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Business Analytics Seminars

The seminars are on Fridays at 11am in Room 2150, Abercrombie Building (H70), unless otherwise specified.

The seminar organiser is Dr Andrey Vasnev.


31st Aug 2016 - 11:00 am

Venue: Room 5050 Abercrombie Business School Bldg H70

Speaker: Professor Bala Rajaratnam, Discipline of Business Analytics; University of Sydney

Title: MCMC-Based Inference in the Era of Big Data: A Fundamental Analysis of the Convergence Complexity of High-Dimensional Chains

Markov chain Monte Carlo (MCMC) lies at the core of modern Bayesian methodology, much of which would be impossible without it. Thus, the convergence properties of Markov chains relevant to MCMC have received significant attention, and in particular, proving (geometric) ergodicity is of critical interest. Nevertheless, current methods do not yield convergence rates sharp enough to permit a meaningful analysis in terms of the dimension of the parameter p and sample size n.  Thus, a clear theoretical characterization of the behavior of modern Markov chains in high dimensions is not available.

In this paper, we first demonstrate that contemporary methods for establishing Markov chain convergence behavior have serious limitations when the dimension grows, such as in the so-called "Big Data" setting. We then employ novel theoretical approaches to rigorously establish the convergence behavior of Markov chains typical of high-dimensional MCMC. Unlike many comparable results in the literature, we obtain exact convergence rates in total variation distance by establishing upper and lower bounds that share the same rate constant in n and p. We are thus able to overcome some of the stated challenges in contemporary research on convergence of MCMC. We also show a universality result for the convergence rate across an entire spectrum of models. We then demonstrate the precise nature and severity of convergence problems that can occur in some important models when implemented in high dimensions, including phase transitions in the convergence rates in various n and p regimes. These convergence problems effectively eliminate the apparent safeguard of geometric ergodicity. We then demonstrate theoretical principles by which Markov chains can be analyzed to yield bounded geometric convergence rates (essentially recovering geometric ergodicity) even as the dimension p grows without bound. Additionally, we propose a diagnostic tool for establishing convergence (or the lack thereof) in high-dimensional MCMC
.


2nd Sep 2016 - 11:00 am

Venue: Room 2150 H70

Speaker: A/Prof Felix Chan, School of Economics and Finance; Curtin University

Title: The Conditional Duration Models

This seminar presents an overview on modelling duration between changes in asset price using ultra-high frequency data. It first focus on the conventional approach by proposing a Generalized Logarithmic Autoregressive Conditional Duration (GLACD) model to examine the interaction between duration and variation in asset prices. This provides a convenient framework to test statistically the existence of such relationship. The model is flexible and contains various well known models as special cases, including, the Exponential Generalised Autoregressive Heteroskedasticity (EGARCH) model of Nelson (1991) and the Logarithmic Conditional Duration (Log-ACD) model of Bauwens and Giot (2000). The paper also obtains theoretical results for the Quasi-Maximum Likelihood Estimator (QMLE) for the proposed model. Specifically, sufficient conditions for consistency and asymptotic normality are derived under mild assumptions. Monte Carlo experiments also pro- vide further support of the theoretical results and demonstrate that the QMLE has reasonably good finite sample performance.

 

The paper then applies the model to nine different assets from three different asset classes, namely two exchange rate, two commodities and five stocks. The two currencies are Australia/US and British Pound/US exchange rates; the two commodities are Gold and Silver and the five stocks are BHP, Rio Tinto, CBA, ANZ and Apple. The sample spans from 1 March 2010 to 31 May 2010 with the number of observations ranges from 44178 to 1109897. The results show that there are strong relationship between duration and variation in price changes. The forecast performance of GLACD is also compared with the Log-ACD model and the results show that the proposed model performed better than the Log-ACD model. The attempt to establish the multivariate extension of the proposed model reveals its limitation. The paper will also propose an alternate approach to model multivariate conditional duration by extending the Hawke's process.

 


9th Sep 2016 - 11:00 am

Venue: Room 2150 Abercrombie Bldg H70

Speaker: A/Prof Joshua Chan, Research School of Economics; Australian National University; ACT

Title: Large Bayesian VARs: A Flexible Kronecker Error Covariance Structure

We introduce a class of large Bayesian vector autoregressions (BVARs) that allows for non-Gaussian, heteroscedastic and serially dependent innovations. To make estimation computationally tractable, we exploit a certain Kronecker structure of the likelihood implied by this class of models. We propose a unified approach for estimating these models using Markov chain Monte Carlo (MCMC) methods. In an application that involves 20 macroeconomic variables, we find that these BVARs with more flexible covariance structures outperform the standard variant with independent, homoscedastic Gaussian innovations in both in-sample model-fit and out-of-sample forecast performance.