Sample data for a complex structure, with AR(1) \(\beta_{C,t}\)
Format
A data frame with 1000 rows and 4 variables, the data generation process follows the following equation $$Y_t = 40+0.5Y_{t-1}-\beta_{X,t}X_t-0.5X_{t-1}-\beta_{C}C_t+v_t, v_t \sim \text{i.i.d }\mathcal{N}(0,1)\\ \text{where } \beta_{C,t} =0.5 \beta_{C,t-1}-1+w_{\beta,t}, w_{\beta,t}\sim \mathcal{N}(0,0.1)$$
- Date
A simulated date
- y
outcome, with data generating process as above
- c
continous covarite
- x
continous treatment