Frequency decompositions in autoregression models

Autoregression models are used by Ortec Finance to forecast the evolution of economic variables, such as interest rates. To distinguish the impact of short, medium and long term fluctuations, the company decomposes their models into three components: month, business and trend, respectively. We answer the question of how to design a model, so that predictions generated for a given frequency band do not overlap with other frequencies. We also discuss several other related matters, i.e. how to address the frequency leaking problem, how to choose the number of frequencies in each band and how our method generalizes to time-dependent models.