Time Series Analysis - Impact Patterns

The general logic of interrupted time series ARIMA is described in the Overview section (refer also to the Interrupted Time Series ARIMA dialog). Following the standard notation discussed in McDowall, McCleary, Meidinger, & Hay (1980), three major types of impacts are possible: (1) permanent abrupt, (2) permanent gradual, and (3) abrupt temporary.

A permanent abrupt impact pattern simply implies that the overall mean of the time series shifted after the intervention; the overall shift is denoted by ω (parameter name Omega(i) in the spreadsheet).

The gradual permanent impact pattern implies that the increase or decrease due to the intervention is gradual, and that the final permanent impact becomes evident only after some time. This type of intervention can be summarized by the expression: Impact_t=δ*Impact_t-1+ω (for all t ³ time of impact, else = 0). The respective parameter names used in the spreadsheet are Delta(i) and Omega(i). If δ is greater than 0 and less than 1 (the bounds of system stability), the impact will be gradual and result in an asymptotic change (shift) in the overall mean by the quantity: Asymptotic change in level=ω/(1-δ). The asymptotic change for gradual permanent impacts will also be displayed in the spreadsheet. Note that, when evaluating a fitted model, it is important that both parameters are statistically significant; otherwise one could reach paradoxical conclusions. For example, suppose the ω parameter is not statistically significant from 0 (zero) but the δ parameter is; this would mean that an intervention caused a significant gradual change, the final result of which was not significantly different from zero.

The abrupt temporary impact pattern implies an initial abrupt increase or decrease due to the intervention which then slowly decays, without permanently changing the mean of the series. This type of intervention can be summarized by the expressions: