Bayesian estimation for heterogeneous spatial autoregressive models with variance modelling

Heteroscedasticity is often encountered in spatial-data analysis, so a new class of heterogeneous spatial autoregressive models is introduced in this paper, where the variance parameters are allowed to depend on some explanatory variables. Here, we are interested in the problem of parameter estimation and the variable selection for both the mean and variance models. Then, a unified procedure via double-penalized quasi-maximum likelihood is proposed, to simultaneously select important variables. Under certain regular conditions, the consistency and oracle property of the resulting estimators are established. Finally, both simulation studies and a real data analysis of the Boston housing data are carried to illustrate the developed methodology.

The Properties of Realized Correlation: Evidence from the Greek Equity Market

In the international monetary system, gold plays a significant role. Predicting gold prices is a useful and unique skill for anybody. As a result, improving one's ability to anticipate gold futures is critical. The study presented in this paper relates to gold futures predictions, based on heterogeneous autoregressive (HAR) theory, and Heterogeneous Autoregressive model of Realized Volatility (HAR-RV model), coupled with gold's daily trade volume and CBOE Volatility Index (VIX) to create three unique models: Heterogeneous Autoregressive model of Realized Volatility and Trading volume (HAR-RV-T model), Heterogeneous Autoregressive model of Realized Volatility and Volatility Index (HAR- RV-VIX model), and Heterogeneous Autoregressive model of Realized Volatility, Trading Volume, and Volatility Index (HAR-RV-T&VIX model). This paper mainly explores a method to predict the volatility of gold futures. Improve the ability to forecasting the volatility of gold prices is obviously conducive to effectively play the futures, including hedging, risk management, price analysis, and other tasks. The research concludes that adding trading volume and sentiment indicator contributes to a more robust HAR model and performs better on forecasting.

PurposeIn a recent paper, Yoon and Lee (2019) (YL hereafter) propose a weighted Fama and MacBeth (FMB hereafter) two-step panel regression procedure and provide evidence that their weighted FMB procedure produces more efficient coefficient estimators than the usual unweighted FMB procedure. The purpose of this study is to supplement and improve their weighted FMB procedure, as they provide neither asymptotic results (i.e. consistency and asymptotic distribution) nor evidence on how close their standard error estimator is to the true standard error.Design/methodology/approachFirst, asymptotic results for the weighted FMB coefficient estimator are provided. Second, a finite-sample-adjusted standard error estimator is provided. Finally, the performance of the adjusted standard error estimator compared to the true standard error is assessed.FindingsIt is found that the standard error estimator proposed by Yoon and Lee (2019) is asymptotically consistent, although the finite-sample-adjusted standard error estimator proposed in this study works better and helps to reduce bias. The findings of Yoon and Lee (2019) are confirmed even when the average R2 over time is very small with about 1% or 0.1%.Originality/valueThe findings of this study strongly suggest that the weighted FMB regression procedure, in particular the finite-sample-adjusted procedure proposed here, is a computationally simple but more powerful alternative to the usual unweighted FMB procedure. In addition, to the best of the authors’ knowledge, this is the first study that presents a formal proof of the asymptotic distribution for the FMB coefficient estimator.

지리정보시스템은 3차원 위상정보를 표현함으로써 사용자에게 정확하고 정교한 서비스를 제공한다. 이 때에 3차원 위상정보연산을 위해 차원변경방식과 서로 이질적인 공간모델을 사용해야 하는데, 이 방식을 사용할 때는 공간 연산이 어려울 뿐 아니라 서로 호환성이 부족한 문제가 발생한다. 따라서 이 논문에서는 이 문제를 해결하기 위하여 2차원 공간 객체 모델을 수용하는 3차원 공간 객체 모델을 제안하였고, 타당성을 보이기 위하여 구현하여, 그 실행을 보였다. 3차원 공간 위상 관계 연산자를 위하여 DE-9IM 방식을 3차원 개념으로 정의한 DE-9IM을 이용해서 설계하였고, 객체지향 개념을 지원하는 컴포넌트 환경에서 3차원 공간 위상 연산자를 구현하였다. 이 논문에서 제안된 3차원 공간 위상 연산자는 타 시스템과의 상호 운용성을 보장하며, 구현된 공간 위상 관계 연산을 이용하여, 3차원 공간 객체에 대한 효율적인 공간 질의를 수행할 수 있다. As Geographic Information Systems represent three dimensional topological information, The Systems provide accurate and delicate services for users. In order to execute three dimensional topological operations, a dimensional transformation and heterogeneous spatial models should be used. However, the existing systems that use the dimensional transformation and the heterogeneous models, is not only difficult to operate the spatial operators, but also happened to support non-interoperability. Therefore, in order to solve the problems, we proposed three dimensional spatial object models that supported two dimensional object models and implemented them to show validity of the proposed models. When designing the three dimensional topological operators, we used 3DE-9IM which extended DE-9IM to support three dimensional concepts, and implemented operators on the component environment with object oriented concepts. The proposed three dimensional spatial object models and topological operators can support interoperability between systems, and execute spatial queries efficiently on three dimensional spatial objects.

