Pulses and steps

Many series experience abrupt changes in level. They generally come in two types:

  • A sudden, temporary shift, or pulse, in the series level
  • A sudden, permanent shift, or step, in the series level
Figure 1. Series with a pulse
Series with a pulse

When steps or pulses are observed, it is important to find a plausible explanation. Time series models are designed to account for gradual, not sudden, change. As a result, they tend to underestimate pulses and be ruined by steps, which lead to poor model fits and uncertain forecasts. (Some instances of seasonality may appear to exhibit sudden changes in level, but the level is constant from one seasonal period to the next.)

If a disturbance can be explained, it can be modeled using an intervention or event. For example, during August 1973, an oil embargo imposed by the Organization of Petroleum Exporting Countries (OPEC) caused a drastic change in the inflation rate, which then returned to normal levels in the ensuing months. By specifying a point intervention for the month of the embargo, you can improve the fit of your model, thus indirectly improving your forecasts. For example, a retail store might find that sales were much higher than usual on the day all items were marked 50% off. By specifying the 50%-off promotion as a recurring event, you can improve the fit of your model and estimate the effect of repeating the promotion on future dates.