Econometric Computing with R

Readings

• Roger D. Peng, R Programming for Data Sciences, Learnpub.com, 2015.

Table of Contents

• Introduction to R
• Matrix Algebra in R
• Statistical and Probability Functions
• R Programming
  • Control Structures (Peng 2015, pp. 48-55)
  • Functions (Peng 2015, pp. 56-74)
  • Loop Functions (Peng 2015, pp. 75-93)

Examples

1. Do you know the accuracy of your computer's numerical calculation? This example addresses this important problem. Suppose e is a known small positive number, and the 5x4 matrix X is defined as follows:

   1  1  1  1
   e  0  0  0
   0  e  0  0
   0  0  e  0
   0  0  0  e
   

   Verify that the eigenvalues of X'X are 4+e², e², e², and e². How small of the value of e your computer will allow so that X'X can be inverted? (Program).

2. Write R single-line function to convert quarterly time series into the annual series by taking the average of every four data points. (Program).

3. Present and solve the following functions:
   1. f(x) = ln(x) - x²
      Hint: The maximal of f(x) is found at x = Ö½ or 0.707. (Program).

   2. g(x) = (x₁² + x₂ - 11)² + (x₁ + x₂² -7)²
      Hint: There are four minima: (3, 2), (3.5844, -1.8481), (-3.7793, -3.2832), (-2.8051, 3.1313). (Program).