# Forecasting in time series (ARMA, GARCH etc.)

I've read here https://otexts.com/fpp2/arima-forecasting.html how we do forecasting in time series models like the ARMA model, but I'm wondering if we recalculate estimates of parameters of our model after receiving a new observation?

For instance let's say that I fitted MA(2) model: $$y_t=\mu+\varepsilon_t+\theta_1 \varepsilon_{t-1} +\theta_2 \varepsilon_{t-2}$$ based on $$y_1,\ldots,y_T$$ and got estimates $$\hat \theta_1,\ \hat \theta_2,\ \hat \mu$$. I made a prognosis $$\hat y_{T+1}= \hat \mu+\hat \theta_1 \hat \varepsilon_{T}+\hat \theta _2 \hat \varepsilon _{T-1}.$$ Am I supposed to recalculate $$\hat \theta_1,\ \hat \theta_2$$ etc. after receiving the true $$y_{T+1}$$?