Intervention Analysis

Interventions in a time series are measures representing disruptions in the course of a series of data extending over a time period. They are often conceptualized for evaluating policy impacts or other discrete introductions in a historical process. In many cases, they are introduced as the experimental treatment in an INTERRUPTED TIME-SERIES DESIGN (McDowall, McCleary, Meidinger, & Hay, 1980). Because estimates of policy interventions or other factors affecting a time series can be BIASED by contaminating factors, such as TREND (nonstationarity), AUTOREGRESSION (sometimes present even when there is no trend, as in cyclical processes), and MOVING AVERAGE components (random shocks that persist over time and then die away), the analytical model is usually specified as the presence or absence of an intervention (0 or 1), plus a noise model from which unspecified time-related effects have been eliminated—a WHITE NOISE process. The equation for this process is usually represented as

where yt represents an observation in a time series composed of ωIt; effects of the intervention; and a white noise process, Nt. Effects of the intervention can be evaluated by a T-TEST for SIGNIFICANCE of ω. This has the effect of eliminating time-series components extraneous to the impact of the intervention and permits testing of hypotheses regarding impacts of the policy or other intervention.

Although the research takes the form of a QUASIEXPERIMENTAL design suggested by Campbell and Stanley (see INTERRUPTED TIME-SERIES DESIGN), estimation of the intervention effects may take a variety of specifications. When precise information on the form of the intervention is available, such as yearly reductions in allowable pollution (Box & Tiao, 1975), the intervention should be specified accordingly. Most policy interventions are difficult to specify, however, and require DUMMY VARIABLES representing presence or absence of a policy or program. [Page 517]

For these more general effects, there are three basic specification models that account for an intervention (Figure 1).

Tests of these models can be obtained by including a lag of y, yt−1, in the estimating equation,

and evaluating the parameter, δ, by a t-test. If the analyst has no explicit knowledge as to the form of the intervention, alternative specifications can be tested. Specifically, one may try specification of the intervention in the following manner:

1.
If the parameter of a specified pulse function (abrupt, temporary effect) is significant and the parameter, δ, is not significant, the intervention effect takes the form of the pulse function illustrated in Figure 1.
2.
If the parameter of a specified pulse function (abrupt, temporary effect), ω, is significant and the parameter, δ, is also significant, the outcome suggests that a step function (abrupt, permanent effect) is a better specification. For example, if the coefficient of the lagged endogenous variable equals 1, the model is identical with a step function.
3.
If the parameter of a specified step function, ω, is significant, but the parameter, δ, is not significant, a step function specification is probably correct (Figure 1).
4.
Ifthe parameters of both the intervention specified as a step function and the lagged time series, yt−1, prove to be significant, alternative model combinations should be investigated.
5.
If the parameter of a pulse function specification is not significant, but the parameter of yt−1 is significant, a ramp function (Figure 1) should be investigated.

When ambiguities are detected in the model specifications described above, the model may require more complex, alternative specifications, sometimes as combinations of the basic models (see Figure 2).

...