  Traditional white noise testing, for example the Ljung-Box test, studies only
the autocorrelation function (ACF). Time series can be heteroscedastic and
therefore not i.i.d. but still white noise (that is, with zero ACF). An example
of heteroscedasticity is financial time series: times of high variance
(financial crises) can alternate with times of low variance (calm times). Here,
absolute values of time series terms are not white noise. We could test for
white noise separately for original and absolute values, for example using
Ljung-Box tests for both. In this article, we create an omnibus test which
combines these two tests. Moreover, we create a general framework to create
various i.i.d. tests. We apply tests to simulated data, both autoregressive
linear and heteroscedastic.
