Power Computations for Intervention Analysis

TL;DR

This paper develops a methodology to compute the power function for intervention analysis in time series data modeled by ARIMA or fractional ARIMA, aiding in planning and evaluating intervention studies.

Contribution

It introduces formulas for calculating power functions for various intervention types within ARIMA and fractional ARIMA models, with practical applications.

Findings

Provides explicit formulas for power computation in intervention analysis.

Demonstrates applications in traffic safety and environmental assessment.

Facilitates better planning of intervention studies with time series data.

Abstract

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.