Computer Simulates the Effect of Internal Restriction on Residuals in Linear Regression Model with First-order Autoregressive Procedures

Mei-Yu Lee

MPRA Paper from University Library of Munich, Germany

Abstract: This paper demonstrates the impact of particular factors – such as a non-normal error distribution, constraints of the residuals, sample size, the multi-collinear 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 U-quadratic 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 non-normal distribution. Only when the sample size is large enough to eliminate the effects of these linear requirements and multi-collinearity can the residuals be viewed as an estimator of the errors.

Keywords: Time series; Autoregressive model; Computer simulation; Non-normal distribution (search for similar items in EconPapers)
JEL-codes: C15 C32 C63 (search for similar items in EconPapers)
Date: 2014
New Economics Papers: this item is included in nep-ecm
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Citations: View citations in EconPapers (1)

Published in Computer Simulates the Effect of Internal Restriction on Residuals in Linear Regression Model with First-order Autoregressive Procedures 3.3(2014): pp. 1-22

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