Goal: To gain practical experience in statistical modeling of financial data using estimation theory and visualisation.
In this project, I analysed the daily returns of the Dow Jones Industrial Average (DJIA) to model its underlying distribution using Maximum Likelihood Estimation (MLE). After computing the daily return series, I evaluated its statistical properties including skewness and kurtosis, and hypothesised suitable distribution families.
I implemented a custom log-likelihood function and optimised it using scipy.optimize.minimize to find the best-fitting parameters. The results were then compared against parameters estimated via SciPy’s .fit() method. Finally, I plotted both estimated PDFs over the histogram of returns to visually evaluate fit quality.
Key steps:
- Computed return series from historical DJIA data
- Analysed mean, variance, skewness, and kurtosis
- Used MLE to fit candidate distributions
- Compared empirical and fitted PDFs
- Discussed model suitability based on visual and statistical evidence
Tech stack: Python, pandas, scipy, matplotlib, pandas-datareader