Multivariate ARIMA Models Research Articles

Predictive Modeling of Obesity Prevalence for the U.S. Population

Modeling obesity prevalence is an important part of the evaluation of mortality risk. A large volume of literature exists in the area of modeling mortality rates, but very few models have been developed for modeling obesity prevalence. In this study we propose a new stochastic approach for modeling obesity prevalence that accounts for both period and cohort effects as well as the curvilinear effects of age. Our model has good predictive power as we utilize multivariate ARIMA models for forecasting future obesity rates. The proposed methodology is illustrated on the U.S. population, aged 23–90, during the period 1988–2012. Forecasts are validated on actual data for the period 2013–2015 and it is suggested that the proposed model performs better than existing models.

Univariate and Multivariate ARIMA Models for Age-Specific Mortality rates

Univariate and Multivariate ARIMA Models for Age-Specific Mortality rates

Cluster-based hierarchical demand forecasting for perishable goods

Demand forecasting is of particular importance for retailers in the context of supply chains of perishable goods and fresh food. Such goods are daily produced and delivered as they need to be provided as fresh as possible and quickly deteriorate. Demand underestimation and overestimation negatively affect the revenues of the retailer. Stock-outs have an undesired impact on consumers while unsold items need to be discarded at the end of the day. We propose a DSS that supports day-to-operations by providing hierarchical forecasts at different organizational levels based on most recent point-of-sales data. It identifies article clusters that are used to extend the hierarchy based on intra-day sales pattern. We apply multivariate ARIMA models to forecast the daily demand to support operational decisions. We evaluate the approach with point-of-sales data of an industrialized bakery chain and show that it is possible to increase the availability while limiting the loss at the same time. The cluster analysis reveals that substitutable items have similar intra-day sales pattern which makes it reasonable to forecast the demand at an aggregated level. The accuracy of top-down forecasts is comparable to direct forecasts which allows reducing the computational costs.

Time trend in natural-cause, circulatory-cause and respiratory-cause mortality associated with cold waves in Spain, 1975–2008

In general, there are few studies that analyse the impact of low temperatures on mortality, and even fewer that extend this analysis to specific causes of mortality. This study had a twofold aim: Firstly, to analyse the trend in natural-, circulatory- and respiratory-cause mortality associated with cold waves in Castile-La Mancha (Spain) across a period of analysis of 34 years, which would confer an important degree of temporal representativeness on the results obtained; and secondly, to ascertain whether this impact had decreased over the years. Time series analysis using multivariate ARIMA models with data on daily natural-, circulatory- and respiratory-cause mortality in Castile-La Mancha. The independent variables were minimum daily temperature, mean daily pressure and mean daily relative humidity. We controlled for seasonalities and trend of the series, as well as influenza epidemics, cold-wave duration and chronological number in any given year. Data were stratified in three ten-year stages, i.e., 1975–1985, 1986–1996 and 1997–2008. The mortality trigger temperature was set at a minimum daily temperature of −2 °C, corresponding to the 4th ‰ of the minimum temperature series for the winter months considered. The impact on daily natural-cause mortality for each degree that the minimum daily temperature was below −2 °C was: 10.4 % (95 % CI 9.6–11.2) in the first decade; 11.9 % (95 % CI 11.0–12.8) in the second decade; and fell to 1.6 % (95 % CI 0.9–2.3) in the third. This same pattern was observed for circulatory- and respiratory-cause mortality, with the effect of cold being greater for respiratory causes. Socio-economic factors -both of adaptation and demographic- could account for this sharp decrease in mortality associated with low temperatures. These results question climate models which predict the effects of cold over long-term time horizons, while maintaining the risk attributable to low temperatures constant. Studies similar to ours should be undertaken in other regions to confirm whether it is solely local characteristics that explain this pattern or, on the contrary, whether the pattern is generalised.

Nowadays, Is the Group of Age Over 65 the Most Affected by Heat Waves in Spain?

