Modified Breusch-Godfrey Test for Restricted Higher Order Autocorrelation in Dynamic Linear Model – A Distance Based Approach

The four most readily available tests of autocorrelation in dynamic models namely Durbin’s M test, Durbin’s H test, Breusch Godfrey test (BGF) and Ljung & Box (Q) test are compared in terms of their power for varying sample sizes, levels of autocorrelation and significance using Monte Carlo simulations in STATA. Power comparison reveals that the Durbin M test is the best option for testing the hypothesis of no autocorrelation in dynamic models for all sample sizes. Breusch Godfrey’s test has comparable and at times minutely better performance than Durbin’s M test however in small sample sizes, Durbin’s M test outperforms the Breusch Godfrey test in terms of power. The Durbin H and the Ljung & Box Q tests consistently occupy the second last and last positions respectively in terms of power performance with maximum power gap of 63 & 60% respectively from the best test (M test).

The existence of many different dynamic large eddy simulation (LES) methods leads to questions about the theoretical foundation of dynamic LES methods. It was shown recently that the use of stochastic analysis enables a theoretically well based systematic derivation of a realizable linear dynamic model (LDM) and a realizable nonlinear dynamic model (NDM). A priori and a posteriori analyses of turbulent channel flow are used here to study the characteristic properties of these dynamic models. The LDM and NDM are compared with other dynamic models: the non-stabilized and stabilized dynamic Smagorinsky model (DSM), which is used in many applications of LES, and Wang-Bergstrom's dynamic model (WBDM), which represents an extension of the DSM. The DSM and WBDM do not represent realizable models because they are not derived as consequences of a realizable stochastic process. The comparisons reported here show that the LDM and NDM are based on a dynamic model formulation that avoids shortcomings of existing concepts. The LDM and NDM account for backscatter, and they are computationally stable without any modification. The LDM and NDM represent the instantaneous small scale structure of turbulence very well. Compared to the DSM and WBDM, respectively, the LDM and NDM are computationally more efficient.

Research purpose: The current work introduces a novel method for time series discriminant analysis (DA). Proposing a version for the Bayes classifier employing Dynamic Linear Models, which we denote by BCDLM This article explores the application of DLMs and the Bayes Classifier in time series classification to promote application in sustainability across diverse sectors. Method: This paper presents some computer simulation studies in which we generate four different scenarios corresponding to time series observations from various Dynamic Linear Models (DLMs). In Discriminant Analysis, we investigated strategies for estimating variance in models and compared the performance of the BCDLM with other common classifiers. Such datasets are composed of real-time series (data from SONY AIBO Robot and spectrometry of coffee types) and pseudo-time series (data from Swedish leaves adapted for time series). We also point out that algorithm was used to determine training and test sets in real-world applications. Results: Considering the real-time series examined in this paper, The results obtained indicate that the parametric approach developed represents a promising alternative for this class of DA problems, with observations of time series in a situation that is quite difficult in practice when we have series with large sizes with respect to the number of observations in the classes, even though more thorough studies are required. Conclusions: It concludes that the BCDLM performed comparably to the results of the classifiers 1NN, RDA, NBND and NBK and superior to the methods LDA and QDA. This offers a powerful combination for time series classification, enabling accurate predictions and informed decision-making in areas such as energy consumption, waste management, and resource allocation.

The increasing prevalence of multiple, long time series data fuels the hope for gaining better understanding and more precise prediction of various phenomena in many domains, hence calling for the development of new methodologies in time series analysis. Two features pertinent to the practical usefulness of any time series model are sparsity and causality. A sparse time series model means that only a small subset of model parameters are non-zero, which is usually preferable to its non-sparse counterparts in terms of interpretability, robustness, parsimony and estimation variability. Causality refers to the dependence structure for which only past and present information is used. Causality is an indispensable feature for certain purposes such as prediction, and is usually desirable when modeling real-world phenomena. This dissertation devotes to the development of two time series methodologies that incorporate sparsity and causality. In the first part of the thesis, we introduce the sparse causal dynamic linear regression model. Two approaches are proposed for construction of such models. The first one utilizes the frequency domain solution of a classic two-sided dynamic linear model and augments it with a simple soft-thresholding operator. This approach is computationally efficient and enjoys good performance theoretically and empirically under the assumption that the true dynamic regression relationship is causal and sparse. The second approach constructs a sparse causal dynamic linear model by minimizing certain penalized mean squared prediction error. This approach is computationally intensive but is superior to the first approach as it does not require the causal assumption. It enjoys better empirical performance and opens up meaningful extensions. In the second part of the thesis, we introduce the sparse causal dynamic principal component analysis. This procedure also has two variants. The first one computes the principal component series as a sparse and causal linear filter of the original data. The filter is obtained by minimizing a penalized reconstruction loss functional in the frequency domain. The principal component series so obtained enjoys good performance in terms of summarizing high-dimensional data, estimating factors in dynamic factor models, and prediction. However, it is computationally intensive. The second approach imposes sparsity structure on the innovation representation of the data generating process, which leads to simpler computational algorithms. In addition, this method is of interest in its own right for certain applications in finance and econometrics.

