Time Series Analysis, Regression, and Forecasting

1.0 CONCEPTS
- 1.1 Correlation
  - 1.1.1 The Intuition Behind Correlation
  - 1.1.2 Understanding Partial Auto-correlation And The PACF
- 1.2 Probability, Variance And Covariance
  - 1.2.1 The Three Conditionals: Conditional Probability, Conditional Expectation And Conditional Variance
  - 1.2.2 An In-depth Study of Conditional Variance and Conditional Covariance
- 1.3 Random Processes
  - 1.3.1 The Poisson Process
    - 1.3.1.1 Getting to Know The Poisson Process And The Poisson Probability Distribution
    - 1.3.1.2 A Deeper Dive Into The Poisson Probability Distribution Function
  - 1.3.2 The Markov Process
    - 1.3.2.1 The Discrete Time Markov Process
      - 1.3.2.1.1 An Introduction To Discrete Time Markov Processes
      - 1.3.2.1.2 An Introduction To Hidden Markov Models
  - 1.4 Statistical Estimation
    - 1.4.1 Properties Of The Statistical Estimator
    - 1.4.2 Estimating The Range Of A Population Parameter: A Guide To Interval Estimation
2.0 DATA TRANSFORMATIONS
- 2.1 How To Adjust For Inflation In Monetary Data Sets
- 2.2 How To Isolate Trend, Seasonality And Noise From Time Series Data Sets
3.0 REGRESSION MODELS
- 3.1 The Basics
- 3.2 Linear Regression Models
  - 3.2.1 The Assumptions Of Linear Regression, And How To Test Them
  - 3.2.2 An Overview Of The Variance-Covariance Matrices Used In Linear Regression
  - 3.2.3 A Deep Dive Into The Variance-Covariance Matrices Used In Linear Regression
  - 3.2.4 The Consequences of Omitting Important Variables From A Linear Regression Model
  - 3.2.5 The Consequences of Including Irrelevant Variables In Linear Regression Models
  - 3.2.6 The Effect Of Measurement Errors On A Linear Regression Model
  - 3.2.6 Heteroscedasticity
  - 3.2.7 What Are Dummy Variables And How To Use Them In A Regression Model
  - 3.2.8 Introduction To The Difference In Differences Regression Model
  - 3.2.9 A Guide To Building Linear Models For Discontinuous Data
  - 3.2.10 Introduction To The Quantile Regression Model
  - 3.2.11 How To Use Proxy Variables In A Regression Model
  - 3.2.12 Instrumental Variables Regression
    - 3.2.12.1 Introduction To Instrumental Variables
    - 3.2.12.2 Introduction To Two-Stage Least Squares (2SLS) Estimation
  - 3.2.13 Systems of Regression Equations
    - 3.2.13.1 [COMING SOON] An Introduction To Systems Of Regression Equations
    - 3.2.13.2 [COMING SOON] A Tutorial On Solving Systems Of Regression Equations Using Python and Statsmodels
    - 3.2.13.3 [COMING SOON] Simultaneous Equation Systems
- 3.3 Regression Models For Counts Data Sets
- 3.4 Generalized Linear Models
  - 3.4.1 An Overview of Generalized Linear Regression Models
  - 3.4.2 The Binomial Regression Model
- 3.5 Time Series Regression Models
  - 3.5.1 Exponential Smoothing Models
    - 3.5.1.1 Holt Winters Exponential Smoothing
  - 3.5.2 ARIMA, SARIMA And SARIMAX models
    - 3.5.2.1 Introduction to Regression With ARIMA Errors Model
  - 3.5.3 Hidden Markov Models For Time Series Data Sets
    - 3.5.3.1 Markov Switching Dynamic Regression (MSDR) Model
  - 3.5.4 Models For Integer Valued Time Series Data Sets
  - 3.5.5 Time Series Models for Panel Data Sets
- 3.6 Models for Survival Data
  - 3.6.1 Introduction to Survival Analysis – Concepts, Techniques and Regression models
  - 3.6.2 The Stratified Cox Proportional Hazards Model
- 3.7 Less Commonly Used (But Important) Nonlinear Regression Models
  - 3.7.1 The Nonlinear Least Squares (NLS) Regression Model
4.0 MODEL EVALUATION AND GOODNESS OF FIT
- 4.1 Analysis of Residual Errors
  - 4.1.1 Testing For Normality of Residual Errors Using Skew And Kurtosis based Tests
  - 4.1.2 Dealing with Multi-modality of Residual Errors
- 4.2 Goodness of Fit Measures
- 4.3 Model Selection Tests
  - 4.3.1 Model Selection Tests For Nested and Non-Nested Regression Models
- 4.4 Model Evaluation Techniques for Survival Models
  - 4.4.1 Testing The Assumptions Of the Cox Proportional Hazards Model Using Schoenfeld Residuals
5.0 BIO-STATISTICS
- 5.1 Vaccine Efficacy
  - 5.1.1 Estimation of Vaccine Efficacy Using a Logistic Regression Model
5.0 BIBLIOGRAPHY AND REFERENCES