Master Financial Econometrics for Time Series Analysis

Embark on a Journey into Financial Econometrics and Time Series Analysis

This comprehensive learning experience will equip you with the skills to master financial econometrics, with a particular emphasis on the intricacies of time series analysis. Get ready to delve into both the theoretical underpinnings and practical applications, all while wielding the power of Excel.

Here’s a glimpse into the terrain we’ll explore:

1. Foundations: Building Your Statistical Arsenal

• Data Acquisition: Begin your journey by discovering prime sources for financial data, such as Kaggle and direct exchanges. While you’ll have access to diverse sources, we’ll primarily use the provided course data to ensure a smooth, consistent learning experience.

• Statistical Essentials: Grasp the core statistical measures—mean, variance, standard deviation—and unlock their power in deciphering data distributions. The exploration will extend to central moments, including the intriguing skewness and kurtosis.

• Probability Distributions: Dive into the world of probability density functions (PDFs) and cumulative distribution functions (CDFs). Discover the nuances between discrete and continuous data, and master the art of representing probabilities using histograms and cumulative sums. We’ll also uncover the secrets of the ubiquitous normal distribution.

• Random Variables: Unravel the concept of random variables and their intimate relationship with probability functions.

2. Hands-On Data Mastery: Transforming Raw Data into Insights

• Empirical vs. Theoretical: Construct empirical PDFs and CDFs from real-world data and engage in a fascinating comparison with theoretical distributions, like the elegant normal and the robust Student’s T. This hands-on experience will involve sorting returns, standardizing data, and scaling empirical PDFs using Z-scores.

• QQ Plots: Master the art of visual comparison using QQ plots, pitting empirical distributions against their theoretical counterparts. Quantiles will become your new best friends as you gain deeper insights into the distribution of financial returns.

• Data Transformation: Equip yourself with essential data transformation techniques. Learn to calculate log returns and standardise your data, preparing it for rigorous analysis.

3. Statistical Modelling: Unveiling the Patterns Within

• The Normal Distribution: Delve deeper into the fascinating properties of the normal distribution, examining it both as a density function and a cumulative distribution. Discover how to expertly fit this fundamental distribution to your data.

• Mixture Densities: Expand your modelling toolkit by exploring mixture densities. Learn to blend multiple density functions, crafting mixed distributions that capture complex real-world scenarios.

• Linear Regression: Explore the world of linear regression, both simple and multiple. Understand the foundational concepts of intercepts and slopes, and master the calculation of these crucial parameters using Ordinary Least Squares (OLS).

• ANOVA Metrics: Get acquainted with essential ANOVA metrics: Residual Sum of Squares (RSS), Total Sum of Squares (TSS), Explained Sum of Squares (ESS), and the ever-important R-squared.

• Hypothesis Testing: Develop a solid grasp of hypothesis testing, framing null and alternative hypotheses with precision. Statistical tests, including t-tests and the insightful p-values, will become your trusted tools for determining the significance of your findings.

• Maximum Likelihood Estimation (MLE): Embrace Maximum Likelihood Estimation (MLE) as a powerful technique for estimating model coefficients. Delve into the concepts of likelihood and log-likelihood functions, and harness numerical methods to unlock their potential.

• Time Series Models: Enter the realm of time series with Autoregressive (AR), Moving Average (MA), and ARMA models. Decode their components and master their estimation. We’ll also touch upon the versatile ARIMA models.

4. Multivariate Analysis: Exploring Relationships in Higher Dimensions

• Bivariate Joint PDFs: Venture into the realm of bivariate joint probability density functions. Learn to combine two normal distributions, understanding the crucial role of correlation in shaping their joint behaviour.

• Copulas: Discover the power of copulas in modelling the intricate dependency structures between random variables. The Gaussian copula will be a key focus, and you’ll learn how to calculate copula density using empirical CDFs.

5. Advanced Time Series Concepts: Mastering the Nuances

• Stationarity: Unpack the concept of stationarity, both strict and weak. This understanding is the bedrock of robust time series modelling, and you’ll see why using stationary data is so critical.

• Unit Roots: Confront the concept of unit roots and their relationship to stationarity. Experiment by generating both stationary and non-stationary data to solidify your understanding.

• ACF and PACF: Harness the power of the Autocorrelation Function (ACF) and Partial Autocorrelation Function (PACF) to dissect and analyse your time series data.

• Dickey-Fuller Tests: Learn to deploy the Dickey-Fuller and Augmented Dickey-Fuller (ADF) tests, essential tools for rigorously assessing stationarity.

• Cointegration and the Engel-Granger Test: Unlock the secrets of cointegration and use the Engel-Granger test to reveal if two time series share a long-run equilibrium relationship.

• Error Correction Model (ECM): Dive into the Error Correction Model (ECM), a powerful tool that integrates both the short-term and long-term dynamics of cointegrated time series.

• Volatility Modelling: Explore the dynamic world of Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models, specifically designed for modelling volatility. We’ll also venture into Asymmetric GARCH (AGARCH) models for a more nuanced approach.

6. Practical Implementation: Putting Theory into Action with Excel

• Excel as Your Tool: Leverage the familiar power of Excel to implement all the models and calculations we’ll explore.

• Software Savvy: Develop a critical eye for understanding software assumptions. Learn to meticulously verify your results, ensuring accuracy and reliability.

• Templates and Examples: Benefit from provided templates designed to guide you through each step, and compare your work against completed examples for enhanced understanding.

This comprehensive learning journey will empower you with both the theoretical knowledge and the practical skills needed to excel in financial econometrics and the analysis of financial time series data. Get ready to transform data into actionable insights!