# Tag Info

Did you try solving for $w_k$? $$\bar{r}_t = \sum_{k=0}^p w_k r_{t-k}$$ $$\bar R = W R$$ Since you probably have $t>>k$, you can solve for $W$ using OLS $$\bar R = W R +\varepsilon$$ -- UPDATE You can try applying Kalman filter. Here, your state evolution is $$r_t=\mu+\varepsilon_t$$. You introduce new vector $x_t=(r_t, r_{t-1}, \dots, ... 1 Thanks @Aksakal for suggesting Kalman Filter. Here I provide more details. We will view it as a state-space model: $$\begin{split} z_t &= A_t z_{t-1} + B_t u_t + \epsilon_t, \\ y_t &= C_t z_t + D_t u_t + \delta_t, \\ \epsilon_t &\sim \mathcal{N}(0, Q_t),\ \delta_t \sim \mathcal{N}(0, R_t), \end{split}$$ where$z_t\$ is the latent variable, ...