Autoregressive Error Model Research Articles

Bayesian uncertainty analysis in distributed hydrologic modeling: A case study in the Thur River basin (Switzerland)

Calibration and uncertainty analysis in hydrologic modeling are affected by measurement errors in input and response and errors in model structure. Recently, extending similar approaches in discrete time, a continuous time autoregressive error model was proposed for statistical inference and uncertainty analysis in hydrologic modeling. The major advantages over discrete time formulation are the use of a continuous time error model for describing continuous processes, the possibility of accounting for seasonal variations of parameters in the error model, the easier treatment of missing data or omitted outliers, and the opportunity for continuous time predictions. The model was developed for the Chaohe Basin in China and had some features specific for this semiarid climatic region (in particular, the seasonal variation of parameters in the error model in response to seasonal variation in precipitation). This paper tests and extends this approach with an application to the Thur River basin in Switzerland, which is subject to completely different climatic conditions. This application corroborates the general applicability of the approach but also demonstrates the necessity of accounting for the heavy tails in the distributions of residuals and innovations. This is done by replacing the normal distribution of the innovations by a Student t distribution, the degrees of freedom of which are adapted to best represent the shape of the empirical distribution of the innovations. We conclude that with this extension, the continuous time autoregressive error model is applicable and flexible for hydrologic modeling under different climatic conditions. The major remaining conceptual disadvantage is that this class of approaches does not lead to a separate identification of model input and model structural errors. The major practical disadvantage is the high computational demand characteristic for all Markov chain Monte Carlo techniques.

Bayesian Model Averaging for Spatial Econometric Models

We extend the literature on Bayesian model comparison for ordinary least‐squares regression models to include spatial autoregressive and spatial error models. Our focus is on comparing models that consist of different matrices of explanatory variables. A Markov Chain Monte Carlo model composition methodology labeled MC3 by Madigan and York is developed for two types of spatial econometric models that are frequently used in the literature. The methodology deals with cases where the number of possible models based on different combinations of candidate explanatory variables is large enough such that calculation of posterior probabilities for all models is difficult or infeasible. Estimates and inferences are produced by averaging over models using the posterior model probabilities as weights, a procedure known as Bayesian model averaging. We illustrate the methods using a spatial econometric model of origin–destination population migration flows between the 48 U.S. states and the District of Columbia during the 1990–2000 period.

Analyzing spatial autocorrelation in species distributions using Gaussian and logit models

Analyses of spatial distributions in ecology are often influenced by spatial autocorrelation. While methods to deal with spatial autocorrelation in Normally distributed data are already frequently used, the analysis of non-Normal data in the presence of spatial autocorrelation are rarely known to ecologists. Several methods based on the generalized estimating equations (GEE) are compared in their performance to a better known autoregressive method, namely spatially simultaneous autoregressive error model (SSAEM). GEE are further used to analyze the influence of autocorrelation of observations on logistic regression models. Originally, these methods were developed for longitudinal data and repeated measures models. This paper proposes some techniques for application to two-dimensional macroecological and biogeographical data sets displaying spatial autocorrelation. Results are presented for both computationally simulated data and ecological data (distribution of plant species richness throughout Germany and distribution of the plant species Hydrocotyle vulgaris). While for Normally distributed data SSAEM perform better than GEE, GEE provide far better results than frequently used autologistic regressions and remove residual spatial autocorrelation substantially when having binary data.

Prospects for river discharge and depth estimation through assimilation of swath‐altimetry into a raster‐based hydrodynamics model

Surface water elevation profiles for a reach of the Ohio River were produced by the Jet Propulsion Laboratory Instrument Simulator to represent satellite measurements representative of those that would be observed by a wide swath altimeter being considered jointly by U.S. and European space agencies. The Ensemble Kalman filter with a river hydrodynamics model as its dynamical core was used to assimilate the water elevation synthetic observations, and to estimate river discharge. The filter was able to recover water depth and discharge, reducing the discharge RMSE from 23.2% to 10.0% over an 84‐day simulation period, relative to a simulation without assimilation. An autoregressive error model was instrumental in correcting boundary inflows, and increasing the persistence of error reductions between times of observations. The nominal 8‐day satellite overpass produced discharge relative errors of 10.0%, while 16‐day and 32‐day overpass frequencies resulted in errors of 12.1% and 16.9% respectively.

