In statistics, the BreuschâGodfrey test, named after Trevor S. Breusch and Leslie G. Godfrey,[1][2] is used to assess the validity of some of the modelling assumptions inherent in applying regression-like models to observed data series. In particular, it tests for the presence of serial correlation that has not been included in a proposed model structure and which, if present, would mean that incorrect conclusions would be drawn from other tests, or that sub-optimal estimates of model parameters are obtained if it is not taken into account. The regression models to which the test can be applied include cases where lagged values of the dependent variables are used as independent variables in the model's representation for later observations. This type of structure is common in econometric models.
Hi, I used Eviews programming to calculate the LM test statistics for residual serial correlation. The result I calculated is different from the one provided by Eviews function. In this set of lecture notes we will learn about heteroskedasticity and serial correlation. They are closely related problems so I will deal with them. Sep 14, 2015 Re: LM test for serial correlation. I am new to the programming of Eviews. My intention was to conduct LM test for lag order from 1 to 6, so I use the for loop. In the attached code, the @nan could not be used with lag order, so I generate 6 residual series with zero presample for the case of lag.
Formula a symbolic description for the model to be tested (or a ï¬tted 'lm' object). Order integer. Maximal order of serial correlation to be tested. Order.by Either a vector z or a formula with a single explanatory variable like z.
Because the test is based on the idea of Lagrange multiplier testing, it is sometimes referred to as LM test for serial correlation.[3]
A similar assessment can be also carried out with the DurbinâWatson test and the LjungâBox test.
Background[edit]![]()
The BreuschâGodfrey serial correlation LM test is a test for autocorrelation in the errors in a regression model. It makes use of the residuals from the model being considered in a regression analysis, and a test statistic is derived from these. The null hypothesis is that there is no serial correlation of any order up to p.[4]
The test is more general than the DurbinâWatson statistic (or Durbin's h statistic), which is only valid for nonstochastic regressors and for testing the possibility of a first-order autoregressive model (e.g. AR(1)) for the regression errors.[citation needed] The BG test has none of these restrictions, and is statistically more powerful than Durbin's h statistic.[citation needed]
Procedure[edit]
Consider a linear regression of any form, for example
Windows 8 boot to desktop instead of metro. where the errors might follow an AR(p) autoregressive scheme, as follows:
The simple regression model is first fitted by ordinary least squares to obtain a set of sample residuals u^t{displaystyle {hat {u}}_{t}}.
Breusch and Godfrey[citation needed] proved that, if the following auxiliary regression model is fitted
and if the usual R2{displaystyle R^{2}} statistic is calculated for this model, then the following asymptotic approximation can be used for the distribution of the test statistic
when the null hypothesis H0:{Ïi=0 for all i}{displaystyle {H_{0}:lbrace rho _{i}=0{text{ for all }}irbrace }} holds (that is, there is no serial correlation of any order up to p). Here n is the number of alttext='{displaystyle {hat {u}}_{t}}'>u^t{displaystyle {hat {u}}_{t}},
where T is the number of observations in the basic series. Note that the value of n depends on the number of lags of the error term (p).
Software[edit]
See also[edit]References[edit]Serial Correlation Problem
Further reading[edit]![]()
Lm Test Serial Correlation Eviews
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