Imposing Frequency-Domain Restrictions on Time-Domain Forecasts

This paper proposes a new model selection criterion for choosing the number of discontinuity points in piecewise constant frequency-domain models for stationary time series. In order to facilitate the use of this criterion in practice, penalties are calculated for various levels of complexity and sample sizes using an efficient algorithm which is based on the principle of dynamic programming. Moreover, it is shown how the selected frequency-domain model can be used to estimate in a first step the autocovariances via their spectral representation and then, in a second step, also the parameters of autoregressive models via the Durbin-Levinson algorithm. In an empirical study with macroeconomic data, the forecasts based on these restricted autoregressive models strikingly outperform conventional ARMA forecasts.