Hydrological modelling of the Chaohe Basin in China: Statistical model formulation and Bayesian inference

Calibration of hydrologic models is very difficult because of measurement errors in input and response, errors in model structure, and the large number of non-identifiable parameters of distributed models. The difficulties even increase in arid regions with high seasonal variation of precipitation, where the modelled residuals often exhibit high heteroscedasticity and autocorrelation. On the other hand, support of water management by hydrologic models is important in arid regions, particularly if there is increasing water demand due to urbanization. The use and assessment of model results for this purpose require a careful calibration and uncertainty analysis. Extending earlier work in this field, we developed a procedure to overcome (i) the problem of non-identifiability of distributed parameters by introducing aggregate parameters and using Bayesian inference, (ii) the problem of heteroscedasticity of errors by combining a Box–Cox transformation of results and data with seasonally dependent error variances, (iii) the problems of autocorrelated errors, missing data and outlier omission with a continuous-time autoregressive error model, and (iv) the problem of the seasonal variation of error correlations with seasonally dependent characteristic correlation times. The technique was tested with the calibration of the hydrologic sub-model of the Soil and Water Assessment Tool (SWAT) in the Chaohe Basin in North China. The results demonstrated the good performance of this approach to uncertainty analysis, particularly with respect to the fulfilment of statistical assumptions of the error model. A comparison with an independent error model and with error models that only considered a subset of the suggested techniques clearly showed the superiority of the approach based on all the features (i)–(iv) mentioned above.

Relationship Between Secondary Variables and Soybean Oil and Protein Concentration

The spatial variation of soybean seed oil and protein concentration has been demonstrated at a field scale. We hypothesize that aerial images of crops during the late growing season, in combination with site property maps, can be used to delineate areas of similar seed oil and protein concentration within a given field. If these areas can be identified, then they can be harvested differentially. The main objective of this is study was to predict soybean yield and seed composition using site properties (elevation, slope, soil electrical conductivity (ECdeep and ECshallow), soil organic matter (SOM), and soil reflectance) as well as indices derived from hyperspectral remote sensing images (NNDVI, PRI, NDVI, GNDVI, and the ratio between NDVI and GNDVI). The study was conducted on two adjacent 16 ha subsections during the 2000 and 2001 growing seasons. Since the predictor variables presented multicollinearity, three groups of principal components (PC) were defined: a group corresponding to the site properties, a group corresponding to vegetation indices, and a group corresponding soybean performance (seed yield, and seed oil and protein concentrations). Then a spatial autoregressive error model predicted the soybean performance PC using site properties and vegetation indices while accounting for spatial the autocorrelation. Relationship between site properties, hyperspectral vegetation indices, and soybean seed protein and oil concentration were found for both environments. The regression analysis indicated that PCs of vegetation indices predicted soybean seed protein and oil concentration more consistently than site properties.

Forecasting electricity market pricing using artificial neural networks

Electricity price forecasting is extremely important for all market players, in particular for generating companies: in the short term, they must set up bids for the spot market; in the medium term, they have to define contract policies; and in the long term, they must define their expansion plans. For forecasting long-term electricity market pricing, in order to avoid excessive round-off and prediction errors, this paper proposes a new artificial neural network (ANN) with single output node structure by using direct forecasting approach. The potentials of ANNs are investigated by employing a rolling cross validation scheme. Out of sample performance evaluated with three criteria across five forecasting horizons shows that the proposed ANNs are a more robust multi-step ahead forecasting method than autoregressive error models. Moreover, ANN predictions are quite accurate even when the length of the forecast horizon is relatively short or long.

