Minnesota

Description

Discount previous time points exponentially

Definition

$$\begin{array}{rl}{y}_t& \sim \text{normal}({\mu }_t,{\sigma }^2),t=p+1,\dots ,T\\ {\mu }_t& =\sum _{i=1}^p{\varphi }_i{y}_{t-i}+x_t^{\prime }\beta \\ {\varphi }_i& \sim \text{normal}(0,{\kappa }_1/i^2),{\beta }_j\sim N(0,\frac{{\sigma }_y^2}{{\sigma }_{x_j}^2}{\kappa }_2),j=1,\dots ,m\\ {\kappa }_1& \sim \text{gamma}(1,1/0.04),{\kappa }_2\sim \text{gamma}(1,1/{0.04}^2),{\sigma }^2\sim p({\sigma }^2)\end{array}$$

Stan code