I am a Lecturer in Business Analytics at the University of Sydney Business School, where I specialise in the fields of statistics, econometrics, machine learning, and data science. I am also affiliated with the Centre for Translational Data Science. I received my Ph.D. from the VU University Amsterdam and the Tinbergen Institute.
My areas of expertise and interest are:
- Bayesian methods.
- Monte Carlo methods and computational statistics.
- Statistical machine learning.
- Time series.
- Causal analysis for business applications.
"Leverage, asymmetry and heavy tails in the high-dimensional factor stochastic volatility model" (with Mengheng Li)
We introduce a new Markov chain Monte Carlo (MCMC) sampler that iterates by constructing conditional importance sampling (IS) approximations to target distributions. We present Markov interacting importance samplers (MIIS) in general form, followed by examples to demonstrate their flexibility. A leading application is when the exact Gibbs sampler is not available due to infeasibility of direct simulation from the conditional distributions. The MIIS algorithm uses conditional IS approximations to jointly sample the current state of the Markov Chain and estimate conditional expectations (possibly by incorporating a full range of variance reduction techniques). We compute Rao-Blackwellized estimates based on the conditional expectations to construct control variates for estimating expectations under the target distribution. The control variates are particularly efficient when there are substantial correlations in the target distribution, a challenging setting for MCMC. We also introduce the MIIS random walk algorithm, designed to accelerate convergence and improve upon the computational efficiency of standard random walk samplers. Simulated and empirical illustrations for Bayesian analysis of the mixed Logit model and Markov modulated Poisson processes show that the method significantly reduces the variance of Monte Carlo estimates compared to standard MCMC approaches, at equivalent implementation and computational effort.
We propose an approach to Bayesian inference that uses importance sampling to generate the parameters for models where the likelihood is analytically intractable can be estimated unbiasedly. We refer to this procedure as importance sampling squared (IS^2), as we can often estimate the likelihood itself by importance sampling or sequential importance sampling. The IS^2 method can lead to fast and accurate estimates of expectations with respect to the posterior, along with their standard errors. A key motivation for the IS^2 method is that we can use it as a tool for estimating the marginal likelihood (and the standard error of the estimator), irrespective of whether we use IS$2 or Markov chain Monte Carlo (MCMC) to estimate the model. The marginal likelihood is a fundamental tool in Bayesian model choice, but estimating it has proved difficult using other approaches. Our article formally justifies the IS^2 method and studies its convergence properties. We analyze the effect of estimating the likelihood on the resulting inference and provide guidelines on how to determine the precision of the likelihood estimator in order to obtain an optimal tradeoff between computational cost and accuracy for posterior inference on the model parameters. We illustrate the advantages of the IS^2 procedure empirically for a generalized multinomial logit model and a stochastic volatility model.
"Predicting time-varying parameters with parameter-driven and observation-driven models" (with S.J. Koopman and André Lucas). Review of Economics and Statistics, Volume 98, Issue 1, March 2016.
>> [abstract] [working paper] [published version]
We verify whether parameter-driven and observation-driven classes of dynamic models can outperform each other in predicting time-varying parameters. We consider existing and new dynamic models for counts and durations but also for volatility, intensity and dependence parameters. In an extended Monte Carlo study, we present evidence that observation-driven models based on the score of the predictive likelihood function have similar predictive accuracy compared to their correctly specified parameter-driven counterparts. In most cases, the differences in mean squared errors are smaller than 1% and model confidence sets have low power when comparing the two different model classes. Within the class of observation-driven models, dynamic models relying on the predictive score outperform specifications based on moments. Our main findings are supported by the results from an extensive empirical study in volatility forecasting. We conclude that dynamic models driven by the score function lead to accurate forecasts without the large computational costs associated with parameter-driven models.
The efficient importance sampling (EIS) method is a general principle for the numerical evaluation of high-dimensional integrals that uses the sequential structure of target integrands to build variance minimising importance samplers. Despite a number of successful applications in high dimensions, it is well known that importance sampling strategies are subject to an exponential growth in variance as the dimension of the integration increases. We solve this problem by recognising that the EIS framework has an offline sequential Monte Carlo interpretation. The particle EIS method is based on non-standard resampling weights that take into account the construction of the importance sampler as a sequential approximation to the state smoothing density. We apply the method for a range of univariate and bivariate stochastic volatility specifications. We also develop a new application of the EIS approach to state space models with Student's $t$ state innovations. Our results show that the particle EIS method strongly outperforms both the standard EIS method and particle filters for likelihood evaluation in high dimensions. We illustrate the efficiency of the method for Bayesian inference using the particle marginal Metropolis-Hastings and importance sampling squared algorithms.