Bayesian Model Averaging for Spatial Econometric Models

We extend the literature on Bayesian model comparison for ordinary least-squares regression models to include spatial autoregressive and spatial error models. Our focus is on comparing models that consist of different matrices of explanatory variables. A Markov Chain Monte Carlo model composition methodology labelled MC to the third by Madigan and York (1995) is developed for two types of spatial econometric models that are frequently used in the literature. The methodology deals with cases where the number of possible models based on different combinations of candidate explanatory variables is large enough that calculation of posterior probabilities for all models is difficult or infeasible. Estimates and inferences are produced by averaging over models using the posterior model probabilities as weights, a procedure known as Bayesian model averaging. We illustrate the methods using a spatial econometric model of origin-destination population migration flows between the 48 US States and District of Columbia during the 1990 to 2000 period.

On the property of diffusion in the spatial error model

The aim of this paper is to illustrate the property of global spillover effects in the first-order spatial autoregressive error model and the associated diffusion process of spatial shocks. An application is provided on a sample of 145 regions over 1989–1999 and highlights the most influential regions.

Flow Data, Inflow/Infiltration Ratio, and Autoregressive Error Models

Sanitary sewer overflows (SSOs) are a major environmental issue. One of the major factors causing SSOs is the rain-derived inflow and infiltration (RDII) to a separate sanitary sewer system. If a wastewater collection system is not well maintained, cumulative system-wide RDII could easily cause the wastewater conveyance and treatment capacity to be overwhelmed, and thus lead to SSOs. Monitoring system condition is a key component in system management. The industry’s standard approaches to system monitoring include the practice of collecting and analyzing continuous rainfall and flow data at certain key locations in the system to estimate the level of RDII. However, the writer is of the opinion that the current standard analytical methodologies of the industry can be significantly improved. This paper introduces a basic regression approach with autoregressive errors to support statistical inferences with respect to the level of RDII.

Non-Stationarity Effects in Causal Sales Forecasting Models

One fundamental assumption of classical econometrics that is gaining a lot of attention in econometric modeling is that of stationarity of variables used to specify a regression model. We analyze some of the benefits and drawbacks in applying econometric models of nonstationary behavior to forecasts involving marketing variables. We use standard residual-based unit root and cointegration tests to identify non-stationary variables in the sales and marketing data of two CPG brands and any potential long-run equilibrium. The out-of-sample forecast Mean Absolute Percent Errors (MAPE) from single-equation causal forecast models of sales volume for the brands, with the identified non-stationary regressors is compared to that from benchmark univariate models, to gauge the effect of nonstationarity on forecast quality. The model is then re-specified after appropriately stationarizing these models. The forecasts from the stationarized models are compared to the benchmark models to analyze potential improvements in forecast quality. The results show that it may not be necessary to difference nonstationary, non-cointegrating regressors, when the dependent variable is stationary, and when the dependent variable is nonstationary, it might be possible to obtain a stable regression model with levels variable by using an autoregressive error model.

Goodness-of-Fit of Time Series Model for the Storage of Water in Agricultural Reservoir

The efficient management of the agricultural reservoir may well supply stable water for irrigation. In this article, time series analysis has been used for analyzing the storage of water data in Kihung agricultural reservoir that is located in Yongin City, Korea. For analyzing the storage of water data, three models, the ARIMA model, the autoregressive error model, and the dynamic regression model have been used. The result shows that the autoregressive error model is best suited for describing the storage of water data.

Space and Growth: A Survey of Empirical Evidence and Methods

This paper reviews the empirical literature on growth and convergence that has addressed the importance of spatial factors. An important distinction in this literature is the one between absolute and relative location. The literature on absolute location predominantly uses non-spatial econometric techniques, and is strongly linked to the economic growth literature. In contrast, studies on relative location tend to be weakly linked to theory, but apply relatively sophisticated econometric techniques to account for spatial effects. Most studies of the latter type are regional in nature, although there is a growing interest in extending the analysis to a cross-country setting. Both regional and cross-country studies typically make use of so-called spatial process models. Rather than modelling the impediments of space and distance directly, spatial process models start from exogenously provided information about the spatial structure. Our review shows that the usage of simple spatial autoregressive lag and error models abounds in the spatial econometrics literature. We assess the appropriateness of such models, and identify areas of potential concern. The rather weak linkage between theory and operational models, the dominance of 'global' over 'local' spatial association patterns, and the implicit restrictions on spatial interaction induced by many of the habitual specifications of the spatial weights matrix concurrently constitute areas where improvements can be made.

