scholarly journals Research of New Criteria for Detecting First-order Residuals Autocorrelation in Regression Models

2018 ◽  
pp. 13-25
Author(s):  
M. P. Bazilevsky
Keyword(s):  
Mathematical Programming ◽  
Regression Model ◽  
Least Squares ◽  
Regression Models ◽  
Linear Constraints ◽  
Mathematical Programming Problem ◽  
First Order ◽  
Watson Statistic ◽  
Auto Regression ◽  
New Criteria

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.

scholarly journals Formulating Intuitionistic Fuzzy Regression Models: A Mathematical Programming Approach

2021 ◽  
Author(s):  
Sheng-Hsing Nien ◽  
Liang-Hsuan Chen
Keyword(s):  
Mathematical Programming ◽  
Regression Models ◽  
Fuzzy Regression ◽  
Distance Measures ◽  
Programming Approach ◽  
Mathematical Programming Problem ◽  
Explanatory Variables ◽  
Intuitionistic Fuzzy ◽  
Mathematical Programming Approach ◽  
Ordinary Regression

Abstract This study develops a mathematical programming approach to establish intuitionistic fuzzy regression models (IFRMs) by considering the randomness and fuzziness of intuitionistic fuzzy observations. In contrast to existing approaches, the IFRMs are established in terms of five ordinary regression models representing the components of the estimated triangular intuitionistic fuzzy response variable. The optimal parameters of the five ordinary regression models are determined by solving the proposed mathematical programming problem, which is linearized to make the resolution process efficient. Based on the concepts of randomness and fuzziness in the formulation processes, the proposed approach can improve on existing approaches’ weaknesses with establishing IFRMs, such as the limitation of symmetrical triangular membership (or non-membership) functions, the determination of parameter signs in the model, and the wide spread of the estimated responses. In addition, some numerical explanatory variables included in the intuitionistic fuzzy observations are also allowed in the proposed approach, even though it was developed for intuitionistic fuzzy observations. In contrast to existing approaches, the proposed approach is general and flexible in applications. Comparisons show that the proposed approach outperforms existing approaches in terms of similarity and distance measures.

Time Series Analysis of Ultrasonic Observations of Gross Fetal Body Movements during the Last 10 Weeks of Pregnancy

1981 ◽  
Vol 3 (4) ◽  
pp. 330-341 ◽  
Author(s):  
Karen Campbell ◽  
Ian MacNeill ◽  
John Patrick
Keyword(s):  
Time Series ◽  
Spectral Analysis ◽  
Time Series Analysis ◽  
Regression Model ◽  
Body Movement ◽  
Frequency Range ◽  
Body Movements ◽  
Significant Power ◽  
First Order ◽  
Auto Regression

Thirty fetuses were observed for 24 hours and one fetus was observed for 20 hours during the last 10 weeks of gestation. Observations were made of the amount of gross fetal body movement in each successive 5 minute observation epoch, thus resulting in 30 time series of 288 observations and one time series of 240 observations. Spectral analysis of these time series demonstrated the presence of significant power in the frequency range of 0.002 to 0.0175 cpm. Application of Box-Jenkins techniques to the time series resulted in the choice of a first-order auto-regression model to fit the data. It was concluded that the incidence of episodes of gross fetal body movements were non-random and were, in fact, pseudoperiodic.

scholarly journals Approach to optimizing charging infrastructure of autonomous trolleybuses for urban routes

Informatics ◽  
2021 ◽  
Vol 18 (4) ◽  
pp. 79-95
Author(s):  
М. Ya. Kovalyov ◽  
B. M. Rozin ◽  
I. A. Shaternik
Keyword(s):  
Mathematical Programming ◽  
Service Life ◽  
Objective Function ◽  
Heuristic Method ◽  
Cost Effective ◽  
Linear Constraints ◽  
Mathematical Programming Problem ◽  
Electric Transport ◽  
Charging Infrastructure ◽  
Charging Stations

