Stata panel serial correlation test

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Dissertation Writing Service. MBA Writing Service. Technical and Statistical Services. Editing and Proofreading Service. Personal Statement Writing Service. Overview When performing a panel regression analysis in Stata , additional diagnostic tests are run to detect potential problems with residuals and model specification.

Diagnostics Tests Unlike traditional OLS regressions, panel regression analysis in Stata does not come with a good choice of diagnostic tests such as the Breusch-Pagan test for panel regressions. Serial Correlation Similar to the heteroscedasticity test, serial correlation in panel regressions is also tested by downloading user-written modules in Stata.

Therefore, when du and dl are plotted on the scale, the results are as follows figure below. The Durbin Watson test relies upon the assumption that the distribution of residuals are normal whereas the Breusch-Godfrey LM test is less sensitive to this assumption.

Another advantage of this test is that it allows researchers to test for serial correlation through a number of lags besides one lag that is a correlation between the residuals between time t and t-k where k is the number of lags.

This is unlike the Durbin Watson test which allows testing for only correlation between t and t Therefore if k is 1, then the results of the Breusch-Godfrey test and Durbin Watson test will be the same. Since from the above table, chi2 is less than 0. In other words, there is a serial correlation between the residuals in the model. Therefore correct for the violation of the assumption of no serial correlation.

At the end of the results, finally, calculate original and new Durbin Watson statistics as follows. The New D-W statistic value is 2. Thus it has been corrected. Furthermore, the next article discusses the issue of multicollinearity. Multicollinearity arises when two or more two explanatory variables in the regression model highly correlate with each other.

Notify me of follow-up comments by email. Sign in. Obtain the statistical significance of a correlation using the pwcorr command. In statistics, the Breusch—Godfrey 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. Because the test is based on the idea of Lagrange multiplier testing, it is sometimes referred to as LM test for serial correlation. The Breusch—Godfrey 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. The test is more general than the Durbin—Watson 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.

AR 1 for the regression errors. Breusch and Godfrey [ citation needed ] proved that, if the following auxiliary regression model is fitted. Note that the value of n depends on the number of lags of the error term p. Autocorrelation , also known as serial correlation , is the correlation of a signal with a delayed copy of itself as a function of delay. Informally, it is the similarity between observations as a function of the time lag between them. The analysis of autocorrelation is a mathematical tool for finding repeating patterns, such as the presence of a periodic signal obscured by noise, or identifying the missing fundamental frequency in a signal implied by its harmonic frequencies.

It is often used in signal processing for analyzing functions or series of values, such as time domain signals. Different fields of study define autocorrelation differently, and not all of these definitions are equivalent.

In some fields, the term is used interchangeably with autocovariance. Unit root processes, trend stationary processes, autoregressive processes, and moving average processes are specific forms of processes with autocorrelation.

In statistics, the autocorrelation of a real or complex random process is the Pearson correlation between values of the process at different times, as a function of the two times or of the time lag.

Note that the expectation may be not well defined. Note that this expression is not well-defined for all-time series or processes, because the mean may not exist, or the variance may be zero for a constant process or infinite for processes with distribution lacking well-behaved moments, such as certain types of power law.

This gives the more familiar forms for the auto-correlation function [1] : p. It is common practice in some disciplines e. However, in other disciplines e. The definition of the auto-correlation coefficient of a stochastic process is [2] : p.

The normalization is important both because the interpretation of the autocorrelation as a correlation provides a scale-free measure of the strength of statistical dependence, and because the normalization has an effect on the statistical properties of the estimated autocorrelations.

The Cauchy—Schwarz inequality, inequality for stochastic processes: [1] : p. For real-valued functions, the symmetric autocorrelation function has a real symmetric transform, so the Wiener—Khinchin theorem can be re-expressed in terms of real cosines only:.

In signal processing, the above definition is often used without the normalization, that is, without subtracting the mean and dividing by the variance. When the autocorrelation function is normalized by mean and variance, it is sometimes referred to as the autocorrelation coefficient [3] or autocovariance function.

It has no specific meaning. The above definitions work for signals that are square integrable, or square summable, that is, of finite energy.