Groundwater pollution source identification using Metropolis-Hasting algorithm combined with Kalman filter algorithm

Understanding the resilience of infrastructures, such as a transportation network, has significant importance for our daily life. Recently, a homogeneous spatial network model was developed for studying spatial embedded networks with characteristic link length such as power-grids and the brain. However, although many real-world networks are spatially embedded and their links have characteristics length such as pipelines, power lines or ground transportation lines they are not homogeneous but rather heterogeneous. For example, density of links within cities are significantly higher than between cities. Here we develop and study numerically and analytically a similar realistic heterogeneous spatial modular model using percolation process to better understand the effect of heterogeneity on such networks. The model assumes that inside a city there are many lines connecting different locations, while long lines between the cities are sparse and usually directly connecting only a few nearest neighbours cities in a two dimensional plane. We find that our heterogeneous model experiences two distinct continuous transitions, one when the cities disconnect from each other and the second when each city breaks apart. This is in contrast to the homogeneous model where a single transition is found. Although the critical threshold for site percolation in 2D grid remains an open question we analytically find the critical threshold for site percolation in this model. In addition, it has been found that the homogeneous model experience a single transition having a unique phenomenon called critical stretching where a geometric crossover from random to spatial structure in different scales found to stretch non-linearly with the characteristic length at criticality. In marked contrast, we show here that the heterogeneous model does not experience such a phenomenon indicating that critical stretching strongly depends on the network structure.

In this study, we investigate the impacts of common information between oil futures and the United States stock markets on forecasting oil volatility using the multivariate heterogeneous autoregressive realized volatility model. We have several noteworthy findings. First, the in‐sample estimation results show that the negative returns and the ‘bad’ jumps have larger influence on oil futures volatility than positive returns and ‘good’ jumps, respectively. Second, the out‐of‐sample results further indicate that our multivariate heterogeneous autoregressive (HAR) model can generate higher forecast accuracy than individual HAR model for the realized volatility‐type models, which highlights the importance of incorporating volatility information from the stock Market. Third, our findings are robust across the direction‐of‐change test and different windows. Furthermore, from the perspective of the investors' allocation portfolio in the future, the use of common information can also bring greater gains.

When estimating the mean value of a variable, or the total amount of a resource, within a specified region it is desirable to report an estimated standard error for the resulting estimate. If the sample sites are selected according to a probability sampling design, it usually is possible to construct an appropriate design-based standard error estimate. One exception is systematic sampling for which no such standard error estimator exists. However, a slight modification of systematic sampling, termed 2-step tessellation stratified (2TS) sampling, does permit the estimation of design-based standard errors. This paper develops a design-based standard error estimator for 2TS sampling. It is shown that the Taylor series approximation to the variance of the sample mean under 2TS sampling may be expressed in terms of either a deterministic variogram or a deterministic covariance function. Variance estimation then can be approached through the estimation of a variogram or a covariance function. The resulting standard error estimators are compared to some more traditional variance estimators through a simulation study. The simulation results show that estimators based on the new approach may perform better than traditional variance estimators.

Diastolic fractional flow reserve (dFFR) has been shown to be highly sensitive for detection of inducible myocardial ischemia. However, its reliance on measurement of left-ventricular pressure for zero-flow pressure correction, as well as manual extraction of the diastolic interval, has been its major limitation. Given previous reports of minimal zero-flow pressure at end-diastole, we compared instantaneous ECG-gated end-diastolic FFR with conventional full-cardiac cycle FFR and other diastolic indices in the porcine model. Measurements of FFR in the left anterior descending and left circumflex arteries were performed in an open-chest swine model with an external occluder device on the coronary artery used to produce varying degrees of epicardial stenosis. An ultrasound flow-probe that was placed proximal to the occluder measured absolute blood flow in ml/min, and it was used as a gold standard for FFR measurement. A total of 17 measurements at maximal hyperemia were acquired in 5 animals. Correlation coefficient between conventional mean hyperemic FFR with pressure-wire and directly measured FFR with flow-probe was 0.876 (standard error estimate=0.069; P<0.0001). The hyperemic end-diastolic FFR with pressure-wire correlated better with FFR measured directly with flow-probe (r=0.941, standard error estimate=0.050; P<0.0001). Instantaneous hyperemic ECG-gated FFR acquired at end-diastole, as compared with conventional full-cardiac cycle FFR, has an improved correlation with FFR measured directly with ultrasound flow-probe.

