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Stochastic Models
Introduction to R
Walt Pohl
Universität Zürich
Department of Business Administration
February 28, 2013
What is R?
R is a freely-available general-purpose statistical package,
developed by a team of volunters on the Internet.
It is widely used among statisticians, and frequently new
statistical techniques are first implemented in R.
It is less widely-used by economists, who tend to prefer
commercial statistical packages or Matlab.
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Stochastic Models
February 28, 2013
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R versus Excel
R has many more probability and statistical
functions built in or avaiable in free packages.
R is command-driven. You enter a sequence of
commands to manipulate your data.
While everything in Excel is in terms of cells, R has
a bunch of different data types: vectors, arrays,
objects. You can define your own.
Normally you will create a “.R” command file that
is separate from your data.
Note: Excel also has a separate command language –
VBA.
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Stochastic Models
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R versus Matlab
The real target audience for Matlab is engineers.
Matlab has many features useful for engineers but
not useful for us.
The target application for R is statistics. R has
many more statistical functions than Matlab.
Matlab started as a package for manipulating
matrices, and added other features later.
Non-matrix based operations are awkward.
R was designed for general-purpose programming
from the beginning.
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Stochastic Models
February 28, 2013
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R versus Other Statistics Programs
R is free.
R is more command-driven and less GUI driven.
R is very close to S-Plus.
R supports as broad of an array of operations as any
other statistics program.
R’s programming language is better-designed than
most of its competitors.
Since different packages are written by different
volunteers, R is not as uniform as some other
systems.
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Stochastic Models
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Important URLs
R home page – http://www.r-project.org/
Closest R mirror site – http://stat.ethz.ch/CRAN/
R tutorial –
http://cran.r-project.org/doc/manuals/R-intro.html
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Stochastic Models
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Monte Carlo Simulation in R
R has many, built-in probability distributions. For each
supported distribution XXX, R comes with four functions:
dXXX – density function
pXXX – cumulative distribution function
qXXX – quantile function (inverse of the CDF)
rXXX – random draw
XXX = unif, norm, chisq, t, etc.
Example: For the normal distribution, we have dnorm,
pnorm, qnorm, rnorm.
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Stochastic Models
February 28, 2013
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Vectors in R
For us, the basic R datatype is a vector of numbers.
The c command creates vectors:
Example: If you type c(1, 3, 4.5), R returns the vector
(1, 3, 4.5).
You can assign vectors to variables, using the < −
operator.
x < − c(1, 3, 4.5);
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Stochastic Models
February 28, 2013
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Vectors in R, cont’d
You can get the value of individual entries by using the []
operator.
x[3] will return 4.5.
You can also get subvectors by using ranges.
x[1:2] will return the vector 1, 3.
The length function allows you to refer to the end in a
range:
x[2:length(x)] will return the vector 3, 4.5.
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Stochastic Models
February 28, 2013
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Operations on Vectors
Where possible, any operation on vectors will be applied
elementwise.
So if x and y are two vectors, then z = x * y will be the
vector where z[i] = x[i] * y[i].
Likewise log(x) will be the vector whose each entry will
be log(x[i]), etc.
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Stochastic Models
February 28, 2013
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Sample Statistics
R has built-in functions for the usual sample statistics:
mean(x) – Mean of vector x
var(x) – Variance of vector x
sd(x) – Standard Deviation of vector x
quantile(x, q) – The q-th quantile of vector x.
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Stochastic Models
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Reading Data
The easiest way to import data into R is through CSV
files. Excel can export files in this format.
The function read.csv imports a file as a CSV file.
Example: apple < − read.csv(”apple.csv”) imports the
file named ”apple.csv” into the variable apple. The data
is returned in the form of a data frame.
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Data frames
A data frame is a named list of vectors. In the case of
”apple.csv”, we get four entries on the list:
DATE – end date of month.
RET – monthly return on Apple stock.
VWRETD – monthly return on CRSP
value-weighted index.
rf – monthly risk-free rate.
You access the vector by using $. Example: apple$RET.
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Regression
R has a very easy to use interface for regression: the lm
function. For example, to fit the CAPM for Apple, we
would use
lm(RET ∼ VWRETD, data=apple)
The first argument uses the tilde operator indicate
that we want to regress RET on VWRETD.
The second argument indicates that the data comes
from the apple frame.
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Stochastic Models
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Regression cont’d
lm by itself only returns the coefficients. To get more
detail, including t stats, use
summary(lm(RET ∼ VWRETD, data=apple))
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Built-In Mathematical Functions
R has various built-in mathematical functions:
exp(x) – e x .
log(x) – natural logarithm, log x. (Use log(x, b) for
logb x).
xˆy – x y .
√
sqrt(x) – x
Note these all work on vectors. exp(c(1, 2)) gives you
c(2.718282, 7.389056).
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Special Mathematical Values
Floating point supports some special values
1/0 = Inf.
−1/0 = -Inf.
0/0 = NaN.
Mathematical operations are defined for these special
values. For example, Inf + Inf = Inf, and Inf - Inf = NaN.
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Defining Your Own Functions
You can define a function by using R’s function
command:
f < − function(x) xˆ2
This creates a function that squares its argument, and
assigns it to the variable f. Calling f(2) in R will return 4.
Functions can take vector arguments. So f(c(1, 2)) will
return c(1, 4).
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Matrices
R also supports matrices. Use matrix(0, nrow=m,
ncol=n) to create an m-by-n matrix. For example
g = matrix(0, nrow = 3, ncol = 4);
To access the element in the i-th row and j-th column,
use [] with two numbers. For example
g[1,2] < − 3;
assigns 3 to gi,j .
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Logical Operations
R has the following basic logical operations.
==: equality
!−: not equal
<, >: greater or less than
<=, >=: greater/less than or equal
They evaluate to TRUE or FALSE.
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Stochastic Models
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Logical Operations on Vectors
Logical operations work on vector arguments, and return
a vector of TRUE or FALSE values.
Example: 1:10 > 5.
You can use the functions any or all to see if any or all of
the entries in the vector are TRUE.
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Stochastic Models
February 28, 2013
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Control Structures
R supports the standard control structures found in most
programming languages:
Branching: if
Definite iteration: for
Indefinite iteration: while
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Control Structures: If
A statement like “if test code1 else code2 ’ executes
code1 if the test is true, and code2 if the test is false.
(“else code2 can be missing, means to do nothing).
Example: if (0 == 0) print(“is zero”) else print(“is not
zero”).
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Control Structures: For
For allows you to do something a fixed number of times:
Example: for (i in 1:10) print(i);
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Control Structures: While
While allows you to do something until a condition
becomes TRUE. (It may take forever).
Example:
i = 10;
while (i>0) {
print(i);
i = i - 1;
}
(Notice the use of braces here. This is because the body
of the while loop contains multiple statements.)
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Stochastic Models
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Writing Fast R Code
R is faster for vector operations than for loops.
Example: x < − (1:1000)2
is faster than
x < − rep(0, 1000); # create an array of all zeros.
for (i in 1:1000) {
x[i] < − iˆ2;
}
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