Background/Obj:Traditionally, the group of age older than 65 has been the most affected by heat waves. However, improvements in health services and the interaction of high temperatures with other underlying diseases (diabetes, kidney problems, alcoholism,even neurological problems) not unique to this age group, could cause that the impact of extreme temperatures start to be important in other age groups. The objective is to analyze the evolution of the relationship between high temperature and daily mortality in Castile-La Mancha (CLM) in the period 1975-2008 in the group of age over 65. Methods:Daily mortality from natural causes (ICD-10: A00-R99) in CLM, between 01/01/75 and 31/12/08 were provided by the NIS. Data of daily maximum temperature (Tmax) in the observatory which is representative of all CLM were provided by AEMET. Three stages were differentiated:1986-1996; 1997-2008 and 1975-1985. Temperature heat wave (Theat) was defined as the maximum daily temperature below 37°C (Theat to CLM). Multivariate ARIMA models were conducted to estimate the impact of high temperatures on daily mortality during the months of June to September. The data were controlled by trend, seasonality and autoregressive components of the series Results:The percentage increase in mortality (IM%) obtained in the group over 65 for each degree that the Tmax exceeds 37°C was 16.2 (± 1.7) in the first period, 13 (± 0.9) for the second and 1.6 (± 0.9) for the third. The IM% for the whole population were 13.7 (± 3.1) 13.1 (± 1.8) and 7.4 (± 1.6) respectively Conclusions: Compared with the IM% for the whole population, it is observed that the group older than 65 is not the group with the greatest impact on mortality due to heat in the last decade analyzed (not number of deaths/day). Improvements in health services and the synergistic effect of heat on people with other diseases could be the explanation. These results suggest that the prevention plans should be extended to other age groups

Detection of antibiotic resistances of Mycobacterium tuberculosis on DNA microarrays

Background: This study describes the development of an automated surveillance system using antimicrobial consumption data for the prediction of potential emergence of carbapenem-resistant organisms. It was derived from a retrospective analysis of an intervention to contain a prolonged OXA-48 producing K. pneumoniae outbreak. Methods & Materials: A time series analysis (May 2005-April 2013) was conducted around an intervention to contain an outbreak (Jan2008-April 2010)of anOXA-48-producingK. pneumoniae in the renal unit of a West London teaching hospital. The intervention focused on reinforcement of the renal antimicrobial policy and the decrease of carbapenem usage, as part of the overall stewardship strategy. Three mechanisms were promoted: awareness, education and feedback. A multivariate ARIMA model was developed utilising meropenem consumption data (defined daily dose per 100 occupied bed-days; DDD/100OBD) as a predictor of the incidence of OXA-48-producing organisms. Results: Meropenem usage was increasing by 7.13DDD/100OBD/year (95%CI 3.46-10.80; p<0.001) from 6.30DDD/100OBD/year prior to the intervention but decreased steadily for 4 years thereafter. The changes in slope of the time series were -10.18DDD/100OBD/year (95% CI, -16.63-3.73). Analysis of consumption of other gram negative antimicrobials was also undertaken and showed a significant increase in amikacin usage post-intervention from 0.56 to 4.07DDD/100OBD/year (slope= +0.83; 95%CI, 0.13-1.53). The incidence of OXA-48producing organisms was significantly increasing by 2.2 cases per year pre-intervention, and decreased thereafter. Meropenem usage at lag-1 year was highly correlated to the incidence of OXA-48-producing organisms (r =0.74, pvalue =0.04) and was included as a predictor within the ARIMA model for forecasting the incidence of resistant isolates. Conclusion: Our findings support an association between reinforcement of a specific antimicrobial policy and both meropenem usage, and a decreasing incidence of OXA-48-producing K. pneumoniae. Meropenem usage at lag-1 year was found to be a good predictor of the incidence of OXA-48-producing K. pneumoniae in the ARIMA model, although we need to remain cautious about the causality. This prediction model requires further development but shows early signs of how close surveillance of antimicrobial consumption can act as a warning indicator to anticipate potential outbreaks of drug resistance organisms and should be considered as part of healthcare organisations’ antimicrobial stewardship programmes.

