The Haar Wavelet Transfer Function Model and Its Applications

In the paper the Haar wavelet transfer function models are suggested as a way to parsimoniously parametrise the impulse responses and construct models with parameters providing an insight into the frequency content of the relationships under scrutiny. Besides, the models enable to verify hypotheses concerning changes of the regression parameters across dyadic scales (octave frequency bands). In the paper some theoretical properties of the models are investigated and an empirical illustration is provided. In the empirical study returns on WIG are modelled with the help of returns on S&P 500. Interestingly, besides the insight into the frequency content of the relationship, the empirical wavelet transfer function models also provided good forecasts.