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Multivariate conditional autoregressive range process is considered and conditions for existence of the first moment, stationarity, geometric ergodicity and β-mixing property with exponential decay are obtained.

Expectile models are derived using asymmetric least squares. A simple formula has been presented that relates the expectile to the expectation of exceedances beyond the expectile. We use this as the basis for estimating the expected shortfall. It has been proposed that the θ quantile be estimated by the expectile for which the proportion of observations below the expectile is θ. In this way, an expectile can be used to estimate value at risk. Using expectiles has the appeal of avoiding distributional assumptions. For univariate modeling, we introduce conditional autoregressive expectiles (CARE). Empirical results for the new approach are competitive with established benchmarks methods. Copyright , Oxford University Press.

This paper proposes a multivariate extension of the conditional autoregressive range (CARR) model recently proposed in the literature. The CARR model provides an interesting alternative to the traditional volatility models (e.g. GARCH and stochastic volatility). We derive conditions for the existence of the first moment, stationarity, geometric ergodicity and beta-mixing property with exponential decay for the multivariate CARR.

In this article different spatial statistics techniques to analyze the behavior of used dwelling market prices are compared. We fit two lattice models: simultaneous and conditional autoregressive, a geostatistical model, the so-called universal kriging and finally, a linear mixed-effect model. Different spatial neighborhood structures are considered, as well as different spatial weight matrices and covariance models. The results are illustrated through a real data set of 293 properties from Pamplona, Spain.

Promoting cycling aims at reducing congestion and pollution and encouraging healthy and sustainable lifestyles, but generally clashes with the perception of crash risk while riding a bicycle that is still the most significant disincentive to cycling. The current study analyzed the factors contributing to increase crash risk while riding a bicycle by focusing on the variation of 5349 cyclist-motorist collisions within 269 traffic zones in the Copenhagen Region. The model controlled for traffic exposure for both bicycles and motorized transport modes, evaluated the effects of infrastructure and socio-economic characteristics of the zones, and accounted for heterogeneity and spatial correlation across the zones. A Poisson-lognormal model with second-order CAR priors confirmed the existence of the safety in numbers phenomenon, contradicted previous literature about bicycle facilities not being helpful in reducing crash risk, highlighted the need for Copenhagen-style bicycle paths especially in suburban areas, and emphasized how heterogeneity and spatial correlation play a significant role in explaining the probability of cyclist-motorist crash occurrence., Proceedings from the Annual Transport Conference at Aalborg University, Vol 1 Nr 1 (2014): Proceedings from the Annual Transport Conference at Aalborg University

Objectives To analyze the spatio-temporal evolution of brain cancer relative mortality risks in young population (under 20 years of age) in Spanish provinces during the period 1986–2010. Methods A new and flexible conditional autoregressive spatio-temporal model with two levels of spatial aggregation was used. Results Brain cancer relative mortality risks in young population in Spanish provinces decreased during the last years, although a clear increase was observed during the 1990s. The global geographical pattern emphasized a high relative mortality risk in Navarre and a low relative mortality risk in Madrid. Although there is a specific Autonomous Region–time interaction effect on the relative mortality risks this effect is weak in the final estimates when compared to the global spatial and temporal effects. Conclusions Differences in mortality between regions and over time may be caused by the increase in survival rates, the differences in treatment or the availability of diagnostic tools. The increase in relative risks observed in the 1990s was probably due to improved diagnostics with computerized axial tomography and magnetic resonance imaging techniques.

In this chapter, we estimate the Expected Shortfall (ES) in conditional autoregressive expectile models by using a nonparametric multiple expectile regression via gradient tree boosting. This approach has the advantages generated by the flexibility of not having to rely on data assumptions and avoids the drawbacks and fragilities of a restrictive estimator such as Historical Simulation. We consider distinct specifications for the information sets that produce the ES estimates. The results obtained with simulated and real market data indicate that the proposed approach has good performance, with some distinctions between the specifications.

