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.

heterogeneity(x)

## Arguments

x

a univariate time series

## Value

A vector of numeric values.

## Author

Yanfei Kang and Rob J Hyndman