Adaptive state space models with applications to the business cycle and financial stress

In this paper we develop a new theoretical framework for the analysis of state space models with time-varying parameters. We let the driver of the time variation be the score of the predictive likelihood and derive a new filter that allows us to estimate simultaneously the state vector and the time-varying parameters. In this setup the model remains Gaussian, the likelihood function can be evaluated using the Kalman filter and the model parameters can be estimated via maximum likelihood, without requiring the use of computationally intensive methods. Using a Monte Carlo exercise we show that the proposed method works well for a number of different data generating processes. We also present two empirical applications. In the former we improve the measurement of GDP growth by combining alternative noisy measures, in the latter we construct an index of financial stress and evaluate its usefulness in nowcasting GDP growth in real time. Given that a variety of time series models have a state space representation, the proposed methodology is of wide interest in econometrics and statistics.