Determining the range of a species and exploring species--habitat associations are central questions in ecology and can be answered by analyzing presence--absence data. Often, both the sampling of sites and the desired area of inference involve neighboring sites; thus, positive spatial autocorrelation between these sites is expected. Using survey data for the Southern Ground Hornbill (Bucorvus leadbeateri) from the Southern African Bird Atlas Project, we compared advantages and disadvantages of three increasingly complex models for species occupancy: an occupancy model that accounted for nondetection but assumed all sites were independent, and two spatial occupancy models that accounted for both nondetection and spatial autocorrelation. We modeled the spatial autocorrelation with an intrinsic conditional autoregressive (ICAR) model and with a restricted spatial regression (RSR) model. Both spatial models can readily be applied to any other gridded, presence--absence data set using a newly introduced R package. The RSR model provided the best inference and was able to capture small-scale variation that the other models did not. It showed that ground hornbills are strongly dependent on protected areas in the north of their South African range, but less so further south. The ICAR models did not capture any spatial autocorrelation in the data, and they took an order, of magnitude longer than the RSR models to run. Thus, the RSR occupancy model appears to be an attractive choice for modeling occurrences at large spatial domains, while accounting for imperfect detection and spatial autocorrelation.

Background The first step in evaluating potential geographic clusters of disease calls for an evaluation of the disease risk comparing the risk in a defined location to the risk in neighboring locations. Environmental exposures, however, represent continuous exposure levels across space not an exposure with a distinct boundary. The objectives of the current study were to adapt, apply and evaluate a geostatistical approach for identifying disease clusters. Methods The exceedance probability for very low birth weight (VLBW; < 1.5 kg) infants was mapped using an Intrinsic Conditional Autoregressive model. The data were applied to a 20 by 20 grid of 1 km2 pixels centered on each of the 13 National Priority List Superfund Sites in Harris County, Texas. Results Large clusters of VLBW were identified in close proximity to four of the 13 Superfund Sites. Three of the Superfund Sites, associated with disease clusters, were located close together in central Houston and these sites may have been surrounded by a single, confluent disease cluster. Conclusions Geostatistical modeling of the exceedance probability for very low birth weights identified disease clusters of varying size, shape and statistical certainty near Superfund Sites in Harris County, Texas. The approach offers considerable potential as the first step for investigating potential disease clusters.

Value‐at‐Risk (VaR) has become a mainstream risk management technique employed by a large proportion of financial institutions. There exists a substantial amount of research dealing with this task, most commonly referred to as VaR backtesting. A new generation of “self‐learning” VaR models (Conditional Autoregressive Value‐at‐Risk or CAViaR) combine backtesting results with ex ante VaR estimates in an ARIMA framework in order to forecast P/L distributions more accurately. In this commentary, the authors present a systematic overview of several classes of applied statistical techniques that can make VaR backtesting more comprehensive and provide valuable insights into the analytical properties of VaR models in various market environments. In addition, they discuss the challenges associated with extending traditional backtesting approaches for VaR horizons longer than one day and propose solutions to this important problem.

Groups of potentially violent drinkers may frequent areas of communities with large numbers of alcohol outlets, especially bars, leading to greater rates of alcohol-related assaults. This study assessed direct and moderating effects of bar densities on assaults across neighborhoods.We analyzed longitudinal population data relating alcohol outlet densities (total outlet density, proportion bars/pubs, proportion off-premise outlets) to hospitalizations for assault injuries in California across residential ZIP code areas from 1995 through 2008 (23,213 space-time units). Because few ZIP codes were consistently defined over 14 years and these units are not independent, corrections for unit misalignment and spatial autocorrelation were implemented using Bayesian space-time conditional autoregressive models.Assaults were related to outlet densities in local and surrounding areas, the mix of outlet types, and neighborhood characteristics. The addition of one outlet per square mile was related to a small 0.23% increase in assaults. A 10% greater proportion of bars in a ZIP code was related to 7.5% greater assaults, whereas a 10% greater proportion of bars in surrounding areas was related to 6.2% greater assaults. The impacts of bars were much greater in areas with low incomes and dense populations.The effect of bar density on assault injuries was well supported and positive, and the magnitude of the effect varied by neighborhood characteristics. Posterior distributions from these models enabled the identification of locations most vulnerable to problems related to alcohol outlets.

