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The traditional test for the presence of first-order autocorrelation is the Durbin–Watson statistic or, if the explanatory variables include a lagged dependent variable, Durbin's h statistic. The Durbin-Watson can be linearly mapped however to the Pearson correlation between values and their lags. [12]
The Breusch–Godfrey 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. [3]
The first term in the RHS describes short-run impact of change in on , the second term explains long-run gravitation towards the equilibrium relationship between the variables, and the third term reflects random shocks that the system receives (e.g. shocks of consumer confidence that affect consumption). To see how the model works, consider two ...
A plot showing 100 random numbers with a "hidden" sine function, and an autocorrelation (correlogram) of the series on the bottom. In the analysis of data, a correlogram is a chart of correlation statistics.
For jointly wide-sense stationary stochastic processes, the definition is = = [() (+) ¯] 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 ...
Durbin and Watson (1950, 1951) applied this statistic to the residuals from least squares regressions, and developed bounds tests for the null hypothesis that the errors are serially uncorrelated against the alternative that they follow a first order autoregressive process. Note that the distribution of this test statistic does not depend on ...
A correlation coefficient is a numerical measure of some type of linear correlation, meaning a statistical relationship between two variables. [a] The variables may be two columns of a given data set of observations, often called a sample, or two components of a multivariate random variable with a known distribution. [citation needed]
Plotting the partial autocorrelation function and drawing the lines of the confidence interval is a common way to analyze the order of an AR model. To evaluate the order, one examines the plot to find the lag after which the partial autocorrelations are all within the confidence interval. This lag is determined to likely be the AR model's order ...