Tools and Techniques¶

This section of the course contains foundational mathematical and statistical tools and techniques

Lectures¶

• Linear Algebra
  • Overview
  • Vectors
  • Matrices
  • Solving Systems of Equations
  • Eigenvalues and Eigenvectors
  • Further Topics
  • Exercises
  • Solutions
• Orthogonal Projections and Their Applications
  • Overview
  • Key Definitions
  • The Orthogonal Projection Theorem
  • Orthonormal Basis
  • Projection Using Matrix Algebra
  • Least Squares Regression
  • Orthogonalization and Decomposition
  • Exercises
  • Solutions
• LLN and CLT
  • Overview
  • Relationships
  • LLN
  • CLT
  • Exercises
  • Solutions
• Linear State Space Models
  • Overview
  • The Linear State Space Model
  • Distributions and Moments
  • Stationarity and Ergodicity
  • Noisy Observations
  • Prediction
  • Code
  • Exercises
  • Solutions
• Finite Markov Chains
  • Overview
  • Definitions
  • Simulation
  • Marginal Distributions
  • Irreducibility and Aperiodicity
  • Stationary Distributions
  • Ergodicity
  • Computing Expectations
  • Exercises
  • Solutions
• Continuous State Markov Chains
  • Overview
  • The Density Case
  • Beyond Densities
  • Stability
  • Exercises
  • Solutions
  • Appendix
• A First Look at the Kalman Filter
  • Overview
  • The Basic Idea
  • Convergence
  • Implementation
  • Exercises
  • Solutions
• Cass-Koopmans Optimal Growth Model
  • Overview
  • The Growth Model
  • Competitive Equilibrium