The authors provide a convergence theory for adaptive learning algorithms useful for the study of learning by economic agents. Their results extend the framework of L. Ljung previously utilized by A. Marcet-T. J. Sargent and M. Woodford by permitting nonlinear laws of motion driven by stochastic...

We analyze use of a quasi-likelihood ratio statistic for a mixture model to test the null hypothesis of one regime versus the alternative of two regimes in a Markov regime-switching context. This test exploits mixture properties implied by the regime-switching process, but ignores certain...

Engle and Manganelli (2004) propose CAViaR, a class of models suitable for estimating conditional quantiles in dynamic settings. Engle and Manganelli apply their approach to the estimation of Value at Risk, but this is only one of many possible applications. Here we extend CAViaR models to...

Contemporary tests for structural change are designed to detect a structural break within a given historical data set of fixed size. Due to the law of the iterated logarithm, these one-shot tests cannot be applied to monitor out-of-sample stability each time new data arrive. The authors propose...