Abstract: Conditional heteroscedasticity is prevalent in many time series. By viewing conditional heteroscedasticity as the consequence of a dynamic mixture of independent random variables, we develop a simple yet versatile observable mixing function, leading to the conditionally heteroscedastic AR model with thresholds, or a T-CHARM for short. We demonstrate its many attributes and provide comprehensive theoretical underpinnings with efficient computational procedures and algorithms. We compare, via simulation, the performance of T-CHARM with the GARCH model. We report some experiences using data from economics, biology, and geoscience.

Key words and phrases: Compound Poisson process, conditional variance, heavy tail, heteroscedasticity, limiting distribution, quasi-maximum likelihood estimation, random field, score test, T-CHARM, threshold model, volatility.