Using a novel three-phase model based upon a conditional autoregressive Wishart (CAW) framework for the realized (co)variances of the US Dow Jones and the German stock index DAX, we analyze intra-daily volatility spillovers between the US and German stock markets. The proposed model explicitly accounts for three distinct intraday periods resulting from the non-synchronous and partially overlapping opening hours of the two markets. We find evidence of significant short-term volatility spillovers from one intraday period to the next within both markets ('heat-wave effects') as well as across the two markets ('meteor-shower effects'). Furthermore, we find that during the subprime crisis the general persistence of short-term volatility shocks is considerably higher and the spillovers effects between the US and the German stock markets are significantly larger than before the crisis, indicating substantial volatility contagion effects.

The paper is concerned with multivariate conditional autoregressive CAR models, also known as Gaussian Markov random fields. This is an important class of models which is frequently used in epidemiological analysis and in health care research in general. Several multivariate CAR models have been proposed to date, any of which could be applied, for example, to multiple-disease mapping. This paper discusses their theoretical background and proposes a generalized form which encompasses the formulation of recent proposed models.

Introduction : In the last ten to twenty years, a stabilization or decline in colorectal cancer (CRC) incidence has been observed in some countries across the world but not in Spain. Our objective here is to assess the gender-specific CRC spatio-temporal pattern in the health areas of Navarre, a Spanish province, during the period 1990–2005. Methods : For each gender, a model with spatio-temporal CAR (Conditional Autoregressive) distributions is used for smoothing the incidence risks. Smoothing is carried out in two dimensions: space and time, allowing for a different time evolution in each health area. An estimated incidence trend curve for each health area and the corresponding confidence bands are obtained. To analyze the evolution of the geographical patterns of CRC incidence risks, maps are also provided. Results : In both genders, CRC shows an increasing trend in most of the areas. In the second half of the period 1998–2005 most of the areas have risks above one although not all statistically significant. In general females present equal or lower risks than males in all areas during the studied period. Conclusions : Colorectal cancer incidence risk is still increasing in the health areas of Navarre. Promoting healthful lifestyles for primary prevention and early detection programs could help to reverse the trend in the province.

Reliable surveillance models are an important tool in public health because they aid in mitigating disease outbreaks, identify where and when disease outbreaks occur, and predict future occurrences. Although many statistical models have been devised for surveillance purposes, none are able to simultaneously achieve the important practical goals of good sensitivity and specificity, proper use of covariate information, inclusion of spatio-temporal dynamics, and transparent support to decision-makers. In an effort to achieve these goals, this paper proposes a spatio-temporal conditional autoregressive hidden Markov model with an absorbing state. The model performs well in both a large simulation study and in an application to influenza/pneumonia fatality data. Copyright © 2012 John Wiley & Sons, Ltd.

Syndromic surveillance can be used to assess change in drug abuse rates and to find regions in which abuse is most common. This paper compares the power of three syndromic surveillance procedures (a paired-sample test, a process control chart, and a conditional autoregressive model) for detecting change in opioid drug abuse patterns, using data from two reporting systems (the OTP and PCC datasets). We find that the conditional autoregressive model provides good power and geographic information and that the OTP data carry the strongest signal.

This paper compares the forecasting performance of the conditional autoregressive range (CARR) model with the commonly adopted GARCH model. Two major stock indices, FTSE 100 and Nikkei 225, are studies using the daily range data and daily close price data over the period 1990 to 2000. Our results suggest that improvements of the overall estimation are achieved when the CARR models are used. Moreover, we find that the CARR model gives better volatility forecasts than GARCH, as it can catch the extra informational contents of the intra-daily price variations. Finally, we also find that the inclusion of the lagged return and the lagged trading volume can significantly improve the forecasting ability of the CARR models. Our empirical results also significantly suggest the existence of a leverage effect in the U.K. and Japanese stock markets.

