Computes various measures of heterogeneity of a time series. First the series is pre-whitened using an AR model to give a new series y. We fit a GARCH(1,1) model to y and obtain the residuals, e. Then the four measures of heterogeneity are: (1) the sum of squares of the first 12 autocorrelations of y^2; (2) the sum of squares of the first 12 autocorrelations of e^2; (3) the R^2 value of an AR model applied to y^2; (4) the R^2 value of an AR model applied to e^2. The statistics obtained from y^2 are the ARCH effects, while those from e^2 are the GARCH effects.
a univariate time series
A vector of numeric values.
Yanfei Kang and Rob J Hyndman
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