Homework 1

Due by 10/9/2016.

Complete exercises and replicate outputs. Note that only PDF and HTML formats will be accepted. All R code you used to generate figures should be included in the document.

There are plenty of options for creating PDF documents with inline R code such as knitr, sweave, sense.io, jupyter, Anaconda cloud or simply save the plots as .png images and add them manually to your document together with R code.

Your output can be stylistically different from the outputs below (e.g. vectors or matrices will show up with row/column numbers). This doesn't matter as long as you have the correct numbers, labels and graphs.

1. Matrices and vectors

Find a generation mechanism for the following vectors / matrices and replicate it in R using for loops or vectors / matrices.

a)

1. 1
2. 4
3. 10
4. 20
5. 35
6. 56
7. 84
8. 120
9. 165
10. 220

b)

1. 1
2. 1
3. 2
4. 3
5. 5
6. 8
7. 13
8. 21
9. 34
10. 55
11. 89
12. 144
13. 233
14. 377
15. 610

c)

1	2	3	4	5	6	7	8	9	10
2	4	6	8	10	12	14	16	18	20
3	6	9	12	15	18	21	24	27	30
4	8	12	16	20	24	28	32	36	40
5	10	15	20	25	30	35	40	45	50

2. Plotting

Plot density function and cumulative distribution function of normally distributed random variable with $\mu = 0$ and $\sigma^2 = 1$. Plot them side by side. Don't forget to include proper labels and titles.

3. Dataframes

Load data from dow_jones_index.csv into a dataframe and do the following:

hint: Don't forget to convert date from Factor type to Date type. You can see the representation and type with str(myobject) command.

a) Plot MSFT stock price in time.

hint: if you're having problems displaying english month names, try Sys.setlocale("LC_TIME", "C")

'C'

b) Calculate weekly MSFT stock returns and display their histogram with 5 bins.

hint: Let $p_t$ stand for stock price at time $t$, stock return is then defined as $$ r_t = \frac{p_t}{p_{t-1}} - 1 $$

c) Calculate mean and standard deviation of MSFT returns.

Mean of MSFT returns:  -0.00598
Standard deviation of MSFT returns:  0.02062