  The volatility modeling for autoregressive univariate time series is
considered. A benchmark approach is the stationary ARCH model of Engle (1982).
Motivated by real data evidence, processes with non constant unconditional
variance and ARCH effects have been recently introduced. We take into account
such possible non stationarity and propose simple testing procedures for ARCH
effects. Adaptive McLeod and Li's portmanteau and ARCH-LM tests for checking
for second order dynamics are provided. The standard versions of these tests,
commonly used by practitioners, suppose constant unconditional variance. We
prove the failure of these standard tests with time-varying unconditional
variance. The theoretical results are illustrated by mean of simulated and real
data.