Surveillance of antimicrobial consumption data: Development of an early warning system for carbapenem resistance derived from a retrospective analysis of an OXA-48 producing K. pneumoniae outbreak

Background: This study describes the development of an automated surveillance system using antimicrobial consumption data for the prediction of potential emergence of carbapenem-resistant organisms. It was derived from a retrospective analysis of an intervention to contain a prolonged OXA-48 producing K. pneumoniae outbreak. Methods & Materials: A time series analysis (May 2005-April 2013) was conducted around an intervention to contain an outbreak (Jan2008-April 2010)of anOXA-48-producingK. pneumoniae in the renal unit of a West London teaching hospital. The intervention focused on reinforcement of the renal antimicrobial policy and the decrease of carbapenem usage, as part of the overall stewardship strategy. Three mechanisms were promoted: awareness, education and feedback. A multivariate ARIMA model was developed utilising meropenem consumption data (defined daily dose per 100 occupied bed-days; DDD/100OBD) as a predictor of the incidence of OXA-48-producing organisms. Results: Meropenem usage was increasing by 7.13DDD/100OBD/year (95%CI 3.46-10.80; p<0.001) from 6.30DDD/100OBD/year prior to the intervention but decreased steadily for 4 years thereafter. The changes in slope of the time series were -10.18DDD/100OBD/year (95% CI, -16.63-3.73). Analysis of consumption of other gram negative antimicrobials was also undertaken and showed a significant increase in amikacin usage post-intervention from 0.56 to 4.07DDD/100OBD/year (slope= +0.83; 95%CI, 0.13-1.53). The incidence of OXA-48producing organisms was significantly increasing by 2.2 cases per year pre-intervention, and decreased thereafter. Meropenem usage at lag-1 year was highly correlated to the incidence of OXA-48-producing organisms (r =0.74, pvalue =0.04) and was included as a predictor within the ARIMA model for forecasting the incidence of resistant isolates. Conclusion: Our findings support an association between reinforcement of a specific antimicrobial policy and both meropenem usage, and a decreasing incidence of OXA-48-producing K. pneumoniae. Meropenem usage at lag-1 year was found to be a good predictor of the incidence of OXA-48-producing K. pneumoniae in the ARIMA model, although we need to remain cautious about the causality. This prediction model requires further development but shows early signs of how close surveillance of antimicrobial consumption can act as a warning indicator to anticipate potential outbreaks of drug resistance organisms and should be considered as part of healthcare organisations’ antimicrobial stewardship programmes.

Autocorrelation in Stochastic Models of Dutch Mortality Rates

This paper studies different stochastic mortality models with respect to its underlying assumptions. The Lee-Carter model, the rank-p SVD approximation model, the Weighted Least Squares model and the Poisson Bilinear model are discussed and applied to a Dutch data set. In an empirical analysis, it is illustrated how to obtain parameter estimates and how mortality rates can be forecasted. In a second step, the paper examines the model’s underlying assumptions on a residual basis. Several tests are employed testing for normality, homogeneity of variance and autocorrelation. The test results seem to invalidate the models applicability due to failure in the underlying assumptions. In particular the crucial assumption of observational independence does not seem to hold, which may result in prediction intervals that are too narrow. Furthermore, a theoretical explanation for autocorrelation is given and an alternative model (multivariate ARIMA model) is proposed, that does not only rely on a weaker set of assumptions, but also requires less computational effort. Comparing the initial models’ estimates with the estimates of the alternative model, it is concluded that all five stochastic mortality models tend to deliver similar estimates.

Forecasting wind speed with recurrent neural networks

This research presents a comparative analysis of the wind speed forecasting accuracy of univariate and multivariate ARIMA models with their recurrent neural network counterparts. The analysis utilizes contemporaneous wind speed time histories taken from the same tower location at five different heights above ground level. A unique aspect of the study is the exploitation of information contained in the wind histories for the various heights when producing forecasts of wind speed for the various heights. The findings indicate that multivariate models perform better than univariate models and that the recurrent neural network models outperform the ARIMA models. The results have important implications for a variety of engineering applications and business related operations.

Generation Of Time Series Models With Given Spectral Properties

Abstract. We give a method for generation of periodically correlated and multivariate ARIMA models whose dynamic characteristics are partially or fully specified in terms of spectral poles and zeroes or their equivalents in the form of eigenvalues/eigenvectors of associated model matrices. Our method is based on the spectral decomposition of multi‐companion matrices and their factorization into products of companion matrices. Generated models are needed in simulation but may also be used in estimation, e.g. to set sensible initial values of parameters for nonlinear optimization.We are not aware of any other general method for multivariate linear systems of comparable generality and control over the spectral properties of the generated model.

