Disentangling low-frequency versus high-frequency economic relationships via regression parameter stability tests

This dissertation develops and applies new tools for distinguishing and disentangling high-frequency and low-frequency relationships among stationary economic time series. The new approach proposed here is a three-step procedure; the first step transforms the regression model in the time domain to a real-valued model in the frequency domain, which is functionally identical to an ordinary regression model, the only different being that "observations" of this model correspond to different frequencies rather than to different time periods. Consequently, in the second step, well established regression parameter stability tests are used to detect and assess the frequency dependence of relationships among economics time series. This new approach allows one to not only detect model misspecification of this type but also to correct it. In the third step, the results of the parameter stability across frequency tests is used to sensibly choose the best varying-parameter model in the frequency domain, which is then back-transformed to a time domain model and to be used for forecasting.

The empirical example (using macroeconomic data) presented in this dissertation shows that the back-transformed model that allows varying parameter across frequencies significantly improves the forecasting performance of the misspecified fixed-parameter model.