Simulation smoothing for state–space models: A computational efficiency analysis

A Bayesian approach for mixed effects state-space models under skewness and heavy tails

Human immunodeficiency virus (HIV) dynamics have been the focus of epidemiological and biostatistical research during the past decades to understand the progression of acquired immunodeficiency syndrome (AIDS) in the population. Although there are several approaches for modeling HIV dynamics, one of the most popular is based on Gaussian mixed-effects models because of its simplicity from the implementation and interpretation viewpoints. However, in some situations, Gaussian mixed-effects models cannot (a) capture serial correlation existing in longitudinal data, (b) deal with missing observations properly, and (c) accommodate skewness and heavy tails frequently presented in patients' profiles. For those cases, mixed-effects state-space models (MESSM) become a powerful tool for modeling correlated observations, including HIV dynamics, because of their flexibility in modeling the unobserved states and the observations in a simple way. Consequently, our proposal considers an MESSM where the observations' error distribution is a skew-t. This new approach is more flexible and can accommodate data sets exhibiting skewness and heavy tails. Under the Bayesian paradigm, an efficient Markov chain Monte Carlo algorithm is implemented. To evaluate the properties of the proposed models, we carried out some exciting simulation studies, including missing data in the generated data sets. Finally, we illustrate our approach with an application in the AIDS Clinical Trial Group Study 315 (ACTG-315) clinical trial data set.

Forecasting emergency department waiting time using a state space representation

The provision of waiting time information in emergency departments (ED) has become an increasingly popular practice due to its positive impact on patient experience and ED demand management. However, little scientific attention has been given to the quality and quantity of waiting time information presented to patients. To improve both aspects, we propose a set of state space models with flexible error structures to forecast ED waiting time for low acuity patients. Our approach utilizes a Bayesian framework to generate uncertainties associated with the forecasts. We find that the state-space models with flexible error structures significantly improve forecast accuracy of ED waiting time compared to the benchmark, which is the rolling average model. Specifically, incorporating time-varying and correlated error terms reduces the root mean squared errors of the benchmark by 10%. Furthermore, treating zero-recorded waiting times as unobserved values improves forecast performance. Our proposed model has the ability to provide patient-centric waiting time information. By offering more accurate and informative waiting time information, our model can help patients make better informed decisions and ultimately enhance their ED experience.

Dividend suspensions and cash flows during the Covid-19 pandemic: A dynamic econometric model

Firms suspended dividend payments in unprecedented numbers in response to the outbreak of the Covid-19 pandemic. We develop a multivariate dynamic econometric model that allows dividend suspensions to affect the conditional mean, volatility, and jump probability of growth in daily industry-level dividends and demonstrate how the parameters of this model can be estimated using Bayesian Gibbs sampling methods. We find considerable heterogeneity across industries in the dynamics of daily dividend growth and the impact of dividend suspensions.

An Alternative Estimation Method for Time-Varying Parameter Models

A multivariate, non-Bayesian, regression-based, or feasible generalized least squares (GLS)-based approach is proposed to estimate time-varying VAR parameter models. Although it has been known that the Kalman-smoothed estimate can be alternatively estimated using GLS for univariate models, we assess the accuracy of the feasible GLS estimator compared with commonly used Bayesian estimators. Unlike the maximum likelihood estimator often used together with the Kalman filter, it is shown that the possibility of the pile-up problem occurring is negligible. In addition, this approach enables us to deal with stochastic volatility models, models with a time-dependent variance–covariance matrix, and models with non-Gaussian errors that allow us to deal with abrupt changes or structural breaks in time-varying parameters.

