In many intervention analysis applications time series data may be expensive or otherwise difficult to collect. In this case the power function is helpful since it can be used to determine the probability that a proposed intervention analysis application will detect a meaningful change. Assuming that an underlying ARIMA or fractional ARIMA model is known or can be estimated from the pre-intervention time series, the methodology for computing the required power function is developed for pulse, step and ramp interventions with ARIMA and fractional ARIMA errors. Convenient formulae for computing the power function for important special cases are given. Illustrative applications in traffic safety and environmental impact assessment are discussed.