PART A
A Suppose that
rt follows the model
rt =
rt−1 +
at −0.9
at−1, and we have
r101 = 1.2 and
r100 (1) = 1.0, where
rt(1) denotes the 1 step ahead prediction of rt+1 at the forecast origin
t. Compute
r101(1).
B Suppose we have daily log returns of the S&P500 index for 1841 trading days. Please answer following questions, using the RStudio output in the second page.
1. Let
µ be the expected value of rt. Test H0 : µ = 0 versus Ha : µ ≠ 0. Obtain the test statistic and draw your conclusion.
2. Is the distribution of
rt skew? Why?
3. Does the distribution of
rt have heavy tails? Why?
4. Let
ρ1 be the lag-1 ACF of rt. Test H0: ρ1 = 0 versus Ha : ρ ≠ 0. The sample lag-1 ACF is −0.086. Obtain the test statistic and draw your conclusion.
5. An MA(1) model is fitted. Write down the fitted model, including σ2 of the residuals.
C The file assignment_3.txt contains monthly returns for five portfolios (e.g. dec1~dec10). The data span is from 01/1961 to 09/2011. Answer following two questions:
1. For the return series of dec5 and dec9, test the null hypothesis that the first 12 lags of autocorrelations are 0 at the 5% level. Draw your conclusion.
2. Build an ARMA model for the return series of dec1. Perform model checking and write down the fitted model.
Part B
1.Give an Example of a Comparative and Absolute Advantage from your own life
2.List things that impact your overall spending each month, for example your paycheck. Graph your consumption Function
3.What is Money? List things that you think of when you think of money. For example, I might think of Shopping or Bill Gates.
4.What’s your opinion about whether we should be more concerned with a recession and high unemployment, or inflation based on the current state of the economy and Why?
Perfect competition
1.What are the characteristics of a PC firm?
2.Using Hot Dogs, Graph the market and the individual supply, demand
and costs for Hot dogs side by side. Make sure to include the S.R. and
L.R profits.
Monopoly
1) What are the characteristics of a Monopoly
2) Using DeBeer’s Diamonds, Graph a Monopoly
3) Compare the price, quantity, and ATC of a monopoly with a perfectly competitive firm. Who is more efficient and why?
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