Forecasting correlated time series with exponential smoothing models

Abstract This paper presents the Bayesian analysis of a general multivariate exponential smoothing model that allows us to forecast time series jointly, subject to correlated random disturbances. The general multivariate model, which can be formulated as a seemingly unrelated regression model, includes the previously studied homogeneous multivariate Holt-Winters’ model as a special case when all of the univariate series share a common structure. MCMC simulation techniques are required in order to approach the non-analytically tractable posterior distribution of the model parameters. The predictive distribution is then estimated using Monte Carlo integration. A Bayesian model selection crite…

A Bayesian unified framework for risk estimation and cluster identification in small area health data analysis.

Many statistical models have been proposed to analyse small area disease data with the aim of describing spatial variation in disease risk. In this paper, we propose a Bayesian hierarchical model that simultaneously allows for risk estimation and cluster identification. Our model formulation assumes that there is an unknown number of risk classes and small areas are assigned to a risk class by means of independent allocation variables. Therefore, areas within each cluster are assumed to share a common risk but they may be geographically separated. The posterior distribution of the parameter representing the number of risk classes is estimated using a novel procedure that combines its prior …

A Forecasting Support System Based on Exponential Smoothing

This chapter presents a forecasting support system based on the exponential smoothing scheme to forecast time-series data. Exponential smoothing methods are simple to apply, which facilitates computation and considerably reduces data storage requirements. Consequently, they are widely used as forecasting techniques in inventory systems and business planning. After selecting the most adequate model to replicate patterns of the time series under study, the system provides accurate forecasts which can play decisive roles in organizational planning, budgeting and performance monitoring.

Conditional predictive inference for online surveillance of spatial disease incidence

This paper deals with the development of statistical methodology for timely detection of incident disease clusters in space and time. The increasing availability of data on both the time and the location of events enables the construction of multivariate surveillance techniques, which may enhance the ability to detect localized clusters of disease relative to the surveillance of the overall count of disease cases across the entire study region. We introduce the surveillance conditional predictive ordinate as a general Bayesian model-based surveillance technique that allows us to detect small areas of increased disease incidence when spatial data are available. To address the problem of mult…

Application of a Bayesian Spatiotemporal Surveillance Method to NYC Syndromic Data

Incorporating prior knowledge (e.g., the spatial distribution of zip codes and background population effects) into a model using Bayesian methods could potentially improve outbreak detection. We adapted a previously described Bayesian model-based spatiotemporal surveillance technique to daily respiratory syndrome counts in NYC Emergency Department data in 2009, the year of the H1N1 influenza pandemic. Citywide, 56 alarms were produced across 15 zip codes, all during days of elevated respiratory visits. Future work includes evaluating our choice of baseline length, considering other alarm thresholds, and conducting a formal evaluation of the method across five syndromes in NYC.

Forecasting time series with missing data using Holt's model

This paper deals with the prediction of time series with missing data using an alternative formulation for Holt's model with additive errors. This formulation simplifies both the calculus of maximum likelihood estimators of all the unknowns in the model and the calculus of point forecasts. In the presence of missing data, the EM algorithm is used to obtain maximum likelihood estimates and point forecasts. Based on this application we propose a leave-one-out algorithm for the data transformation selection problem which allows us to analyse Holt's model with multiplicative errors. Some numerical results show the performance of these procedures for obtaining robust forecasts.

Modeling Chickenpox Dynamics with a Discrete Time Bayesian Stochastic Compartmental Model

[EN] We present a Bayesian stochastic susceptible-exposed-infectious-recovered model in discrete time to understand chickenpox transmission in the Valencian Community, Spain. During the last decades, different strategies have been introduced in the routine immunization program in order to reduce the impact of this disease, which remains a public health's great concern. Under this scenario, a model capable of explaining closely the dynamics of chickenpox under the different vaccination strategies is of utter importance to assess their effectiveness. The proposed model takes into account both heterogeneous mixing of individuals in the population and the inherent stochasticity in the transmiss…

Prospective surveillance of multivariate spatial disease data

Surveillance systems are often focused on more than one disease within a predefined area. On those occasions when outbreaks of disease are likely to be correlated, the use of multivariate surveillance techniques integrating information from multiple diseases allows us to improve the sensitivity and timeliness of outbreak detection. In this article, we present an extension of the surveillance conditional predictive ordinate to monitor multivariate spatial disease data. The proposed surveillance technique, which is defined for each small area and time period as the conditional predictive distribution of those counts of disease higher than expected given the data observed up to the previous t…