This study investigates the pattern of knowledge spillovers arising from patent activity between European regions. A Bayesian hierarchical model is developed that specifies region-specific latent effects parameters modeled using a connectivity structure between regions that can reflect geographical proximity in conjunction with technological and other types of proximity. This approach exploits the fact that interregional relationships may exhibit industry-specific technological linkages or transportation network linkages, which is in contrast to traditional studies relying exclusively on geographical proximity. We also allow for both symmetric and asymmetric knowledge spillovers between regions, and for heterogeneity across the regional sample. A series of formal Bayesian model comparisons provides support for a model based on technological proximity combined with spatial proximity, asymmetric knowledge spillovers, and heterogeneity in the disturbances. Estimates of region-specific latent effects parameters structured in this fashion are produced by the model and used to draw inferences regarding the character of knowledge spillovers across the regions. The method is illustrated using sample data on patent activity covering 323 regions in nine European countries. Copyright © 2008 John Wiley & Sons, Ltd.

Regional differences in mean birthweight in rural Papua New Guinea (PNG) and the importance of differences in family diet and maternal education and socio-economic status on such patterns were explored using birthweight data collected by the 1982/83 PNG National Nutrition Survey. A total of 6137 birthweight measurements from 85 PNG districts were available, representing 22% of all children included in the survey. The nature of possible selection biases are assessed and their implications discussed. Hierarchical Bayesian spatial models based on conditional autoregressive (CAR) priors were used to model spatial patterns in birthweights and their relation to different sets of covariates. Birthweights were found to exhibit striking geographical differences. Children from the central PNG highlands and from affluent lowland areas had the highest birthweights, while they were lowest in the (largely lowland) Sepik, Western, Madang and Milne Bay Provinces and in remote highland fringe areas. Maternal education, socio-economic status and diet were all important predictors, but only differences in family diet were correlated with the observed spatial patterns. The results of the present study highlight the importance of nutrition and socio-economic status in explaining differences in birthweights in PNG. Besides improving maternal health, interventions for improving birthweights in PNG should therefore aim at strengthening the economic base of rural populations and promote the cultivation and consumption of high quality foods.

Background/Aims: This study examined the impact of socioecologic factors on the transmission of dengue fever (DF) and assessed the difference in the potential predictors of DF between locally and overseas acquired cases, Queensland, Australia.Methods: We obtained data from the Queensland Health on numbers of notified DF cases by local government area (LGA) in Queensland for the period 1 January 2002–31 December 2005. The data on weather and socioeconomic index for areas (SEIFA) and overseas visitors were obtained from the Australian Bureau of Meteorology and the Australian Bureau of Statistics. A Bayesian spatial conditional autoregressive (CAR) model was used to quantify the relationship between variation of DF and socioecologic factors and to determine spatial patterns of DF. Results: Our results show that the average increase of locally acquired DF was 6% (95% credible interval [CI]: 2%–11%) and 61% (95% CI: 2%–241%) for a 1-mm increase in average monthly rainfall and a 1°C increase in average monthly maximum temperature between 2002 and 2005, respectively. The average increase of overseas-acquired DF cases was 1% (95% CI: 0%–3%) and 1% (95% CI: 0%–2%) for a 1-mmincrease in average rainfall and a 1 unit increase in SEIFA. No significant association between numbers of overseas travellers, SEIFA, and DF was found for locally acquired DF cases. For overseas-acquired cases, DF had no significant associations with temperature and numbers of overseas travellers. Conclusion: The results of this study indicated that socioecological factors may have played a significant role in the transmission of DF. Socioecological drivers of locally and overseas-acquired DF appear to differ in Queensland, Australia.