"Numerically accelerated importance sampling for nonlinear
non-Gaussian state space models" (with S.J. Koopman and André Lucas). Journal of Business and Economic Statistics, Volume 33, Issue 1, pages 114-127.
>> [abstract] [paper]
We propose a general likelihood evaluation method for nonlinear non-Gaussian state space models using the simulation based method of efficient importance sampling. We minimise the simulation effort by replacing some key steps of the likelihood estimation procedure by numerical integration. We refer to this method as numerically accelerated importance sampling. We show that the likelihood function for models with a high-dimensional state vector and a low-dimensional signal can be evaluated more efficiently using the new method. We report many efficiency gains in an extensive Monte Carlo study as well as in an empirical application using a stochastic volatility model for U.S. stock returns with multiple volatility factors.
This paper performs a thorough statistical examination of the time-series properties of the daily market volatility index (VIX) from the Chicago Board Options Exchange (CBOE). The motivation lies not only on the widespread consensus that the VIX is a barometer of the overall market sentiment as to what concerns investors’ risk appetite, but also on the fact that there are many trading strategies that rely on the VIX index for hedging and speculative purposes. Preliminary analysis suggests that the VIX index displays long-range dependence. This is well in line with the strong empirical evidence in the literature supporting long memory in both options-implied and realized variances. We thus resort to both parametric and semiparametric heterogeneous autoregressive (HAR) processes for modeling and forecasting purposes. Our main findings are as follows. First, we confirm the evidence in the literature that there is a negative relationship between the VIX index and the S&P 500 index return as well as a positive contemporaneous link with the volume of the S&P 500 index. Second, the term spread has a slightly negative long-run impact in the VIX index, when possible multicollinearity and endogeneity are controlled for. Finally, we cannot reject the linearity of the above relationships, neither in sample nor out of sample. As for the latter, we actually show that it is pretty hard to beat the pure HAR process because of the very persistent nature of the VIX index.
We develop a systematic framework for the joint modeling of returns and multiple daily realized measures. We assume a linear state space representation for the log realized measures, which are noisy and biased estimates of the log daily integrated variance, at least due to Jensen's inequality. We incorporate filtering methods for the estimation of the latent log-volatility process. The dependence between daily returns and realized measurement errors leads us to develop a two-step estimation method for all parameters in our model specification. The estimation method is computationally straightforward even when the stochastic volatility model has non-Gaussian return innovations and leverage effects. Our extensive empirical study for nine Dow Jones stock return series reveals that measurement errors become significantly smaller after filtering and that the forecasts from our model outperforms those from a set of recently developed alternatives.
Does volatility reflect a continuous reaction to past shocks or do changes in the markets induce shifts in the volatility dynamics? In this paper, we provide empirical evidence that cumulated price variations convey meaningful information about multiple regimes in the realized volatility of stocks, where large falls (rises) in prices are linked to persistent regimes of high (low) variance in stock returns. Incorporating past cumulated daily returns as an explanatory variable in a flexible and systematic nonlinear framework, we estimate that falls of different magnitudes over less than two months are associated with volatility levels 20% and 60% higher than the average of periods with stable or rising prices. We show that this effect accounts for large empirical values of long memory parameter estimates. Finally, we show that, while introducing more realistic dynamics for volatility, the model is able to overall improve or at least retain out-of-sample performance in forecasting when compared to standard methods. Most importantly, the model is more robust to periods of financial crises, when it attains significantly better forecasts.
Statistical Learning and Data Mining (QBUS6810, GitHub page)
Predictive Analytics (QBUS2820, forecasting section, GitHub page)
Python for Business Analytics (for students getting started with Python)
Discipline of Business Analytics
The University of Sydney Business School
University of Sydney NSW 2006
Telephone: +61 2 9036 9120
email: marcel.scharth [at] sydney.edu.au