Autocorrelated Disturbances Research Articles

Handbook of Regression Analysis with Applications in R (Second Edition)

The second edition of ‘Handbook of Regression Analysis with Applications in R’ motivated at providing a practical and comprehensive guide to practitioners of regression analysis using R programming language. The book has been divided into seven parts containing 16 chapters. The part I of the book consist of first 2 chapters discussing the basic concepts of linear regression model, model estimation, prediction and selection methodologies. Part II containing three chapters, 3–5, address the implications of violations of assumptions, analysis of leverage and outliers, robust regression techniques, estimation of linearisable non-linear models and models with auto-correlated disturbances. Part III of the book includes two chapters 6 and 7 on analysis of variance and analysis of covariance. Part IV covered in chapters 8–11 discuss various non-Gaussian regression models including Logistic and multinomial regression, count data model and survival models for time to event. The part V of the book consisting of chapters 12–14 demonstrates non-linear regression and non-linear least squares regression, longitudinal and nested data models, the sparsity in regression and regularisation methods of estimation. The last part VI covered in chapters 15 and 16 focusses on non-parametric and semi-parametric methods including smoothing and additive models and tree-based models such as CART.

Bayesian estimation of simultaneous equation model with lagged endogenous variables and first order serially correlated errors

Most simultaneous equation models involve the inclusion of lagged endogenous and/or exogenous variables and sometimes it may be misleading to assume that the errors are normally distributed when in reality they exhibit functional formsthat are not normal especially in practical situations. The classical methods of estimating parameters of simultaneous equation models are usually affected by the presence of autocorrelation among the error terms. Unfortunately, in practice the form of correlation between the pairs of the random deviates is unknown.In this paper classical and Bayesian methods for the estimation of simultaneous equation model withlagged endogenous variables and first order serially correlated errors are considered. The smallsample properties of the methods at different levels of correlation for ρ = 0.2, 0.5 and 0.8are compared.Better parameter estimates were produced by the Bayesian estimator with smaller standard errors compared to the classical method. The standard deviations of the Bayesian estimator are consistently better than those of the OLS estimator for the sample sizes considered. For example, the standard deviations of the Bayesian for b14 (the coefficient of the lagged endogenous variable,y 1t-1) when ρ = 0.2 at N = 10, 15, 20 and 25 were 0.07712781, 0.05433923, 0.03230012 and 0.03177252 respectively while those of OLS were 0.0784732, 0.4718914, 0.05701936 and 1.31422868. However, when ρ = 0.8, the standard deviations were 0.0548055, 0.03860254, 0.02572899 and 0.02126175 for Bayesian and 0.0562190, 0.03882345, 0.053676 and 0.0315632 for OLS. Interestingly, notice that even at high correlation level, the estimates produced by the Bayesian method are closer to the parameter values and the standard deviations decrease as the sample size increases. Hence, the Bayesian estimation method might be a better choice when lagged endogenous variables are included in a simultaneous equation model with auto-correlated disturbances since it appeared to give better results compared to the classical approach.Keywords: Bayesian estimation, Lagged endogenous variables, Simultaneous equations, Monte-Carlo Simulation, First-order autoregressive process.

Conducting Interrupted Time-series Analysis for Single- and Multiple-group Comparisons

In this article, I introduce the itsa command, which performs interrupted time-series analysis for single- and multiple-group comparisons. In an interrupted time-series analysis, an outcome variable is observed over multiple, equally spaced time periods before and after the introduction of an intervention that is expected to interrupt its level or trend. The itsa command estimates the effect of an intervention on an outcome variable either for a single treatment group or when compared with one or more control groups. Additionally, its options allow the user to control for autocorrelated disturbances and to estimate treatment effects over multiple periods.

Understanding closed-loop identification with ITCLI

Prior work by the authors (featured in software sessions held during SYSID 2009 and 2012) described ITSIE and ITCRI, a series of interactive tools designed to aid students and practitioners in better understanding the role of design variables associated with classical prediction-error and control-relevant identification, respectively. This paper presents ITCLI (Interactive Tool for Closed-Loop Identification), an interactive software tool for understanding design variables in closed-loop identification of LTI SISO systems using prediction-error techniques. The tool enables an interactive evaluation regarding how bias and variance effects are manifested when identification is performed under closed-loop circumstances. The role of external signal design, choice of model structure, controller tuning during identification testing, and signal injection points (at either the manipulated variable or the setpoint) while in the presence of autocorrelated disturbances can be evaluated in a comprehensive and easy-to-operate tool. The software is developed using Sysquake and is provided as a stand-alone executable version in the Windows and Mac OS operating environments.

