Teaching notes: Financial Statistics

Lecture summaries and worked solutions I wrote as Graduate Teaching Assistant for Financial Statistics, a graduate econometrics course at Imperial Business School, shared for academic use.

Teaching · Project · MSc Risk Management & Financial Engineering, autumn 2023 · 96 pages · All projects

Teaching notes (PDF, 96 pages, 15 MB, shared for academic use)

What I built

  • Eight summaries covering Lectures 1–16, seven weekly solution sets and a worked example of the delta method, with proofs and answers to students’ questions written out step by step.
  • Topics: least squares and the role of the intercept; hypothesis tests; the method of moments and GMM; likelihood-ratio, Wald and F tests; stationarity, white noise and autoregressive processes; the delta method.
  • The summaries follow the module’s lectures; the explanations, solutions and worked examples are mine.

Why it is here The econometrics I use in research (regression inference, GMM, likelihood-based tests, time-series basics), written out step by step for students.

Skills and tools econometrics and statistical inference technical writing teaching and mentoring

Read with care. Written for the 2023–24 cohort; not peer-reviewed; some pages are handwritten. This public edition leaves out the original’s dedication, preface letter, cohort photograph and cohort-only notice. Shared for academic use: the notes may be read, cited and used in teaching and research with attribution.

Exhibit 1: Two pages from the notes

Page from the notes, Summary of Lectures 13 and 14: a red-headed box on the likelihood-ratio test. It states the null hypothesis R theta equals r, the three-step procedure (unrestricted maximum likelihood, restricted maximum likelihood with Lagrange multipliers, and the statistic LR equal to twice the difference in log-likelihoods, asymptotically chi-squared with q degrees of freedom), the special case for linear regression, and the note that LR is never negative.
Page from the notes, Summary of Lectures 15 and 16: a red-headed box on covariance (weakly) stationary processes. It gives the definition (constant mean, constant variance, autocovariances that depend only on the lag), the autocovariance and autocorrelation functions, a plain-language comment, and five reasons stationarity matters: modelling and forecasting, mean reversion, econometric tests such as unit-root tests, economic theory, and cointegration.

Pages 67 and 76 of the 96-page public edition: the likelihood-ratio test (Lectures 13–14) and weak stationarity (Lectures 15–16). Source: the teaching notes (PDF, shared for academic use).

Exhibit 2: Contents

Part Contents
Summaries Lectures 1–2, 3–4, 5–6, 7–8, 9–10, 11–12, 13–14 and 15–16 (eight parts)
Solutions Weeks 1–7 (seven sets)
Worked examples Least squares in matrix and summation notation, and the role of the intercept; the delta method, with a return-on-investment example

Exhibit 3: Reception

Student rating 4.8 out of 5 (2024–25 cohort survey). Nominated by students for the Excellence in Teaching Award in both years (2023, 2024).

Where this connects

  • CV: Teaching: the course and the teaching record.
  • Research: the papers in which these methods are used.