Bayesian Analysis of Intraday Stochastic Volatility Models of High-Frequency Stock Returns with Skew Heavy-Tailed Errors

Intraday high-frequency data of stock returns exhibit not only typical characteristics (e.g., volatility clustering and the leverage effect) but also a cyclical pattern of return volatility that is known as intraday seasonality. In this paper, we extend the stochastic volatility (SV) model for application with such intraday high-frequency data and develop an efficient Markov chain Monte Carlo (MCMC) sampling algorithm for Bayesian inference of the proposed model. Our modeling strategy is two-fold. First, we model the intraday seasonality of return volatility as a Bernstein polynomial and estimate it along with the stochastic volatility simultaneously. Second, we incorporate skewness and excess kurtosis of stock returns into the SV model by assuming that the error term follows a family of generalized hyperbolic distributions, including variance-gamma and Student’s t distributions. To improve efficiency of MCMC implementation, we apply an ancillarity-sufficiency interweaving strategy (ASIS) and generalized Gibbs sampling. As a demonstration of our new method, we estimate intraday SV models with 1 min return data of a stock price index (TOPIX) and conduct model selection among various specifications with the widely applicable information criterion (WAIC). The result shows that the SV model with the skew variance-gamma error is the best among the candidates.

Understanding the Correlations between Social Attention and Topic Trends of Scientific Publications

Purpose

We propose and apply a simplified nowcasting model to understand the correlations between social attention and topic trends of scientific publications.

Design/methodology/approach

First, topics are generated from the obesity corpus by using the latent Dirichlet allocation (LDA) algorithm and time series of keyword search trends in Google Trends are obtained. We then establish the structural time series model using data from January 2004 to December 2012, and evaluate the model using data from January 2013. We employ a state-space model to separate different non-regression components in an observational time series (i.e. the tendency and the seasonality) and apply the “spike and slab prior” and stepwise regression to analyze the correlations between the regression component and the social media attention. The two parts are combined using Markov-chain Monte Carlo sampling techniques to obtain our results.

Findings

The results of our study show that (1) the number of publications on child obesity increases at a lower rate than that of diabetes publications; (2) the number of publication on a given topic may exhibit a relationship with the season or time of year; and (3) there exists a correlation between the number of publications on a given topic and its social media attention, i.e. the search frequency related to that topic as identified by Google Trends. We found that our model is also able to predict the number of publications related to a given topic.

Research limitations

First, we study a correlation rather than causality between topics’ trends and social media. As a result, the relationships might not be robust, so we cannot predict the future in the long run. Second, we cannot identify the reasons or conditions that are driving obesity topics to present such tendencies and seasonal patterns, so we might need to do “field” study in the future. Third, we need to improve the efficiency of our model by finding more efficient variable selection models, because the stepwise regression method is time consuming, especially for a large number of variables.

Practical implications

This paper analyzes publication topic trends from three perspectives: tendency, seasonality, and correlation with social media attention, providing a new perspective for identifying and understanding topical themes in academic publications.

Originality/value

To the best of our knowledge, we are the first to apply the state-space model to examine the relationships between healthcare-related publications and social media to investigate the relationships between a topic’s evolvement and people’s search behavior in social media. This paper thus provides a new viewpoint in the correlation analysis area, and demonstrates the value of considering social media attention in the analysis of publication topic trends.

Wavelet-Variance-Based Estimation for Composite Stochastic Processes

This article presents a new estimation method for the parameters of a time series model. We consider here composite Gaussian processes that are the sum of independent Gaussian processes which, in turn, explain an important aspect of the time series, as is the case in engineering and natural sciences. The proposed estimation method offers an alternative to classical estimation based on the likelihood, that is straightforward to implement and often the only feasible estimation method with complex models. The estimator furnishes results as the optimization of a criterion based on a standardized distance between the sample wavelet variances (WV) estimates and the model-based WV. Indeed, the WV provides a decomposition of the variance process through different scales, so that they contain the information about different features of the stochastic model. We derive the asymptotic properties of the proposed estimator for inference and perform a simulation study to compare our estimator to the MLE and the LSE with different models. We also set sufficient conditions on composite models for our estimator to be consistent, that are easy to verify. We use the new estimator to estimate the stochastic error's parameters of the sum of three first order Gauss-Markov processes by means of a sample of over 800,000 issued from gyroscopes that compose inertial navigation systems. Supplementary materials for this article are available online.