Detectives of Change: Indicator Saturation

Abstract

Structural changes are pervasive from innovations affecting many disciplines. These can shift distributions, altering relationships and causing forecast failure. Many empirical models also have outliers: both can distort inference. When the dates of shifts are not known, they need to be detected to be handled, usually by creating an indicator variable that matches the event. The basic example is an impulse indicator equal to unity for the date of an outlier and zero elsewhere. We discuss an approach to finding multiple outliers and shifts called saturation estimation. For finding outliers, an impulse indicator is created for every observation and the computer program searches to see which, if any, match an outlier. Similarly for location shifts: a step indicator equal to unity till time t is created for every t and searched over. We explain how and why this approach works.

Are the Forecasts of Professionals Compatible with the Taylor Rule? Evidence from the Euro Area

“…Output gap expectations are especially significant within the crisis period, for which professionals expected the ECB to lower its policy rate to stimulate economic activity and to fight against the recession. To check for robustness, Table 2 provides additional estimation results including several types of location shifts, which account for quarterly periodicity in the forecasts, for decisions of the ECB to change the policy rate and for further location shifts endogenously determined by the split-sample algorithm approach outlined by Castle and Hendry (2019), which basically selects all possible location shift dates that turn out to be significant at the 5% level. Overall, the estimates of the coefficients for the expected inflation and output gap do not differ considerably compared to the initial findings reported in Panel (b) in Table 1.…”

A Brief History of General‐to‐specific Modelling*

“…ISEs are versatile and can be generalized to designed indicators, as with $$$ \nu $$$‐shaped to detect volcanic eruptions from the dendrochronological temperature record (see Pretis et al, 2016). Parameter shifts can be detected using multiplicative‐indicator saturation (see Castle, Doornik and Hendry, 2019a), where every regressor is interacted with step indicators; or after finding location shifts by SIS, interacting retained SIS indicators just with the lagged regressand can help discriminate between direct shifts and those induced by changes in dynamics (see Castle, Doornik and Hendry, 2023).…”