Use R to get the below analysis:

1. (10 points) Using the pdfetch package, download the monthly stock price of Tesla (an American electric vehicle and clean energy company) since January 1, 2011. Teslas ticker symbol is tsla. Suppose we download tsla along with the S&P 500 index, > ticker yahoodb <- zoo( pdfetch YAHOO(ticker, fields = adjclose, from = 2011-01-01, interval = 1m) ) What is the average stock price of tsla? What about the minimum and the maximum of tsla? How many observations are there in tsla?

2. (5 points) Draw a time series plot of tsla (on vertical axis) where the time information is on the horizontal axis. Add an appropriate title to the plot. Be sure to include R plot in your answer.

3. (5 points) (1) Estimate a regression model with a linear trend for tsla: tslat = 0 + 1t + et where the regressor t is the time trend. (2) Interpret 1. Clearly indicate the unit of measurement in your interpretation.

4. (5 points) (1) Write the estimated regression equation with an exponential trend for tsla. (2) Interpret the estimated coefficient on the trend term. Clearly indicate the unit of measurement in your interpretation.

5. (5 points) (1) Estimate an AR(1) model for tsla: that is, tslat = 0 + 1tslat1 + ut. (2) Create a table of regression outputs which includes the estimation results in Q3, Q4 and Q5 (Hint: use the stargazer package). You may want to use a smaller font size in Microsoft Word to present the table nicely.

6. (5 points) Download your favorite companys (other than Tesla) daily stock prices since January 1, 2019 along with tslas daily prices: you need to find your favorite companys ticker symbol (you can google it.) and download the data using the method in Q1. Draw the two time series line plots in a single graph.

7. Consider an AR(1) model for yt with t = 2, , T: yt = yt1 + et. (a) (5 points) Using the recursive substitution method, show that yt = t1y1 + et + et1 + + t2e2. (b) (10 points) Let y1 = 0, Var et = 2 for all t, and Cov(et, es) = 0 for t = s. Prove or disprove that Var(yt) = 2(1 + 2 + + 2t4