Box–Ljung test

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A test of whether a proposed ARMA model describes a time series. Suppose that the model has p parameters and the time series has n observations. Let xj and j be, respectively, the jth observed and fitted values, define aj by aj=xjj and define rk by . The Box–Ljung statistic, Q, is given by , where m is arbitrary and very much smaller than n, but usually about 24. If the model is correct then Q is an observation from a chi-squared distribution with (mp) degrees of freedom.

Subjects: Probability and Statistics.

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