Jonathan R. Stroud

Bayesian Forecasting of an Inhomogeneous Poisson Process With Applications to Call Center Data

A call center is a centralized hub where customer and other telephone calls are handled by an organization. In todays economy, call centers have become the primary points of contact between customers and businesses. Thus accurate predictions of call arrival rates are indispensable to help call center practitioners staff their call centers efficiently and cost-effectively. This article proposes a multiplicative model for modeling and forecasting within-day arrival rates to a U.S. commercial banks call center. Markov chain Monte Carlo sampling methods are used to estimate both latent states and model parameters. One-day-ahead density forecasts for the rates and counts are provided. The calibration of these predictive distributions is evaluated through probability integral transforms. Furthermore, 1-day-ahead forecasts comparisons with classical statistical models are given. Our predictions show significant improvements of up to 25% over these standards. A sequential Monte Carlo algorithm is also proposed for sequential estimation and forecasts of the model parameters and rates.

Optimal Filtering of Jump Diffusions: Extracting Latent States from Asset Prices

This paper provides an optimal filtering methodology in discretely observed continuous-time jump-diffusion models. Although the filtering problem has received little attention, it is useful for estimating latent states, forecasting volatility and returns, computing model diagnostics such as likelihood ratios, and parameter estimation. Our approach combines time-discretization schemes with Monte Carlo methods. It is quite general, applying in nonlinear and multivariate jump-diffusion models and models with nonanalytic observation equations. We provide a detailed analysis of the filters performance, and analyze four applications: disentangling jumps from stochastic volatility, forecasting volatility, comparing models via likelihood ratios, and filtering using option prices and returns. The Author 2009. Published by Oxford University Press on behalf of The Society for Financial Studies. All rights reserved. For Permissions, please e-mail: journals.permissions@oxfordjournals.org, Oxford University Press.

Nonlinear State-Space Models With State-Dependent Variances

Nonlinear state-space models with state-dependent variances (SDVs) are commonly used in financial time series. Important examples include stochastic volatility (SV) and affine term structure models. We propose a methodology for state smoothing in this class of models. Our smoothing technique is simulation based and uses an auxiliary mixture model. Key features of the auxiliary mixture model are the use of state-dependent weights and efficient block sampling algorithms to jointly update all unobserved states given latent mixture indicators. Conditional on latent indicator variables, the auxiliary mixture model reduces to a normal dynamic linear model. We illustrate our methodology with two time series applications. First, we show how to construct the auxiliary model for a logarithmic SV model and compare the performance of our methodology with the current literature. Next, we implement a square-root SV model with jumps for short-term interest rates in Hong Kong.

Sequential State and Variance Estimation within the Ensemble Kalman Filter

Abstract Kalman filter methods for real-time assimilation of observations and dynamical systems typically assume knowledge of the system parameters. However, relatively little work has been done on extending state estimation procedures to include parameter estimation. Here, in the context of the ensemble Kalman filter, a Monte Carlo–based algorithm is proposed for sequential estimation of the states and an unknown scalar observation variance. A Bayesian approach is adopted that yields analytical updating of the parameter distribution and provides samples from the posterior distribution of the states and parameters. The proposed assimilation algorithm extends standard ensemble methods, including perturbed observations, and serial and square root assimilation schemes. The method is illustrated on the Lorenz 40-variable system and is shown to be robust with system nonlinearities, sparse observation networks, and the choice of the initial parameter distribution.

Understanding the Ensemble Kalman Filter

ABSTRACT The ensemble Kalman filter (EnKF) is a computational technique for approximate inference in state-space models. In typical applications, the state vectors are large spatial fields that are observed sequentially over time. The EnKF approximates the Kalman filter by representing the distribution of the state with an ensemble of draws from that distribution. The ensemble members are updated based on newly available data by shifting instead of reweighting, which allows the EnKF to avoid the degeneracy problems of reweighting-based algorithms. Taken together, the ensemble representation and shifting-based updates make the EnKF computationally feasible even for extremely high-dimensional state spaces. The EnKF is successfully used in data-assimilation applications with tens of millions of dimensions. While it implicitly assumes a linear Gaussian state-space model, it has also turned out to be remarkably robust to deviations from these assumptions in many applications. Despite its successes, the EnKF is largely unknown in the statistics community. We aim to change that with the present article, and to entice more statisticians to work on this topic.

Time-series model to predict impact of H1N1 influenza on a children's hospital.

The spring of 2009 witnessed the emergence of a novel influenza A(H1N1) virus resulting in the first influenza pandemic since 1968. In autumn of 2010, the 2009 novel H1N1 influenza strain re-emerged. We performed a retrospective time-series analysis of all patients with laboratory-confirmed H1N1 influenza who presented to our institution during 2009. Cases of influenza were assembled into 3-day aggregates and forecasting models of H1N1 influenza incidence were created. Forecasting estimates of H1N1 incidence for the 2010-2011 season were compared to actual values for our institution to assess model performance. Ninety-five percent confidence intervals calculated around our models forecasts were accurate to ±3·6 cases per 3-day period for our institution. Our results suggest that time-series models may be useful tools in forecasting the incidence of H1N1 influenza, helping institutions to optimize distribution of resources based on the changing burden of illness.

Sequential Monte Carlo Smoothing with Parameter Estimation

We propose two new Bayesian smoothing methods for general state-space models with unknown parameters. The first approach is based on the particle learning and smoothing algorithm, but with an adjustment in the backward resampling weights. The second is a new method combining sequential parameter learning and smoothing algorithms for general state-space models. This method is straightforward but effective, and we find it is the best existing Sequential Monte Carlo algorithm to solve the joint Bayesian smoothing problem. We first illustrate the methods on three benchmark models using simulated data, and then apply them to a stochastic volatility model for daily S&P 500 index returns during the financial crisis.