

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.

Bayesian Analysis Of A Fractional Cointegration Model

The concept of fractional cointegration, whereby deviations from an equilibrium relationship follow a fractionally integrated process, has attracted some attention of late. The extended concept allows cointegration to be associated with mean reversion in the error, rather than requiring the more stringent condition of stationarity. This paper presents a Bayesian method for conducting inference about fractional cointegration. The method is based on an approximation of the exact likelihood, with a Jeffreys prior being used to offset identification problems. Numerical results are produced via a combination of Markov chain Monte Carlo algorithms. The procedure is applied to several purchasing power parity relations, with substantial evidence found in favor of parity reversion.

Asymptotic Properties of Approximate Bayesian Computation

Summary Approximate Bayesian computation allows for statistical analysis using models with intractable likelihoods. In this paper we consider the asymptotic behaviour of the posterior distribution obtained by this method. We give general results on the rate at which the posterior distribution concentrates on sets containing the true parameter, the limiting shape of the posterior distribution, and the asymptotic distribution of the posterior mean. These results hold under given rates for the tolerance used within the method, mild regularity conditions on the summary statistics, and a condition linked to identification of the true parameters. Implications for practitioners are discussed.

Bayesian inference in the triangular cointegration model using a jeffreys prior

This paper presents a strategy for conducting Bayesian inference in the triangular cointegration model. A Jeffreys prior is used to circumvent an identification problem in the parameter region in which there is a near lack of cointegration. Sampling experiments are used to compare the repeated sampling performance of the approach with alternative classical cointegration methods. The Bayesian procedure is applied to testing for substitution between private and public consumption for a range of countries, with posterior estimates produced via Markov Chain Monte Carlo simulators.

Bias Correction of Persistence Measures in Fractionally Integrated Models

This paper investigates the accuracy of bootstrap-based bias correction of persistence measures for long memory fractionally integrated processes. The bootstrap method is based on the semi-parametric sieve approach, with the dynamics in the long memory process captured by an autoregressive approximation. With a view to improving accuracy, the sieve method is also applied to data pre-filtered by a semi-parametric estimate of the long memory parameter. Both versions of the bootstrap technique are used to estimate the finite sample distributions of the sample autocorrelation coefficients and the impulse response coefficients and, in turn, to bias-adjust these statistics. The accuracy of the resultant estimators in the case of the autocorrelation coefficients is also compared with that yielded by analytical bias adjustment methods when available.