# Dynamic factor model for inflation (UIG)

I'm trying to replicate some results of Fed Underlying Inflation Gauge (UIG) model, which is a dynamic factor model to capture inflation trend. https://www.newyorkfed.org/research/policy/underlying-inflation-gauge

I'm getting some not so good results. The following figure shows the UIG results while my is a lot smoother.

I'm trying to investigate the reason. One difference is that I used a dynamic factor model in statsmodels package in Python, which has the static format as following: \begin{align} y_t^i & = \Lambda^i f_t + u_t^i \\ f_t & = A_1 f_{t-1} + \dots + A_p f_{t-p} + \eta_t \qquad \eta_t \sim N(0, I)\\ u_t^i & = \varepsilon_t^i \qquad \varepsilon_t^i \sim N(0, \Sigma) \end{align}

But the UIG is actually doing something like:

\begin{align} y_t^i & = \sum_{h}\beta_h^i f_{t-h} + u_t^i \\ u_t^i & = \varepsilon_t^i \qquad \varepsilon_t^i \sim N(0, \Sigma) \end{align}

Could this cause a problem?