## 13.12 Problems

1. By adapting the code in Section 13.1, fit a regression model that includes the intercept and a slope, modeling the effect of Wind. What is the mean wind effect you estimate?

2. Using the results from the linear regression model fit with no burn-in (Section 13.1.1), calculate the ACF of the beta time series using acf(). Would thinning more be appropriate? How much?

3. Using the fit of the random walk model to the temperature data (Section 13.3), plot the predicted values (states) and 95% CIs.

4. To see the effect of this increased flexibility in estimating the autocorrelation, make a plot of the predictions from the AR(1) model (Section 13.4 and the RW model (13.3).

5. Fit the univariate state-space model (Section 13.5) with and without the autoregressive parameter $$\phi$$ and compare the estimated process and observation error variances. Recall that AR(1) without the $$\phi$$ parameter is a random walk.

6. Run the examples related to the EFI challenge. Work through the questions associated with each exercise