온실가루이의 공간시계열 분석

시간에 따라 얻어진 공간 자료를 공간시계열 자료라 하며 이러한 자료를 분석하기 위해 사용되는 모형이 공간시계열 모형이다. 최근 곤충학과 생태학에서 공간시계열 모형을 이용한 연구가 활발히 진행되고 있다. 본 논문에서는 온실에 있는 곤충의 마리수를 ARMA 모형과 자기회귀 오차모형을 이용한 공간시계열 모형으로 분석하였다. 자료에 포함된 이상점은 분산도(Variogram) 추정에 많은 영향을 주기 때문에 Mugglestone (2000)의 이상점 수정법을 이용하여 수정하였다. 공간시계열 모형들과 시계열 요인을 배제한 공간모형을 MSE와 MAPE를 이용하여 비교하였다. Recently space-time model in spatial data analysis is widly used. In this paper we applied this model to analysis of greenhouse whitefly. For handling time component, we used ARMA model and autoregressive error model and for outliers, we adapted Mugglestone's method. We compared space-time models and geostatistic model with MSE and MAPE.

농업용 저수지에서 저수량 예측 모형과 연계한 저수지 운영 개선 방안의 모색

본 연구에서는 농업용 저수지에서 저수량 예측모형과 함께 저수지의 목표저수량 및 한계저수량을 유지하기 위한 저수지 운영방안을 제시하였다. 대상저수지인 금강저수지에서 1990년부터 200l년까지의 저수량 자료를 이용하여 갈수빈도해석을 적용하고, 2년빈도 한발저수량을 목표저수량(target storage)으로, 10년빈도 한발저수량을 한계저수량(critical storage)으로 설정하였다. 농업용 저수지의 운영의 효율화를 위해서는 우선 합리적인 방법을 통하여 장래 저수량을 예측하여야 한다. 예측된 저수량은 저수지 운영에 관한 계획을 수립하는데 기초자료로 활용될 수 있다. 본 연구에는 저수량 예측모형으로 ARIMA 모형과 자기회귀오차모형을 적용하였다. ARIMA 모형은 과거 저수량 자료만을 근거로 하여 저수량을 예측함으로서 예측정도가 상대적으로 낮은 것으로 나타난 반면, 자기회귀오차모형은 저수량과 관련 있는 설명변수들을 이용함으로써 예측의 효과를 높일 수 있었다. 농업용 저수지의 저수량은 이전 저수량, 강수량, 평균온도, 최고온도, 관개면적, 풍속, 습도의 영향을 받으므로 자기회귀오차모형을 적용하여 저수량과 저수량에 영향을 미치는 요인과의 관계를 분석하였다. 자기회귀오차모형에 의한 저수량 예측 관계식은 저수지의 연속방정식과 유사한 관계식으로 유도되어 실제 적용성이 높을 것으로 판단되며, 금광저수지에서 예측된 2002년도 저수량과 관측된 저수량을 비교한 결과, 양호한 예측결과를 보여 주었다. This paper presents a reservoir operation plan coupled with storage forecasting model to maintain a target storage and a critical storage. The observed storage data from 1990 to 2001 in the Geum-Gang agricultural reservoir in Korea have been applied to the low flow frequency analysis, which yields storage for each return period. Two year return period drought storage is then designated as the target storage and ten year return period drought storage as the critical storage. Storage in reservoir should be forecasted to perform reasonable reservoir operation. The predicted storage can be effectively utilized to establish a reservoir operation plan. In this study the autoregressive error (ARE) model and the ARIMA model are adopted to predict storage of reservoir. The ARIMA model poorly generated reservoir storage in series because only observed storage data were used, but the autoregressive error model made to enhance the reliability of the forecasted storage by applying the explanation variables to the model. Since storages of agricultural reservoir with respect to time have been affected by irrigation area, high or mean temperature, precipitation, previous storage and wind velocity, the autoregressive error model has been adopted to analyze the relationship between storage at a period and affecting factors for storage at the period. Since the equation for predicting storage at a period by the autoregressive error model is similar to the continuity equation, the predicting storage equation may be practical. The results from compared the actual storage in 2002 and the predicted storage in the Geum-Gang reservoir show that forecasted storage by the autoregressive error model is reasonable.