P u r p o s e s.  When designing a system of urban electric transport that charges while driving, including autonomous trolleybuses with batteries of increased capacity, it is important to optimize the charging infrastructure for a fleet of such vehicles. The charging infrastructure of the dedicated routes consists of overhead wire sections along the routes and stationary charging stations of a given type at the terminal stops of the routes. It is designed to ensure the movement of trolleybuses and restore the charge of their batteries, consumed in the sections of autonomous running.The aim of the study is to create models and methods for developing cost-effective solutions for charging infrastructure, ensuring the functioning of the autonomous trolleybus fleet, respecting a number of specific conditions. Conditions include ensuring a specified range of autonomous trolleybus running at a given rate of energy consumption on routes, a guaranteed service life of their batteries, as well as preventing the discharge of batteries below a critical level under various operating modes during their service life.M e t ho d s. Methods of set theory, graph theory and linear approximation are used.Re s u l t s. A mathematical model has been developed for the optimization problem of the charging infrastructure of the autonomous trolleybus fleet. The total reduced annual costs for the charging infrastructure are selected as the objective function. The model is formulated as a mathematical programming problem with a quadratic objective function and linear constraints.Co n c l u s i o n. To solve the formulated problem of mathematical programming, standard solvers such as IBM ILOG CPLEX can be used, as well as, taking into account its computational complexity, the heuristic method of "swarm of particles".  The solution to the problem is to select the configuration of the location of the overhead wire sections on the routes and the durations of charging the trolleybuses at the terminal stops, which determine the corresponding number of stationary charging stations at these stops.

scholarly journals On consistency of recursive least squares identification algorithms for controlled auto-regression models

2008 ◽  
Vol 32 (11) ◽  
pp. 2207-2215 ◽  
Author(s):  
Yongsong Xiao ◽  
Feng Ding ◽  
Yi Zhou ◽  
Ming Li ◽  
Jiyang Dai
Keyword(s):  
Least Squares ◽  
Regression Models ◽  
Recursive Least Squares ◽  
Auto Regression

scholarly journals Identification of Dynamical Systems Through the Structure of Auto-regression With Exogenous Variable by Decreasing Gradient and Least Squares

2021 ◽  
Vol 20 ◽  
pp. 676-682
Author(s):  
Andres Morocho Caiza ◽  
Erik F. Mendez Garces ◽  
Gabriela Mafla ◽  
Joseph Guerra ◽  
Williams Villalba
Keyword(s):  
Dynamical Systems ◽  
Least Squares ◽  
Least Squares Method ◽  
Exogenous Variable ◽  
Pass Band ◽  
Estimation Of Parameters ◽  
Pass Filter ◽  
First Order ◽  
High Pass ◽  
Auto Regression

In this article was made the identification of dynamic systems of first and second order more common in electronics such as low and high pass filters of the first order, pass-band filter and direct current motor through the structure of auto-regression with exogenous variable. The proposed dynamical systems are initially modeled by a continuous-time transfer function using physical laws. Subsequently, a step entry signal was applied and the data for the identification process was recorded in discrete time. The estimation of parameters was performed with the method of decreasing gradient and least squares. It was obtained as a result that the least squares method could not find a model for the first-order high-pass filter, but the decreasing grade method allowed to model all the proposed systems.

Alternative Models for Forecasting Macroeconomic Indicators in Kazakhstan

2017 ◽  
Vol 4 (1) ◽  
pp. 1-15
Author(s):  
Saken Pirmakhanov
Keyword(s):  
Time Series ◽  
Regression Model ◽  
Regression Models ◽  
Error Prediction ◽  
Optimal Model ◽  
Short Term ◽  
Macroeconomic Indicators ◽  
Vector Auto Regression ◽  
In Virtue Of ◽  
Auto Regression

This paper indicates special aspects of using vector auto-regression models to forecast rates of basic macroeconomic indicators in short term. In particular, traditional vector auto-regression model, Bayesian vector auto-regression model and factor augmented vector auto-regression model are shown. For parameter estimation of these models the author uses time series of Kazakhstani macroeconomic indicators between 1996 and 2015 quarterly. In virtue of mean-root-square error prediction the conclusion of optimal model is going to be chosen.

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