If the ordinary least squares (OLS) diagnostics discussed in the previous chapter indicate the existence of spatial lag or spatial error dependence, the researcher will wish to model the type of dependence indicated by these diagnostics. If the OLS diagnostics indicate the presence of a diffusion process, the researcher will wish to estimate a spatial lag model via maximum likelihood (ML) estimation or an instrumental variables specification incorporating instruments for the spatially lagged dependent variable. Alternatively, if the OLS diagnostics indicate the existence of spatial error dependence, the researcher may choose to estimate a more fully specified OLS model to model the spatial dependence or may choose to employ a ML or generalized method of moments (GMM) approach incorporating the spatial dependence in the errors. The spatial dependence diagnosed via the diagnostics discussed in Chapter 5 may alternatively be produced by spatial heterogeneity in the effects of covariates. If this is the only source of spatial dependence, modeling this heterogeneity will be sufficient to capture the spatial dependence. As a consequence, any specification search should also consider the possibility of spatial heterogeneity, which is the focus of Chapter 7. This chapter will first, however, examine alternative approaches for modeling spatial dependence if spatial heterogeneity is not present. This chapter begins by examining ML estimation of spatial lag models that derives from Ord (1975). Next, I explore alternative instrumental variables and GMM estimators for spatial lag dependence. Next, I turn to approaches for estimating spatial error models. I conclude by considering areas of concern in the estimation of spatial models. These include estimators for large sample sizes and diagnostics for continued spatial dependence. MAXIMUM LIKELIHOOD SPATIAL LAG ESTIMATION The mixed regressive, spatial autoregressive model, or spatial lag model, extends the pure spatial autoregressive model considered in Section 3.2 to include also the set of covariates and associated parameters: y = ρ W y +Xβ+e where X is again an N by K matrix of observations on the covariates, β is a K by 1 vector of parameters, and the remaining notation is as discussed in Section 3.2.

Learning outcomes In this chapter, you will learn how to construct models with more than one explanatory variable; derive the OLS parameter and standard error estimators in the multiple regression context; determine how well the model fits the data; understand the principles of nested and non-nested models; test multiple hypotheses using an F -test; form restricted regressions; and test for omitted and redundant variables. Generalising the simple model to multiple linear regression Previously, a model of the following form has been used: Equation (5.1) is a simple bivariate regression model. That is, changes in the dependent variable are explained by reference to changes in one single explanatory variable x . What if the real estate theory or the idea that is sought to be tested suggests that the dependent variable is influenced by more than one independent variable, however? For example, simple estimation and tests of the capital asset pricing model can be conducted using an equation of the form of (5.1), but arbitrage pricing theory does not presuppose that there is only a single factor affecting stock returns. So, to give one illustration, REIT excess returns might be purported to depend on their sensitivity to unexpected changes in (1) inflation; (2) the differences in returns on short-and long-dated bonds; (3) the dividend yield; or (4) default risks.

The expectation-maximization (EM) algorithm is widely used for parameter estimation in item response theory (IRT) modeling. However, when applied to datasets with large numbers of individuals and items, the standard EM algorithm can be slow to converge, with computationally expensive E-steps. We propose a modified EM algorithm to accelerate estimation for unidimensional two-parameter logistic IRT models. The modified algorithm uses a two-stage structure with partial-step updating over data subsets to reduce convergence time, while maintaining comparable accuracy and precision. The first two simulation studies evaluated its performance relative to standard EM, focusing on convergence time, parameter recovery, and standard error estimation across varying subset sizes and item counts. The third study demonstrated its scalability and runtime advantage in a large-scale testing scenario involving one million respondents and 100 items. The fourth study evaluated robustness under departures from unidimensionality. The proposed algorithm showed time reductions under smaller subsets with 36 items, consistent reductions across all subset sizes with 54 items, and the largest reduction (60%) with 40-item forms constructed from 100 items, while maintaining comparable estimation performance. These results highlight the algorithm's potential for large-scale applications involving tens of thousands of respondents and moderate-to-large item pools, with modifications that can be integrated into existing EM routines. We conclude with directions for operational use and potential extensions to multidimensional IRT estimation.

Simulating from distributions with intractable normalizing constants has been a long-standing problem in machine learning. In this letter, we propose a new algorithm, the Monte Carlo Metropolis-Hastings (MCMH) algorithm, for tackling this problem. The MCMH algorithm is a Monte Carlo version of the Metropolis-Hastings algorithm. It replaces the unknown normalizing constant ratio by a Monte Carlo estimate in simulations, while still converges, as shown in the letter, to the desired target distribution under mild conditions. The MCMH algorithm is illustrated with spatial autologistic models and exponential random graph models. Unlike other auxiliary variable Markov chain Monte Carlo (MCMC) algorithms, such as the Møller and exchange algorithms, the MCMH algorithm avoids the requirement for perfect sampling, and thus can be applied to many statistical models for which perfect sampling is not available or very expensive. The MCMH algorithm can also be applied to Bayesian inference for random effect models and missing data problems that involve simulations from a distribution with intractable integrals.

Estimation of spatial autoregressive panel data models with fixed effects