Abstract: We obtain asymptotic expansions for probabilities of moderate deviations for stationary causal processes. The imposed dependence conditions are easily verifiable and they are directly related to the data-generating mechanism of the underlying processes. The results are applied to functionals of linear processes and nonlinear time series. We carry out a simulation study and investigate the relationship between accuracy of tail probabilities and the strength of dependence.
Key words and phrases: Martingale, moderate deviation, nonlinear time series.