TIME SERIES MODELS TO FORECAST AIR TRANSPORT DEMAND: A STUDY ABOUT A REGIONAL AIRPORT

In this work, both univariate and multivariate air transport demand ARIMA models are proposed to estimate the demand levels about Reggio Calabria regional airport (South of Italy), in order to make available a tool able to analyse the impact of recent modifications in the supply (new links, new destinations and lower fares) that are expected to produce an increase in the air transport demand, also due to induced trips generated by the new supply. Differences between the univariate and multivariate models are highlighted. The models calibrations have been obtained by using the Box-Jenkins procedure.

Predictive intervals for age-specific fertility.

A multivariate ARIMA model is combined with a Gamma curve to predict confidence intervals for age-specific birth rates by 1-year age groups. The method is applied to observed age-specific births in Norway between 1900 and 1995, and predictive intervals are computed for each year up to 2050. The predicted two-thirds confidence intervals for Total Fertility (TF) around 2010 agree well with TF errors in old population forecasts made by Statistics Norway. The method gives useful predictions for age-specific fertility up to the years 2020-30. For later years, the intervals become too wide. Methods that do not take into account estimation errors in the ARIMA model coefficients underestimate the uncertainty for future TF values. The findings suggest that the margin between high and low fertility variants in official population forecasts for many Western countries are too narrow.

Influencia de los factores ambientales en el número de ingresos por urgencias en el complejo hospitalario "Juan Canalejo" de la Coruña: elaboración de un modelo de predicción

This study is aimed at establishing the possible associations between the number of admissions through the emergency room at the "Juan Canalejol" Hospital in Corunna in 1994-1994 due to organic, circulatory and respiratory reasons and the weather variables introduced as being exogenous for the purpose of preparing a prediction model. The Box-Jenkins methodology is used for obtaining univariate ARIMA models of the time-based series taken into consideration. Cross-Correlation Functions (CCF's) are established among the series of residuals which afford the possibility of establishing weights and lags among the variables for a subsequent modeling by means of multivariate ARIMA models which include environmental variables. The emergency admissions for organic reasons significantly increase 0-2 days following a rise in temperature. The admissions due to respiratory ailments are associated with drops in temperature with 10-14 lags, whilst the admissions for circulatory reasons increase significantly due to long-lasting spells of hot weather (10 lags). For people over age 65, significant increases in emergency admissions for circulatory reasons are also recorded with cold snaps. The multivariate ARIMA models that take into account the effect of environmental variables provided the best adjustment for all of the admissions variables. The number of emergency room admissions at the "Juan Canalejo" Medical Center Complex in Corunna due to organic, respiratory and circulatory causes shows a seasonal behavior pattern. The admissions for respiratory reasons are associated with a drop in temperature, whilst the admissions for circulatory reasons are affected fundamentally by hot weather, although also by cold weather as regards people over age 65. The multivariate ARIMA models including climate-related variables provide a system for predicting admissions in terms of said variables that can be useful from the standpoint of hospital management.

Asociación entre la contaminación atmosférica por dióxido de azufre y partículas totales en suspensión y la mortalidad diaria en la ciudad de Madrid (1986–1992)

The aim of the study is to quantify the relationship between sulphur dioxide (SO2), total suspended particulate (TSP) and daily mortality in Madrid. Data were plotted to exhibit the functional relationship between SO2, TSO and mortality. Box-Jenkins prewhitening method was used to detect lags and weights from the transfer function. Multivariate ARIMA models were built to control for confounding variables (air temperature and influenza epidemics). Graphic analysis suggested a logarithmic relationship between SO2 and mortality, and lineal relationship with TSP. No evidence of a threshold was found for each pollutant. Cross-correlation functions showed a statistically significant relationship between daily mortality caused by organic, cardiovascular and respiratory diseases and air pollution. The first lag was statistically significant for TSP and the third lag for SO2. Multivariate models gave a coefficient beta = 0.039 for TSP and beta = 1.04 for SO2 indicating a 6.6% increase in mortality for each 100 micrograms/m3 increase in TSP and a 2.2% for SO2. The result suggest a causal relationship between daily mortality and air pollution in Madrid.