Numerical Methods for Stock Market Analysis: Interpolation, Integration & Differentiation on IBM Data

Overview

An individual numerical methods project analysing IBM's stock market data for January 2022 and January 2023. The brief simulated a real analyst problem: parts of the dataset were unreliable or missing, and the task was to reconstruct, visualise, and extract insight from the underlying price and volume data using a set of numerical techniques rather than simple averaging or estimation.

What I did

• •Identified corrupted closing price and volume readings in the dataset and reconstructed them using global polynomial interpolation (Lagrange/Newton), then compared the interpolated values against the flagged originals to assess measurement discrepancies
• •Applied both linear and cubic spline interpolation to the volume data, generating 4x and 8x denser point series to produce smoother, more accurate visualisations
• •Compared the two interpolation methods on accuracy and reliability, evaluating which more faithfully represented the underlying data distribution
• •Computed the cumulative stock volume for January 2022 and January 2023 using numerical integration on the cubic spline interpolated data
• •Calculated the rate of change of the closing price using finite difference methods (forward/backward/central differences)
• •Correlated the calculated derivative with the extrema of the closing price distribution to identify inflection points and the most favourable investment windows
• •Produced comparison plots throughout to support each stage of the analysis
• •Wrote a 1,500-word report documenting the methodology for each task, critically evaluating the findings, and translating the results into practical insight for the company
• •Submitted the accompanying Python codebase alongside the report

Skills & tools