7.1. Introduction to Statsmodels Library

• Trend
  • Upward
  • Stationary / Horizontal
  • Downward
  • Cyclical: trens with no set repetition
• Hodrick-Prescott filter: from statsmodels.tsa.filters.hp_filter import hpfilter
  • separates a time series $y_t$ into a trend component ${\tau }_t$ and cyclical component $c_t$
  • determined by minimizing the following quadradict loss function ${\min }_{{\tau }_t}{\sum }_{t=1}^T{c}_t^2+\lambda {\sum }_{t=1}^T[({\tau }_t-{\tau }_{t-1})-({\tau }_{t-1}-{\tau }_{t-2}){]}^2$
  • Default values for $\lambda$
    • 1600: default (e.g. quarterly)
    • 6.25: annual data
    • 129 600: monthly data