A producao de leite e uma das atividades mais importantes para a economia brasileira e o uso de modelos estatisticos pode auxiliar a tomada de decisao neste setor produtivo. O objetivo deste artigo foi comparar o desempenho do modelo de regressao linear tradicional e do modelo de regressao espacial, denominado de autoregressivo condicional (CAR), para explicar como algumas variaveis preditoras contribuem para a quantidade de leite produzido. Este trabalho usou uma base de dados sobre a producao de leite fornecida pelo Instituto Brasileiro de Geografia e Estatistica (IBGE) e outra base de dados sobre informacoes geograficas do estado de Minas Gerais, fornecida pelo Programa Integrado de Uso da Tecnologia de Geoprocessamento (GEOMINAS). Os resultados mostraram a superioridade do modelo CAR sobre o modelo de regressao tradicional. O modelo CAR possibilitou a identificacao de dois conglomerados espaciais de municipios distintos de producao de leite no estado de Minas Gerais. O primeiro conglomerado representa a regiao onde se observa os maiores niveis de producao de leite, sendo formado pelos municipios do Triângulo Mineiro. O segundo conglomerado e formado pelos municipios do norte do estado que apresentam os menores niveis de producao de leite.

Background The Conditional Autoregressive (CAR) model is widely used in many small-area ecological studies to analyse outcomes measured at an areal level. There has been little evaluation of the influence of different neighbourhood weight matrix structures on the amount of smoothing performed by the CAR model. We examined this issue in detail. Methods We created several neighbourhood weight matrices and applied them to a large dataset of births and birth defects in New South Wales (NSW), Australia within 198 Statistical Local Areas. Between the years 1995–2003, there were 17,595 geocoded birth defects and 770,638 geocoded birth records with available data. Spatio-temporal models were developed with data from 1995–2000 and their fit evaluated within the following time period: 2001–2003. Results We were able to create four adjacency-based weight matrices, seven distance-based weight matrices and one matrix based on similarity in terms of a key covariate (i.e. maternal age). In terms of agreement between observed and predicted relative risks, categorised in epidemiologically relevant groups, generally the distance-based matrices performed better than the adjacency-based neighbourhoods. In terms of recovering the underlying risk structure, the weight-7 model (smoothing by maternal-age 'Covariate model') was able to correctly classify 35/47 high-risk areas (sensitivity 74%) with a specificity of 47%, and the 'Gravity' model had sensitivity and specificity values of 74% and 39% respectively. Conclusion We found considerable differences in the smoothing properties of the CAR model, depending on the type of neighbours specified. This in turn had an effect on the models' ability to recover the observed risk in an area. Prior to risk mapping or ecological modelling, an exploratory analysis of the neighbourhood weight matrix to guide the choice of a suitable weight matrix is recommended. Alternatively, the weight matrix can be chosen a priori based on decision-theoretic considerations including loss, cost and inferential aims.

Incluye 2 ficheros de datos In this paper, space-time patterns of colorectal cancer (CRC) mortality risks are studied by sex and age group (50-69, ≥70) in Spanish provinces during the period 1975-2008. Space-time conditional autoregressive models are used to perform the statistical analyses. A pronounced increase in mortality risk has been observed in males for both age-groups. For males between 50 and 69 years of age, trends seem to stabilize from 2001 onward. In females, trends reflect a more stable pattern during the period in both age groups. However, for the 50-69 years group, risks take an upward trend in the period 2006-2008 after the slight decline observed in the second half of the period. This study offers interesting information regarding CRC mortality distribution among different Spanish provinces that could be used to improve prevention policies and resource allocation in different regions. This research has been supported by the Spanish Ministry of Science and Innovation (project MTM 2011-22664, which is co-funded by FEDER).

This paper extends the results of a previous paper [4], by conditioning the stochastic process of interest rates on current and past values. Conditional autoregressive interest rate models are developed and applied to interest, insurance and annuity functions. Numerical results are also given.