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index_tools_and_techniques.ipynb
Tools and Techniques
Tools and Techniques
¶
This section of the course contains foundational mathematical and statistical tools and techniques
Lectures
¶
Geometric Series for Elementary Economics
Overview
Key Formulas
Example: The Money Multiplier in Fractional Reserve Banking
Example: The Keynesian Multiplier
Example: Interest Rates and Present Values
Back to the Keynesian Multiplier
Multivariate Hypergeometric Distribution
Overview
The Administrator’s Problem
Usage
Modeling COVID 19
Overview
The SIR Model
Implementation
Experiments
Ending Lockdown
Linear Algebra
Overview
Vectors
Matrices
Solving Systems of Equations
Eigenvalues and Eigenvectors
Further Topics
Exercises
Solutions
Complex Numbers and Trigonometry
Overview
De Moivre’s Theorem
Applications of de Moivre’s Theorem
LLN and CLT
Overview
Relationships
LLN
CLT
Exercises
Solutions
Heavy-Tailed Distributions
Overview
Visual Comparisons
Failure of the LLN
Classifying Tail Properties
Exercises
Solutions
Multivariate Normal Distribution
Overview
The Multivariate Normal Distribution
Bivariate Example
Trivariate Example
One Dimensional Intelligence (IQ)
Another representation
Magic of the Cholesky factorization
Math and Verbal Components of Intelligence
Univariate Time Series Analysis
Classic Factor Analysis Model
PCA as Approximation to Factor Analytic Model
Stochastic Difference Equation
Application to Stock Price Model
Filtering Foundations
Univariate Time Series with Matrix Algebra
Overview
Samuelson’s model
Adding a random term
A forward looking model