A Bayesian SIRS model for the analysis of respiratory syncytial virus in the region of Valencia, Spain

We present a Bayesian stochastic susceptible-infected-recovered-susceptible (SIRS) model in discrete time to understand respiratory syncytial virus dynamics in the region of Valencia, Spain. A SIRS model based on ordinary differential equations has also been proposed to describe RSV dynamics in the region of Valencia. However, this continuous-time deterministic model is not suitable when the initial number of infected individuals is small. Stochastic epidemic models based on a probability of disease transmission provide a more natural description of the spread of infectious diseases. In addition, by allowing the transmission rate to vary stochastically over time, the proposed model provides…

Multivariate exponential smoothing: A Bayesian forecast approach based on simulation

This paper deals with the prediction of time series with correlated errors at each time point using a Bayesian forecast approach based on the multivariate Holt-Winters model. Assuming that each of the univariate time series comes from the univariate Holt-Winters model, all of them sharing a common structure, the multivariate Holt-Winters model can be formulated as a traditional multivariate regression model. This formulation facilitates obtaining the posterior distribution of the model parameters, which is not analytically tractable: simulation is needed. An acceptance sampling procedure is used in order to obtain a sample from this posterior distribution. Using Monte Carlo integration the …

A Multivariate Age-Structured Stochastic Model with Immunization Strategies to Describe Bronchiolitis Dynamics

Bronchiolitis has a high morbidity in children under 2 years old. Respiratory syncytial virus (RSV) is the most common pathogen causing the disease. At present, there is only a costly humanized monoclonal RSV-specific antibody to prevent RSV. However, different immunization strategies are being developed. Hence, evaluation and comparison of their impact is important for policymakers. The analysis of the disease with a Bayesian stochastic compartmental model provided an improved and more natural description of its dynamics. However, the consideration of different age groups is still needed, since disease transmission greatly varies with age. In this work, we propose a multivariate age-struct…

A new approach to portfolio selection based on forecasting

In this paper we analyze the portfolio selection problem from a novel perspective based on the analysis and prediction of the time series corresponding to the portfolio’s value. Namely, we define the value of a particular portfolio at the time of its acquisition. Using the time series of historical prices of the different financial assets, we calculate backward the value that said portfolio would have had in past time periods. A damped trend model is then used to analyze this time series and to predict the future values of the portfolio, providing estimates of the mean and variance for different forecasting horizons. These measures are used to formulate the portfolio selection problem, whic…

Integration of animal health and public health surveillance sources to exhaustively inform the risk of zoonosis: An application to echinococcosis in Rio Negro, Argentina

The analysis of zoonotic disease risk requires the consideration of both human and animal geo-referenced disease incidence data. Here we show an application of joint Bayesian analyses to the study of echinococcosis granulosus (EG) in the province of Rio Negro, Argentina. We focus on merging passive and active surveillance data sources of animal and human EG cases using joint Bayesian spatial and spatio-temporal models. While similar spatial clustering and temporal trending was apparent, there appears to be limited lagged dependence between animal and human outcomes. Beyond the data quality issues relating to missingness at different times, we were able to identify relations between dog and …

Un análisis bayesiano de modelos multivariantes de suavizado exponencial

Bayesian forecasting of demand time-series data with zero values

This paper describes the development of a Bayesian procedure to analyse and forecast positive demand time-series data with a proportion of zero values and a high level of variability for the non-zero data. The resulting forecasts play decisive roles in organisational planning, budgeting, and performance monitoring. Exponential smoothing methods are widely used as forecasting techniques in industry and business. However, they can be unsuitable for the analysis of non-negative demand time-series data with the aforementioned features. In this paper, an unconstrained latent demand underlying the observed demand is introduced into the linear heteroscedastic model associated with the Holt-Winters…

Prospective analysis of infectious disease surveillance data using syndromic information.

In this paper, we describe a Bayesian hierarchical Poisson model for the prospective analysis of data for infectious diseases. The proposed model consists of two components. The first component describes the behavior of disease during nonepidemic periods and the second component represents the increase in disease counts due to the presence of an epidemic. A novelty of our model formulation is that the parameters describing the spread of epidemics are allowed to vary in both space and time. We also show how syndromic information can be incorporated into the model to provide a better description of the data and more accurate one-step-ahead forecasts. These real-time forecasts can be used to …