Availability Principle Applied to a Fuzzy Supervisory Control of a Pilot Flotation Column

This work presents a study of fuzzy expert control system, based on the availability principle, of a pilot flotation column at the Hybrid Process Control Laboratory in Santa Maria University. Sensors and actuators are communicated to a programmable Logic Controller (PLC) where calibrations and local control are implemented, and the data is sent to a PC network, where a Distributed Control System (DCS) is running. Process model predictions are obtained by running a simulator fed with actual operating variables and virtual variables associated to feed characteristics. All data is displayed at PC stations and historical data files are also built for further analysis. Operating variables (real and virtual) can also be analyzed off-line by advanced software tools. Supervisory control running on PC network writes DCS set points on PLC.The supervisory control performance was experimentally evaluated by keeping the mineralogical objectives of concentrate grade and recovery in narrow bands. The operation of the supervisor was compared to a base case where there is no supervisory control, and each experiment was subjected to stochastic auto-correlated disturbances in the feed conditions. The fuzzy supervisory control, unlike conventional control, is more capable of maintaining the metallurgical results within control limits during almost 90% of the operating time. An availability principle for manipulated variables was successfully tested acting on top of the fuzzy logic decision system.

Using GLS to Generate Forecasts in Regression Models with Auto-correlated Disturbances with simulation and Palestinian Market Index Data

This paper involves an important statistical problem concerning forecasting in regression models in time series processes. It is well known that the most famous method of estimating and forecasting is the Ordinary Least Squares (OLS). OLS may be not the optimal in this context. So over the years many specialized estimation techniques have been developed, for example Generalized Least Squares (GLS). We are comparing the forecasting based on some estimators with the prediction using the GLS estimate. This comparison will be used by what is known as measures of forecast accuracy. We conduct an extensive computer simulation time series data, to make comparison among these methods. The similar forecasting criteria were developed and evaluated for the real data set on daily closing price in the Palestinian market index (Alquds Index). The data consists of 164 monthly observations and obtained from the website of the Palestine Stock Exchange. The main finding is that, for forecasting purposes there is not much gained in trying to identifying the exact order and form of the auto-correlated disturbances by using GLS estimation method. In addition, we noticed that the accuracy of forecasting using GLS method does not differ substantially than the other methods as Maximum Likelihood Estimation (MLE), Minimize Conditional Sum of Squares (CSS) and the combination of these two methods. Moreover, for parameter estimation, the GLS is nearly as efficient as the exact parameter estimation. On the other hand, the Ordinary Least Squares (OLS) method performs much less efficient than the other estimation methods and producing poor forecasting accuracy.

ITCLI : An Interactive Tool for Closed-Loop Identification

Abstract This paper describes ITCLI , an interactive software tool for understanding SISO closed-loop identification using prediction-error techniques. The tool enables an interactive evaluation regarding how bias and variance effects play a role in identification under closed-loop circumstances. The role of external signal design, choice of model structure, controller tuning during identification testing, and signal injection points (at either the manipulated variable or the setpoint) all under the presence of autocorrelated disturbances are considered. The software is developed using Sysquake and is provided as a stand-alone executable version in multiple operating environments.

A Detrended Range Unit Root (DRUR) Test

We extend the Range Unit Root test in two directions. First, we consider the process with time trend and prove that the modified standardized number of new records converges to a sum of two Rayleigh distributions. Second, more general structures of autocorrelated disturbances are also taken into account. Monte Carlo experiments show the good sample properties of this nonparametric unit root test.

The Cliff and Ord Test for Spatial Correlation of the Disturbances in Unbalanced Panel Models

In many cases, only an unbalanced panel data set with some observations missing at random is available. This note derives a Cliff and Ord test for spatially autocorrelated disturbances for such data. In a small Monte Carlo simulation exercise, the performance of the proposed test is similar to its balanced counterpart. In almost all simulation experiments, the test is properly sized. Naturally, the lower the power of the test, the higher the share of missing data.

A Monte Carlo Study for Pure and Pretest Estimators of a Panel Data Model with Spatially Autocorrelated Disturbances

This paper examines the consequences of model misspecification using a panel data model with spatially autocorrelated disturbances. The performance of several maximum likelihood estimators assuming different specifications for this model are compared using Monte Carlo experiments. These include (i) MLE of a random effects model that ignore the spatial correlation; (ii) MLE described in Anselin (1988) which assumes that the individual effects are not spatially autocorrelated; (iii) MLE described in Kapoor, et al. (2006) which assumes that both the individual effects and the remainder error are governed by the same spatial autocorrelation; (iv) MLE described in Baltagi, et al. (2006) which allows the spatial correlation parameter for the individual effects to be different from that of the remainder error term. The latter model encompasses the other models and allows the researcher to test these specifications as restrictions on the general model using LM and LR tests. In fact, based on these tests, we suggest a pretest estimator which is shown to perform well in Monte Carlo experiments, ranking a close second to the true MLE in mean squared error performance.

