Tools and Techniques¶

Lectures¶

• Orthogonal Projections and Their Applications
  • Overview
  • Key Definitions
  • The Orthogonal Projection Theorem
  • Orthonormal Basis
  • Projection Via Matrix Algebra
  • Least Squares Regression
  • Orthogonalization and Decomposition
  • Exercises
  • Solutions
• Continuous State Markov Chains
  • Overview
  • The Density Case
  • Beyond Densities
  • Stability
  • Exercises
  • Solutions
  • Appendix
• Reverse Engineering a la Muth
  • Friedman (1956) and Muth (1960)
  • A Process for Which Adaptive Expectations are Optimal
  • Some Useful State-Space Math
  • Estimates of Unobservables
  • Relation between Unobservable and Observable
  • MA and AR Representations
• Discrete State Dynamic Programming
  • Overview
  • Discrete DPs
  • Solving Discrete DPs
  • Example: A Growth Model
  • Exercises
  • Solutions
  • Appendix: Algorithms