This chapter provides a step-by-step review of Monte Carlo (MC) methods for filtering in general nonlinear and non-Gaussian dynamic models, also known as state-space models or hidden Markov models. The chapter is organized as follows. Section 11.2 introduces the basic notation, results, and references for the general class of Gaussian dynamic linear models (DLM), the AR(1) plus noise model, and the standard stochastic volatility model with AR(1) dynamics. Sections 11.3 and 11.4 discuss particle filters for state learning with fixed parameters (also known as pure filtering) and particle filters for state and parameter learning, respectively. Section 11.5 deals with general issues, such as MC error, sequential model checking, particle smoothing, and the interaction between particle filters and Markov chain Monte Carlo (MCMC) schemes.

This study examined the impact of private domestic investment on manufacturing sector output in Nigeria from 1970 to 2017. The study specifically looked at the impact of private domestic investment on manufacturing sector’s output in a static and dynamic model. Six variables were employed in the study and were sourced from CBN statistical bulletin and World Development Indicators for the period covering from 1970 to 2017. The analysis of the variables undergoes three approaches, the pre-analysis of data, model estimation and the diagnostic analysis of the model. The first approach employed tables and graphs to explain the behaviour of the data, equally the univariate analysis of the data were examine with the Augmented Dickey-Fuller equations and the possibility of long-term relationship. The models were estimated with the ARDL estimator and model selected with the Akaike Information Criteria, and finally the models estimated were tested using the Jaque-Bera statistics, Ramsey RESET Test, Breusch-Godfrey and Harvey test for residual normality, specification bias, autocorrelation and heteroskedasticity respectively. The results from the analytical methods shows that there is over 82 percent increase in the output of Manufacturing sector in the late 1970s and early 1980s and over 98 percent increase the output of the manufacturing sector in the late within 2010 and 2015. Also, the study observed that the responses of output of the manufacturing sector to private domestic investment are positive and significant in the static and dynamic models. The study found that the impact of private domestic investment on manufacturing sector output were fairly elastic in the static model and fairly inelastic in the dynamic model. Finally, the study found that the model have a weak adjustment mechanism. The adjustment of disequilibrium between static and dynamic equilibrium is weak or just 24.9 percent. Since private domestic investment is significant and positively impacted on the performance of the manufacturing sector irrespective of the time zone, the study recommended for increase in the credit to private sector by the apex monetary authority.

The aim of the study is to analyze and prediction of return for 15 popular banks in Chittagong Stock Exchange. The economic development of a country depends largely on the effective performance of stock market. In this study, secondary data from the CSE, Bangladesh with a sample period 1st January 2009 to 27th December 2015 for selected 15 banks, listed in Chittagong Stock Exchange. Descriptive statistics, important graphs, statistical tests, fitted dynamic regression models with ARCH effect are used to complete the analysis. It is found that for all banks, the return occurs high with a high risk and risk is low for the companies with small amount of return. The daily log returns for all companies are almost normally distributed. Checking the stationarity of the log returns data getting from all banks in both graphical and statistical unit root method, time series data are found to be stationary. In the dynamic regression model the log return Yt is considered as dependent variable and the log daily average Xt is considered as independent variable. The average VIF for the returns of all banks are found less than 10, indicate not severity of multicollinearity and ∆Yt , ∆2Yt , ∆Xt , ∆2Xt can be used as the explanatory variables in the model where ∆ indicates the difference operator. Lagrange multiplier (LM) test based on the residuals of the regression model is significant for all the banks implies that the data have the conditional heteroscadisticity in the behavior of their residuals. The line diagrams conferred the complete randomness in Parkinson’s monthly volatility for every company. The log return of six out of 15 banks have significant ARCH effect with 2 period lags and rest of the banks, the log returns have significant ARCH effect with 1 period lag. The regression coefficients of and have the negative effects on and the other coefficients have both positive and negative effect. A modified ARDL (2,2) model is proposed and 1-step ahead forecasted model for different banks are recommended.One can try to estimate the confidence interval for the parameters used in modified model in his/her advanced research. Moreover, the other dynamic models such as GARCH, TGARCH, PARCH, EGARCH model and different dynamic panel data models such as Areonalo bond could be try to predict the data. Moreover, the other multivariate analysis such as canonical correlation analysis, factor analysis, cluster analysis and discriminant analysis can be done for further research on these data.

