State and prove the 3 properties of an ARIMA(2,0,0). For credit, PLEASE show ALL the steps of your proof, EXACTLY as we did in class.

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

R Exercise

A. Obtaining and Transforming the Data:

1. Download daily and monthly adjusted closing prices for 12 years for the same company you used for the first team project (Recall that each team member had to choose a company for the team project that you submitted before Baruch was closed).

2. Annualize the daily data. See pages 2 – 6 of your textbook.

3. Annualize the Monthly data. See pages 2 – 6 of your textbook.

4. Plot the daily prices versus time (days)

5. Plot the annualized prices (obtained from daily prices) versus time (years).

6. Plot the monthly prices versus time (months).

7. Plot the annualized prices (obtained from monthly prices) versus time (years).

8. Describe, Explain, Compare and Contrast.

B. Calculating Simple and Logarithmic (Continuously Compounded) Returns:

Daily Simple and Logarithmic Returns:

1. Calculate (simple) returns as percentage changes in daily prices. See pages 2 – 6 of your textbook. [This is equal to (p(t) - p(t-1))/(p(t-1)].

2. Calculate daily logarithmic returns (continuously compounded). See pages 2 – 6 of your textbook. [This is equal to Ln((p(t)/(p(t-1))].

Monthly Simple and Logarithmic Returns:

3. Calculate (simple) returns as percentage changes in monthly prices.

4. Calculate monthly logarithmic returns (continuously compounded).

5. Describe, Explain, Compare and Contrast.

C. Distributional Properties of Returns (See pages 20-27 of your textbook):

1. Compute the moments for the continuously compounded (logarithmic) daily returns.

2. Do these daily logarithmic returns come from a normal distribution? Present JB test results.

3. Compute the moments for the continuously compounded (logarithmic) monthly returns.

4. Do these monthly logarithmic returns come from a normal distribution? Present JB test results.

5. Describe, Explain, Compare and Contrast.

D. Working with Autocorrelation Functions (See pages 40 – 50 of your textbook):

1. Obtain and Plot the Autocorrelation Functions (acf) for daily percentage (simple) returns.

2. At the 95% Confidence Level, and using the daily percentage (simple) returns,

a. Perform the Box Pierce and the Ljung-Box tests for autocorrelations.

b. What are your conclusions?

3. Obtain and Plot the Autocorrelation Functions (acf) for daily logarithmic returns.

4. At the 95% Confidence Level, and using the daily logarithmic returns,

a. Perform the Box Pierce and the Ljung-Box tests for autocorrelations.

b. What are your conclusions?

5. Obtain and Plot the Autocorrelation Functions (acf) for monthly percentage (simple) returns.

6. At the 95% Confidence Level, and using the monthly percentage (simple) returns,

a. Perform the Box Pierce and the Ljung-Box tests for autocorrelations.

b. What are your conclusions?

7. Obtain and Plot the Autocorrelation Functions (acf) for monthly logarithmic returns.

8. At the 95% Confidence Level, and using the monthly logarithmic returns,

a. Perform the Box Pierce and the Ljung-Box tests for autocorrelations.

b. What are your conclusions?

9. What do your ACF analyses tell you about:

a. Stationarity of the individual time series of daily and monthly returns? EXPLAIN.

b. Efficient Market Hypothesis with respect to the time series of individual daily and monthly returns? EXPLAIN.

c. Are the daily and monthly returns “White Noise”? EXPLAIN.

Very Important:

1. Absolute maximum of 2 pages in WORD for all the descriptive portions of Sections A, B, C and D.

2. All graphs, Charts, R results, etc, should NOT be part of the 2 pages!! They should be presented in an APPENDIX.

Theory Questions

1. State and prove the 3 properties of an ARIMA(2,0,0). For credit, PLEASE show ALL the steps of your proof, EXACTLY as we did in class. No credit otherwise!

2. State and prove the 3 properties of an ARIMA(0,0,2). For credit, PLEASE show ALL the steps of your proof, EXACTLY as we did in class. No credit otherwise!

Extra Credit:

3. State and prove the 3 properties of an ARIMA(1,0,1). For credit, PLEASE show ALL the steps of your proof, EXACTLY as we did in class. No credit otherwise!

Attachments:

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