Quantitative Analysis

Weightage: 20% $\mid$ Difficulty Level: Medium $\mid$ #Modules: 15 Modules $\mid$ Duration: 2 Months

Course Overview

Welcome to this course on Quantitative Analysis. This course is designed to equip you with the quantitative tools required to model and analyze complex financial scenarios.

Beginning with ‘Fundamentals of Probability,’ you’ll delve into the core principles that underlie uncertainty and randomness in financial data. Understanding ‘Random Variables’ will allow you to model these uncertainties and make informed decisions.
As you progress, you’ll explore ‘Common Univariate Random Variables,’ gaining insight into distributions that frequently appear in financial contexts. ‘Multivariate Random Variables’ will enable you to analyze the interactions between different variables, a crucial skill for risk assessment.
The course then transitions to ‘Sample Moments,’ providing you with techniques to summarize and interpret data. ‘Hypothesis Testing’ equips you to draw meaningful conclusions from data through rigorous statistical methods.
‘Linear Regression’ introduces you to predictive modeling, allowing you to understand relationships between variables and make accurate forecasts. Extending this knowledge, ‘Regression with Multiple Explanatory Variables’ prepares you for complex modeling scenarios.
You’ll master ‘Regression Diagnostics,’ learning how to evaluate and refine your models for accuracy. Diving into time series analysis, ‘Stationary Time Series’ teaches you to analyze data points over time, while ‘Non-Stationary Time Series’ explores dynamic financial trends.
‘Measuring Returns, Volatility, and Correlation’ equips you with tools to quantify risk and interdependencies in financial markets. ‘Simulation and Bootstrapping’ introduces techniques for generating data to simulate financial scenarios, an invaluable skill for risk assessment.
With ‘Machine-Learning Methods,’ you’ll explore modern techniques that leverage data to make predictions and decisions. Finally, ‘Machine Learning and Prediction’ connects machine learning to financial contexts, emphasizing its role in forecasting.

By the end of this course, you’ll have a comprehensive understanding of quantitative analysis, enabling you to analyze financial data, make informed predictions, and navigate the intricate landscape of risk management.

1. Introduction

2. Event and Event Space

3. Independent and Mutually Exclusive Events

4. Independent Vs Conditionally Independent Events

5. Probability Calculation for Discrete Probability Functions

6. Conditional Probability

7. Conditional Vs Unconditional Probability

8. Bayes’ Rule

1. Introduction

2. Probability Mass Function and Cumulative Distribution Function

3. Expectation of a Random Variable

4. Population Moments

5. Probability Mass Function Vs Probability Density Function

6. Quantile Function and Quantile-Based Estimators

7. Linear Transformation on Random Variables

1. Introduction

2. Uniform Distribution

3. Bernoulli Distribution

4. Binomial Distribution

5. Poisson Distribution

6. Normal Distribution

7. Lognormal Distribution

8. Chi-squared Distribution

9. Student's T- Distribution

10. F-Distribution

11. Mixture Distribution

1. Introduction

2. Probability Matrix and Probability Mass Function

3. Marginal and Conditional Distributions

4. Expectation of a Function

6. Correlation, Covariance, and Independence

7. Effects of Linear Transformations on Covariance and Correlation

8. Variance of a Weighted Sum of Two Random Variables

9. Conditional Expectation of a Component

10. Independent and Identically Distributed (IID) Sequence of Random Variables

11. Mean and Variance of a Sum of IID Random Variables

1. Introduction

2. Mean, Variance, and Standard Deviation

3. Population Vs Sample Moments

4. Estimator Vs Estimate

5. Bias of an Estimator

6. BLUE Estimator

7. Consistency of an Estimator

8. Law of Large Numbers and Central Limit Theorem

9. Skewness and Kurtosis

11. Mean of Two Variables and CLT

12. Covariance and Correlation

13. Coskewness and Cokurtosis

1. Introduction

2. Null and Alternative Hypothesis

3. One-sided Vs Two-sided Test

4. Type I and Type II Errors and Power of a Test

5. Confidence Interval

7. One-sided and Two-sided Confidence Intervals

8. Testing Hypotheses about Population Means' Difference

9. Multiple Testing and Biased Results

1. Introduction

2. Models Estimation using Regression

3. Ordinary Least Squares (OLS) Regression

4. Assumptions of OLS Parameter Estimation

5. Properties of OLS Estimators

6. Hypothesis Testing for a Single Regression Coefficient

7. Hypothesis Test in a Linear Regression

8. T-Statistic, P-Value, and Confidence Interval

9. Estimating Correlation Coefficient from $R^2$

1. Introduction

2. Comparing Assumptions of Single Vs Multiple Regression

3. Regression Coefficients in a Multiple Regression

4. Goodness of Fit Measures for Single and Multiple Regressions

5. Joint Hypothesis Tests and Confidence Intervals

6. Regression Sum of Squares

1. Introduction

2. Testing for Heteroskedasticity

3. Approaches to Using Heteroskedastic Data

4. Multicollinearity

5. Model Specification

6. Model Selection Procedures and Bias-Variance Trade-Off

7. Residuals Visualization

8. Identifying Outliers

9. Conditions for OLS to be Best Linear Unbiased Estimator

1. Introduction

2. Covariance Stationarity

3. Autocovariance and Autocorrelation Functions

5. Autoregressive (AR) Processes

6. Moving Average (MA) Processes

7. Lag Operator

8. Mean Reversion

9. Autoregressive Moving Average (ARMA) Processes

10. Application of AR, MA and ARMA Processes

11. Sample and Partial Autocorrelations

12. Box-Pierce Q-Statistic and Ljung-Box Q-Statistic

13. Generating Forecasts from ARMA Models

14. Mean Reversion in Long-Horizon Forecasts

15. Seasonality in Covariance-Stationary ARMA

1. Introduction

2. Linear and Nonlinear Time Trends

3. Modeling Seasonality with Regression Analysis

4. Random Walk and a Unit Root

5. Modeling Time Series Containing Unit Roots

6. Testing for Unit Roots

7. Constructing h-Step-Ahead Point Forecasts

8. Estimated Trend Value and Interval Forecast

1. Introduction

2. Simple and Continuously Compounded Returns

3. Volatility, Variance Rate and Implied Volatility

4. Beyond First Two Moments

5. Jarque-Bera Test for Normality

7. Correlation and Covariance

8. Correlation in the Context of a One-Factor Model

9. Correlation Measures Used to Assess Dependence

1. Introduction

3. Monte Carlo Sampling Error

4. Reducing Monte Carlo Sampling Error using Antithetic and Control Variates

5. Bootstrapping Method

6. Pseudo-Random Number Generation

7. Limitations of Bootstrapping Method

8. Disadvantages of Simulation Approach

1. Introduction

2. Machine-Learning Vs Classical Econometrics

3. Training, Validation and Testing Data Sub-Samples

4. Underfitting and Overfitting

5. Principal Components Analysis

6. K-means Algorithm

7. Natural Language Processing

8. Unsupervised, Supervised, and Reinforcement learning

9. Reinforcement Learning

1. Introduction

2. Linear and Logistic Regression

3. Encoding Categorical Variables

4. Regularization Techniques

5. Decision Trees

6. Ensemble Learning

7. K-Nearest Neighbors and Support Vector Machines

8. Neural Networks

9. Confusion Matrix

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