Lee, MeiYu (2014): Computer Simulates the Effect of Internal Restriction on Residuals in Linear Regression Model with Firstorder Autoregressive Procedures. Published in: Computer Simulates the Effect of Internal Restriction on Residuals in Linear Regression Model with Firstorder Autoregressive Procedures , Vol. 3, No. 3 (October 2014): pp. 122.

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Abstract
This paper demonstrates the impact of particular factors – such as a nonnormal error distribution, constraints of the residuals, sample size, the multicollinear values of independent variables and the autocorrelation coefficient – on the distributions of errors and residuals. This explains how residuals increasingly tend to a normal distribution with increased linear constraints on residuals from the linear regression analysis method. Furthermore, reduced linear requirements cause the shape of the error distribution to be more clearly shown on the residuals. We find that if the errors follow a normal distribution, then the residuals do as well. However, if the errors follow a Uquadratic distribution, then the residuals have a mixture of the error distribution and a normal distribution due to the interaction of linear requirements and sample size. Thus, increasing the constraints on the residual from more independent variables causes the residuals to follow a normal distribution, leading to a poor estimator in the case where errors have a nonnormal distribution. Only when the sample size is large enough to eliminate the effects of these linear requirements and multicollinearity can the residuals be viewed as an estimator of the errors.
Item Type:  MPRA Paper 

Original Title:  Computer Simulates the Effect of Internal Restriction on Residuals in Linear Regression Model with Firstorder Autoregressive Procedures 
English Title:  Computer Simulates the Effect of Internal Restriction on Residuals in Linear Regression Model with Firstorder Autoregressive Procedures 
Language:  English 
Keywords:  Time series; Autoregressive model; Computer simulation; Nonnormal distribution 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C15  Statistical Simulation Methods: General C  Mathematical and Quantitative Methods > C3  Multiple or Simultaneous Equation Models ; Multiple Variables > C32  TimeSeries Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes ; State Space Models C  Mathematical and Quantitative Methods > C6  Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C63  Computational Techniques ; Simulation Modeling 
Item ID:  60362 
Depositing User:  MeiYu Lee 
Date Deposited:  04 Dec 2014 13:08 
Last Modified:  26 Sep 2019 22:02 
References:  [1] B.H. Baltagi, Econometrics, Fifth edition, Springer: New York, 2011. [2] C.F. Roos, Annual Survey of Statistical Techniques: The Correlation and Analysis of Time SeriesPart II, Econometrica, 4(4), (1936), 368381. [3] G.E. Box, D.A. Pierce, Distribution of Residual Autocorrelations in Autoregressiveintegrated Moving Average Time Series Models, Journal of the American Statistical Association, 65(332), (1970), 15091526. [4] G.U. Yule, On the TimeCorrelation Problem, with Especial Reference to the VariateDifference Correlation Method, Journal of the Royal Statistical Society, 84(4), (1921), 497537. [5] J. Durbin, G.S. Watson, Testing for Serial Correlation in Least Squares Regression: I, Biometrika, 37(3/4), (1950), 409428. [6] J. Durbin, G.S. Watson, Testing for Serial Correlation in Least Squares Regression. II, Biometrika, 38(1/2), (1951), 159177. [7] M.Y. Lee, The Pattern of RSquare in Linear Regression Model with FirstOrder Autoregressive Error Process and Bayesian property: Computer Simulation, Journal of Accounting & Finance Management Strategy, 9(1), (2014a). [8] M.Y. Lee, Limiting Property of DurbinWatson Test Statistic, manuscript, (2014b). [9] M.Y. Lee, The Conflict of Residual and Error Simulated in Linear Regression Model with AR(1) Error Process, manuscript, (2014c). [10] T.S. Breusch, L.G. Godfrey, A review of recent work on testing for autocorrelation in dynamic economic models," University of Southampton, (1980). 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/60362 