The paper
This theoretical note connects adaptive learning with rational forecasting. Allowing the learning parameter to vary over time extends adaptive expectations to a broad class of time-series models.
Research findings
- A time-varying adaptation parameter derived from the Kalman filter produces minimum mean squared forecast errors for linear state-space models.
- The result encompasses ARIMA models and generalizes the much narrower case in which conventional, fixed-parameter adaptive expectations are optimal.
Implications for applied research
- Assess forecasting rules against the process generating the data, rather than treating adaptive and rational expectations as mutually exclusive approaches.
- Use state-space methods when the weight placed on new information needs to change over time.