Mickaiel (2004), the test works in the context of ordinary least squares panel data regression (the pooled OLS model). The test was implemented in Stata with the panel data structure by Emad Abd Elmessih Shehata & Sahra Khaleel A. Therefore, the null hypothesis is that data is not suffering from an autocorrelation structure against the alternative which proposes that the data has an autocorrelation structure. The null hypothesis of this test can be defined as H0: Data is distributed independently, against the alternative hypothesis of H1: Data is not distributed independently. The test works with chi-square distribution by the way. The test is closely related to the Ljung & Box (1978) autocorrelation test, and it used to determine the existence of serial correlation in the time series analysis. Where the statistic of Box- Pierce Q is defined as the product between the number of observations and the sum of the square autocorrelation ρ in the sample at lag h. The approach is used to test first-order serial correlation, the general form of the test is given the statistic as: ![]() The test of Box & Pierce was derived from the article “Distribution of Residual Autocorrelations in Autoregressive-Integrated Moving Average Time Series Models” in the Journal of the American Statistical Association (Box & Pierce, 1970).
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