Mathematical models are efficient instrument of engines and their automatic control systems designing. The main areas of the models application are simulation modeling of the controlled object at analysis, synthesis and semi-natural simulation, and also model-based engine controlling algorithms designing. In this case, a set of mathematical models is used that is derived from the initial (base) thermo-gas-dynamic model of working process, which is usually designed and supported by the engine designer. However, it not satisfies the requirement of real-time calculations when the model simulates the engine dynamics at operation with the real electronic hardware. Lacking of the above-listed shortcomings dynamic model of the engine is formed as a combination of simplified static and dynamic models. In this case, the dynamic model has a linear structure and characterizes dynamic relations in a local area close to the engine static characteristics that is represented as the static model. This dynamic model can be determined by linearization of the base thermo-gas-dynamic model. The base model is grounded on characteristics of the engine components, which are built using experimental results and a peace-linear interpolation. Due to the peace-linear interpolation of the characteristics, relations between the engine parameters have breaks, that causes errors in calculations, which are done using the model, and not corresponds to real processes in the engine. The drastic method to overcome this problem is a perfection of thermo-gas-dynamic model by smoothing the characteristics of components. However, this will mismatch the model, which is used by the ASC designer, and the base model of the engine designer. This paper considers approximation of the dynamic model coefficients, which are determined using the component-based thermo-gas-dynamic model with the peace-linear interpolation of the components’ characteristics. The research is aimed in improvement of the used linear dynamic models in a state space and automation of their forming for the engine automatic control systems quality increasing and synthesis acceleration.

The paper presents the research progress on the disturbance rejection of Micro Air Vehicle (MAV) in Atmospheric Boundary Layer (ABL) area. The reaction torque of a bio-inspired reaction wheel mechanism inspired by active flight stabilization of Manduca sexta is applied to attenuate the disturbance resulted from unsteady flow fields. The advantage of using this mechanism is to help to recover the MAV posture quickly by applying reaction torque to attenuate the perturbed angle of the coaxial helicopter MAV flying in unsteady wind environments. Another advantage of adopting reaction wheel in coaxial helicopter is that it will replace traditional stabilizer bar or flyer bar to greatly stabilize flying attitude as well as to reduce the structure complexity and volume size induced by stabilizer bars or flyer bars. In this paper, we start to study the dynamic model and disturbance reject performance of stabilizer bar on the micro helicopter. To compare with stabilizer bars, the wind resistance reaction wheels were designed and a novel bio-inspired coaxial helicopter structure with the reaction wheel stabilization mechanism is presented. In addition, its nonlinear and linear dynamic models are derived by Lagrange method. Based on the established models, the PID controller is designed for reaction wheel stabilization system and dynamic responses of the actively controlled system are then extensively studied through simulations. Preliminary results verify the disturbance rejection and control performance of the bio-inspired reaction wheel stabilization mechanism.

