A limit theory is developed for mildly explosive autoregressions under stationary (weakly or strongly dependent) conditionally heteroskedastic errors. The conditional variance process is allowed to be stationary, integrable and mixingale, thus encompassing general classes of GARCH type or...

Time series models are often fitted to the data without preliminary checks for stability of the mean and variance, conditions that may not hold in much economic and financial data, particularly over long periods. Ignoring such shifts may result in fitting models with spurious dynamics that lead...