| Abstract: |
Threshold models are set up so that there is a switch between regimes for the
parameters of an unobserved components model. When Gaussianity is assumed, the
model is handled by the Kalman filter. The switching depends on a component
crossing a boundary, and, because the component is not observed directly, the
error in its estimation leads naturally to a smooth transition mechanism. A
prominent example motivating thresholds is that of a cyclical time series
characterized by a downturn that is more, or less, rapid than the upturn. The
situation is illustrated by fitting a model with three potentially asymmetric
cycles, each with its own threshold, to observations on ice volume in
Antarctica since 799, 000 BCE. The model is able to produce multi-step
forecasts with associated prediction intervals. A second example shows how a
hidden threshold model is able to deal with the asymmetric cycle in monthly US
unemployment. |