A comparative study of statistical total column ozone forecasting models

Since the beginning of the 1990s, total column ozone is being forecasted on an operational basis at several institutes around the world. It usually serves as an input parameter for the UV index forecast. The ozone forecasting procedures described in the literature are ad hoc statistical regression models. They yield sufficiently accurate predictions. So far, no detailed description, including the validity of the underlying assumptions of regression analysis, has been communicated. We studied this subject and conclude that they are violated by the models currently in use. Taking into account the causes for this violation, we come up with a more sophisticated model, which combines a stepwise multilinear regression model with an autoregressive conditional heteroskedasticity error model. This model still has shortcomings, but it yields a reduction of variance with respect to the commonly used ordinary least squares stepwise regression model of the order of 35%. Expressed in terms of R2, the improvement is 6%. The root‐mean‐square error of the model we propose is 3.2 Dobson units lower than the usually applied regression model.

Forecasting Taiwan stock price with corrected error term

The study is designed to demonstrate how the forecasting models with corrected error term can be effectively used to high performance forecasts for stock price applications. Another purpose of this study is to compare the forecasts generated by the error correction model (ECM), the autoregressive conditional heteroscedastic (ARCH) model, the regression with ARMA error model (Reg-ARMA) and the autoregressive error model (Autoreg). The accuracy of these forecasting models is measured by using the forecasting errors in a post-sample period. The results show that the forecasting performance of the ECM is the best, and the next best in Autoreg model while the worst is Reg-ARMA model.

Testing regularity properties in static and dynamic duality models: the case of Greek agriculture

An error correction model of Greek agriculture for the period 1961-94 is estimated using a dynamic system of output and input share equations derived from a translog profit function. Nested within this model are a static model and three simpler dynamic models: a partial adjustment model, autoregressive error model and finite distributed lag model. The data-generating process rejects the static model and simpler dynamic models in favour of the more general error correction model, which is also found to perform better than the static model in terms of consistency with the regularity properties implied by economic theory. Copyright 1999 by Oxford University Press.

Ecological correlates of trap response of a Neotropical forest rodent, Proechimys semispinosus

ABSTRACTPatterns of trap response in the Central American spiny rat (Proechimys semispinosus), a frugivorous forest rodent, were examined in relation to age, sex, density and resource abundance. Populations on four small islands (designated numbers 4, 8, 14, and 52) in Gatun Lake (central Panama) were sampled by live-trapping for four nights every month for four years. Trappability was calculated as the proportion of all individuals known to be alive that were actually captured. Mean body mass at first capture was within the range of subadult body masses and differed among islands but not between sexes. Trappabilities summed over the entire study were generally low and differed among islands and age classes (juveniles, subadults and adults) and between sexes. In general, adults were more trappable than juveniles and subadults, and females (particularly adults) were more trappable than males. Trappability and the number of captures per individual varied seasonally and were generally greatest during December and January. Monthly estimates of these two variables were examined for autocorrelation, and the order of the autoregressive error model was determined separately for each island population. The arcsine of trappability and the number of captures per individual were regressed on log10 densities of spiny rats and of fruiting trees and lianas after controlling for autocorrelation. Both trappability indices were negatively related to the density of fruiting trees and lianas on islands 8 and 14, indicating that spiny rats may be seasonally food-stressed. The number of captures per individual was related positively to the density of spiny rats on island 52 and negatively on island 8. Results indicate that spiny rat populations must be sampled with greater intensity and duration than temperate forest rodents.

Trend Robust Two-Level Factorial Designs

Limiting the possible influence of time order effects may be an important consideration in designing a sequential experiment. We consider the problem of finding trend robust run orders of two-level factorials when the time effects are modelled via a first order autoregressive error model or via a time series model. In both cases, run orders are trend robust if the factors change level many times. Other run orders can be quite inefficient, even if they are free of low-degree polynomial trends. We present a simple algorithm for constructing run orders of two-level factorial designs with many level changes.