DISTURBANCE INDUCES THE CONTRASTING EVOLUTION OF REINFORCEMENT AND DISPERSIVENESS IS DIRECTED AND RANDOM MOVERS

Spatial models commonly assume that dispersal rates are constant across individuals and environments and that movement directions are unbiased. These random-movement assumptions are inadequate to capture the range of dispersal behaviors revealed in diverse case studies. We examine an alternative assumption of directed movement, in which dispersal is a conditional and directional response by individuals to varying environmental conditions. Specifically, we assume individuals bias their movements to climb spatial fitness gradients. We compare the consequences of random and directed movement for local adaptation, the evolution of dispersal, and the reinforcement process. The implications of each movement strategy depend on the nature of environmental disturbance, and we examine the outcomes for undisturbed environments and with uncorrelated and autocorrelated disturbances. Both movement strategies offer advantages over sedentary life histories by allowing colonization of suitable habitats. However, random movement eventually becomes costly in stable environments because it inhibits local adaptation. In contrast, directed movement accelerates local adaptation. In disturbed environments, random movement offers bet-spreading advantages by distributing offspring across habitats. Despite being a more targeted strategy, an intermediate amount of directed movement provides similar bet-spreading benefits. These fitness consequences have implications for the evolution of dispersal. Dispersiveness is lost by random movers in undisturbed environments, is maintained in polymorphism with infrequent disturbances, and evolves when disturbances are uncorrelated. Directed movement becomes selectively neutral in the absence of disturbance, evolves when disturbances are autocorrelated, and is maintained in polymorphism with uncorrelated disturbances. Disturbance also determines the outcome of the reinforcement process for each strategy. For example, directed movers show no progress toward reinforcement in undisturbed environments, evolve random mating with uncorrelated disturbances, and can evolve assortative mating in infrequently disturbed environments.

DISTURBANCE INDUCES THE CONTRASTING EVOLUTION OF REINFORCEMENT AND DISPERSIVENESS IN DIRECTED AND RANDOM MOVERS

Spatial models commonly assume that dispersal rates are constant across individuals and environments and that movement directions are unbiased. These random-movement assumptions are inadequate to capture the range of dispersal behaviors revealed in diverse case studies. We examine an alternative assumption of directed movement, in which dispersal is a conditional and directional response by individuals to varying environmental conditions. Specifically, we assume individuals bias their movements to climb spatial fitness gradients. We compare the consequences of random and directed movement for local adaptation, the evolution of dispersal, and the reinforcement process. The implications of each movement strategy depend on the nature of environmental disturbance, and we examine the outcomes for undisturbed environments and with uncorrelated and autocorrelated disturbances. Both movement strategies offer advantages over sedentary life histories by allowing colonization of suitable habitats. However, random movement eventually becomes costly in stable environments because it inhibits local adaptation. In contrast, directed movement accelerates local adaptation. In disturbed environments, random movement offers bet-spreading advantages by distributing offspring across habitats. Despite being a more targeted strategy, an intermediate amount of directed movement provides similar bet-spreading benefits. These fitness consequences have implications for the evolution of dispersal. Dispersiveness is lost by random movers in undisturbed environments, is maintained in polymorphism with infrequent disturbances, and evolves when disturbances are uncorrelated. Directed movement becomes selectively neutral in the absence of disturbance, evolves when disturbances are autocorrelated, and is maintained in polymorphism with uncorrelated disturbances. Disturbance also determines the outcome of the reinforcement process for each strategy. For example, directed movers show no progress toward reinforcement in undisturbed environments, evolve random mating with uncorrelated disturbances, and can evolve assortative mating in infrequently disturbed environments.

The Tests of Robinson in the Context of AR(1) Disturbances

This paper examines a version of the tests of P. M. Robinson for testing unit roots and other fractionally integrated hypotheses in the context of autocorrelated disturbances. We use Monte Carlo simulations to examine the finite-sample behaviour of the tests when the disturbances follow AR(1) processes. Using the asymptotic critical values of the normal distribution, we show that the power of the tests is extremely low in some cases. Finite-sample critical values were then computed and the problem still persists unless we calculate these critical values for specific values of the AR parameters. An empirical application, illustrating this problem, is also carried out at the end of the article.

Individual Observation Process Monitoring Charts for Systems with Response Lags

Previously, it has been held that statistical process control and engineering process control were two distinct domains for process improvement. However, we design four control policies to integrate the two approaches using a proportional-integral-derivative feedback controller and Shewhart or moving centerline exponentially weighted moving average charts. We specifically consider the impact of these policies for a system with response lags modeled by a second-order dynamic process and autocorrelated nonstationary outside disturbances. These policies are implemented using simulation and applied in a case study of a liquid tank system. Our investigation shows this approach is effective with respect to overall system performance, including quality and cost.

