Riemann surface
matlab

EXERCISES
1.1 Use software to produce the time series plot shown in Exhibit 1.2, on page 2. The data are in the file named larain. ${ }^{\dot{1}}$
1.2 Produce the time series plot displayed in Exhibit 1.3, on page 3. The data file is named color.
1.3 Simulate a completely random process of length 48 with independent, normal values. Plot the time series plot. Does it look “random”? Repeat this exercise several times with a new simulation each time.
1.4 Simulate a completely random process of length 48 with independent, chi-square distributed values, each with 2 degrees of freedom. Display the time series plot. Does it look “random” and nonnormal? Repeat this exercise several times with a new simulation each time.
1.5 Simulate a completely random process of length 48 with independent, $t$-distributed values each with 5 degrees of freedom. Construct the time series plot. Does it look “random” and nonnormal? Repeat this exercise several times with a new simulation each time.
1.6 Construct a time series plot with monthly plotting symbols for the Dubuque temperature series as in Exhibit 1.7, on page 6. The data are in the file named tempdub.

EXERCISES
2.1 Suppose $E(X)=2, \operatorname{Var}(X)=9, E(Y)=0, \operatorname{Var}(Y)=4$, and $\operatorname{Corr}(X, Y)=0.25$. Find:
(a) $\operatorname{Var}(X+Y)$.
(b) $\operatorname{Cov}(X, X+Y)$.
(c) $\operatorname{Corr}(X+Y, X-Y)$.
2.2 If $X$ and $Y$ are dependent but $\operatorname{Var}(X)=\operatorname{Var}(Y)$, find $\operatorname{Cov}(X+Y, X-Y)$.
2.3 Let $X$ have a distribution with mean $\mu$ and variance $\sigma^2$, and let $Y_t=X$ for all $t$.
(a) Show that $\left{Y_t\right}$ is strictly and weakly stationary.
(b) Find the autocovariance function for $\left{Y_t\right}$.
(c) Sketch a “typical” time plot of $Y_t$.

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