Relationships exist between radiation belt electron flux intensities and solar drivers such as solar wind speed, ion density, and magnetic fields. The particulars of these relationships, however, are not well understood. Many forecasting models have been developed in the last 25 years, attempting to make sense of these relationships and produce accurate forecasts for electron flux intensities. We discuss some of the inherent limitations that many forecasting models (e.g., static models) possess when trying to untangle the intricate and dynamic relationships between electron flux levels and solar wind drivers. Dynamics related to the solar cycle limit physical interpretations for static forecasting models to customized and narrow time windows. Furthermore, the interrelatedness of solar drivers severely limit the ability to uniquely partition and describe the relationship between any one solar driver with electron flux levels. We suggest an alternate approach using dynamic linear models (DLMs). DLMs avoid some of the inherent limitations of physical understanding static models possess. We compare the 1 day ahead forecast accuracy of a relatively simple DLM to the current NOAA relativistic electron forecast model (REFM). The REFM does produce a more favorable prediction efficiency averaged across years when compared to the relatively simple DLM (0.749 to 0.721). However, the competitiveness of the DLM suggests that further development may lead to more accurate and interpretable models in the future.

We consider a single-step Lagrange multiplier (LM) test for joint breaks (at known or unknown dates) in the long memory parameter, the short-run dynamics, and the level of a fractionally integrated time-series process. The regression version of this test is easily implementable and allows to identify the specific sources of the break when the null hypothesis of parameter stability is rejected. However, its size and power properties are sensitive to the correct specification of short-run dynamics under the null. To address this problem, we propose a slight modification of the LM test (labeled LMW-type test) which also makes use of some information under the alternative (in the spirit of a Wald test). This test shares the same limiting distribution as the LM test under the null and local alternatives but achieves higher power by facilitating the correct specification of the short-run dynamics under the null and any alternative (either local or fixed). Monte Carlo simulations provide support for these theoretical results. An empirical application, concerning the origin of shifts in the long-memory properties of forward discount rates in five G7 countries, illustrates the usefulness of the proposed LMW-type test.

Testing panel data regression models with spatial error correlation

Climate-change-based global sea-level rise is of concern because it contributes to significant loss of coastal wetlands and mangroves and to increasing damage from coastal flooding in many regions of the world. Physical mechanisms that describe the dynamic global climate systems and the effect of this system behavior on sea-level rise are inherently complex. In this study, conducted using systematic analysis of historic data on temperature change and sea-level rise, a linear dynamic system model is proposed to predict global sea-level rise and mean surface temperatures. Unlike the semiempirical approaches proposed in the recent literature, this model incorporates the inherent interaction between temperature and sea-level rise into the model. The resulting model, recognized from the historic data, shows that the rate of sea-level rise is proportional to temperature, and this rise is also a function of the temporal state of the sea level. Similarly, the rate of temperature change is a function of the temporal state of the temperature and is also affected by the sea-level rise. The proposed model is also used to predict the sea-level rise during the 21st century. DOI: 10.1061/(ASCE)HE.1943-5584.0000447. © 2012 American Society of Civil Engineers. CE Database subject headings: Climate change; Sea level; Temperature effects; Dynamic models; Predictions. Author keywords: Climate change; Complex systems; Sea-level rise; Temperature change; Dynamic model.

Application of steady-state and dynamic modeling for the prediction of the BOD of an aerated lagoon at a pulp and paper millPart I. Linear approaches

When estimating regression models using the least squares method, one of its prerequisites is the lack of autocorrelation in the regression residuals. The presence of autocorrelation in the residuals makes the least-squares regression estimates to be ineffective, and the standard errors of these estimates to be untenable. Quantitatively, autocorrelation in the residuals of the regression model has traditionally been estimated using the Durbin-Watson statistic, which is the ratio of the sum of the squares of differences of consecutive residual values to the sum of squares of the residuals. Unfortunately, such an analytical form of the Durbin-Watson statistic does not allow it to be integrated, as linear constraints, into the problem of selecting informative regressors, which is, in fact, a mathematical programming problem in the regression model. The task of selecting informative regressors is to extract from the given number of possible regressors a given number of variables based on a certain quality criterion.The aim of the paper is to develop and study new criteria for detecting first-order autocorrelation in the residuals in regression models that can later be integrated into the problem of selecting informative regressors in the form of linear constraints. To do this, the paper proposes modular autocorrelation statistic for which, using the Gretl package, the ranges of their possible values and limit values were first determined experimentally, depending on the value of the selective coefficient of auto-regression. Then the results obtained were proved by model experiments using the Monte Carlo method. The disadvantage of the proposed modular statistic of adequacy is that their dependencies on the selective coefficient of auto-regression are not even functions. For this, double modular autocorrelation criteria are proposed, which, using special methods, can be used as linear constraints in mathematical programming problems to select informative regressors in regression models.