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