Evolutionary operation and control of chromatographic processes

AbstractA novel generalized run‐to‐run control (GR2R) control strategy is presented for the optimization and control of nonlinear preparative chromatographic processes. The GR2R approach synergistically employs a hybrid (both physical and empirical) model to control chromatographic processes in the presence of sporadic and autocorrelated disturbances. First, parameters of the physical model through experiments are determined, and then the physical model is used to estimate initial parameters of the nonlinear empirical model (Hammerstein) using orthogonal forward regression. Parameters of the nonlinear empirical model are updated at the end of each run using a nonlinear recursive parameter estimation method. The updated empirical model is then used in the control algorithm (model predictive control) to estimate operating conditions for the next batch. Processes operating under fixed optimal conditions are compared with those operating with GR2R control for both gradient and displacement chromatography. The GR2R outperforms the fixed conditions in the presence of various disturbances (such as bed capacity, column efficiency, and feed load) and is an effective strategy for the optimization and control of complex chromatographic processes.

Unemployment and input prices: a fractional cointegration approach

This paper examines the relationship between unemployment, real oil price and real interest rates in Canada. Instead of following the classical approach based on I(0) stationarity or I(1) cointegrating relationships, fractional integration/cointegration techniques are used which allow for the possibility that unemployment is highly persistent. In line with other studies, it is found that all three variables are I(1). But only cointegration is found in the presence of autocorrelated disturbances, which means that the relationship between these variables also has a dynamic component. Furthermore, there is evidence of fractional (as opposed to classical) cointegration, which implies long memory and slow reversion to equilibrium. This suggests that an equilibrium model with highly persistent shocks might be adequate to account for the observed behaviour of unemployment.

Specification of autocorrelated disturbances in non-linear regression model

Non-linear regression models are encountered quite often in various business and economic data analysis. In the case of time dependent regression models the autocorrelations in error is almost inevitable. Following Kumar (1987) this paper discusses a new method based on the theory of Pade approximation for the specification of error structure in the context of non-linear regression model. It has been shown through simulation studies that the method can be successfully used to specify the error structure, which follows an ARMA model. An application of the above method on a real data set, which follows a non-linear model, is also given.

Spatially autocorrelated disturbances and patterns in population synchrony

Spatially synchronous population dynamics have been documented in many taxa. The prevailing view is that the most plausible candidates to explain this pattern are extrinsic disturbances (the Moran effect) and dispersal. In most cases disentangling these factors is difficult. Theoretical studies have shown that dispersal between subpopulations is more likely to produce a negative relationship between population synchrony and distance between the patches than perturbations. As analyses of empirical data frequently show this negative relationship between the level of synchrony and distance between populations, this has emphasized the importance of dispersal as a synchronizing agent. However, several weather patterns show spatial autocorrelation, which could potentially produce patterns in population synchrony similar to those caused by dispersal. By using spatially extended versions of several population dynamic models, we show that this is indeed the case. Our results show that, especially when both factors (spatially autocorrelated perturbations and distance–dependent dispersal) act together, there may exist groups of local populations in synchrony together but fluctuating asynchronously with some other groups of local populations. We also show, by analysing 56 long–term population data sets, that patterns of population synchrony similar to those found in our simulations are found in natural populations as well. This finding highlights the subtlety in the interactions of dispersal and noise in organizing spatial patterns in population fluctuations.

A Monte Carlo study of some limited and full information simultaneous equation estimators with normal and nonnormal autocorrelated disturbances

The purpose of this paper is to examine the small sample properties of various limited and full information estimators of the structural coefficients of a system of two equations. Specifically, we consider a first-order autoregressive error structure under normal and nonnormal disturbances — for four different covariance structures — and report on a Monte Carlo study of the small sample behavior of limited and full information estimators according to the criteria of bias and dispersion. The results show that the differences in performance of the estimators for the alternative forms of the disturbance distributions are large. Moreover, none of the examined estimators is superior relative to the others, in the sense that its bias and dispersion are the smallest for at least one form of the disturbance distribution. Finally, no combination of highly or lowly autocorrelated disturbances favors some specific limited or full information estimator.

Teaching Regressions with a Lagged Dependent Variable and Autocorrelated Disturbances

The author attempts to rectify the unsatisfactory textbook treatment of the finite-sample properties of estimators of regression models with a lagged dependent variable and autocorrelated disturbances. He contends that the bias of the OLS estimator of a regression model with a lagged dependent variable and autocorrelated disturbances is determined by two effects, the dynamic effect and the correlation effect, which may be reinforcing or offsetting. The implications of these two effects are explored within a theoretical and a Monte Carlo framework.