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Abstract
This paper provides a basic investigation of an R-square and sum-square error (SSE) in a linear regression model with the errors following a first-order autoregressive process in which the autocorrelation coefficients are non-zero. The consideration and measurement of the model are difficult to control, thus a computer stimulation is necessary to corroborate how the R-square and SSE are affected by the autocorrelation coefficients. The evidence reveals that the R-square and SSE differ in the ranges of positive and negative autocorrelation coefficients. The results show that it would require one to verify the estimators including the R-square or SSE for testing non-zero autocorrelation coefficients.
Keywords: Autocorrelation Coefficient, First-order Autoregressive Process, R-square, Computer Simulation
JEL Classification: C15, C22, C63
1. Introduction
Serial correlation tests play an important role in investigating whether or not data has autocorrelation (Breusch and Godfrey, 1980; Durbin and Watson, 1950, 1951; Silvey, 1959). Those serial correlation tests are composed of the residuals or R-square. In advance, Lagrange multiplier test (LM test) with combination of R-square is applied in hypothesis and testing for dependence both within and between the cross-sectional units (McCoskey and Kao, 1998, Westerlund and Edgerton, 2007), heteroskedasticity test in panel data (Baltagi et al., 2003, 2007, Debarsy and Ertur, 2010, Fumo, 2000, McAleer and Medeiros, 2008, Tse, 2002), bootstrap tests for serial correlation (Godfrey and Tremayne, 2005, and Godfrey, 2007), for example, Godfrey (2007) implemented the F-statistic from LM test with three bootstrapping tests in dynamic regression models of the higher-order autocorrelation models with nonnormal disturbances and proposed that the F-statistic can improve control of finite sample significance levels have been examined. However, LM test is suitable for the large number cases, but no researchers can define how many samples can be viewed as large number. Another question is about that a non-zero autocorrelation coefficient takes a linear regression model into a nonlinear and restricted regression model in a time-series analysis. Literature has supported few studies about the hypothesis and testing-or the point and interval estimation-of non-zero autocorrelation coefficients. Lee (2014a, 2014b) only discussed the limiting properties of Durbin-Watson test statistic and the verification of the residuals that are not good estimator of the errors, while Lee did not discuss in advance the sum-square-error (SSE) or the R-square...