Readings and resources

Read first (in this order)

1. Campbell, Lo & MacKinlay, The Econometrics of Financial Markets (Princeton UP, 1997), ch. 1 (returns, aggregation, the lognormal model) and ch. 2 (random-walk tests, variance ratios). The best single source for 2.1–2.4.
2. Cont, R. (2001). "Empirical properties of asset returns: stylized facts and statistical issues." Quantitative Finance 1(2):223–236. https://doi.org/10.1080/713665670
3. Tsay, Analysis of Financial Time Series (3rd ed., Wiley, 2010), ch. 1 (returns and their distributions), ch. 3 (conditional heteroskedasticity; preview of M13), ch. 7 (extreme values, VaR, ES).

Papers for depth

• Lo, A. W. & MacKinlay, A. C. (1988). "Stock market prices do not follow random walks: evidence from a simple specification test." Review of Financial Studies 1(1):41–66. https://doi.org/10.1093/rfs/1.1.41
• Lo, A. W. & MacKinlay, A. C. (1990). "An econometric analysis of nonsynchronous trading." Journal of Econometrics 45(1–2):181–211.
• Merton, R. C. (1980). "On estimating the expected return on the market: an exploratory investigation." Journal of Financial Economics 8(4):323–361.
• Mandelbrot, B. (1963). "The variation of certain speculative prices." Journal of Business 36(4):394–419.
• Hill, B. M. (1975). "A simple general approach to inference about the tail of a distribution." Annals of Statistics 3(5):1163–1174.
• Gopikrishnan, P., Meyer, M., Amaral, L. A. N. & Stanley, H. E. (1998). "Inverse cubic law for the distribution of stock price variations." European Physical Journal B 3(2):139–140.
• Gopikrishnan, P., Plerou, V., Amaral, L. A. N., Meyer, M. & Stanley, H. E. (1999). "Scaling of the distribution of fluctuations of financial market indices." Physical Review E 60(5):5305–5316.
• Pan, R. K. & Sinha, S. (2008). "Inverse-cubic law of index fluctuation distribution in Indian markets." Physica A 387:2055–2065. arXiv: https://arxiv.org/abs/physics/0607014 (finds $\alpha \approx 3$ for NSE and BSE index returns at 1-minute and daily scales).
• Jarque, C. M. & Bera, A. K. (1980). "Efficient tests for normality, homoscedasticity and serial independence of regression residuals." Economics Letters 6(3):255–259.
• Forbes, K. J. & Rigobon, R. (2002). "No contagion, only interdependence: measuring stock market comovements." Journal of Finance 57(5):2223–2261.
• Longin, F. & Solnik, B. (2001). "Extreme correlation of international equity markets." Journal of Finance 56(2):649–676.
• Ang, A. & Chen, J. (2002). "Asymmetric correlations of equity portfolios." Journal of Financial Economics 63(3):443–494.
• Lo, A. W. (2002). "The statistics of Sharpe ratios." Financial Analysts Journal 58(4):36–52.
• Taleb, N. N. (2020). Statistical Consequences of Fat Tails. STEM Academic Press; free version at arXiv:2001.10488. Read ch. 3–4 after this module for the case that moment-based statistics fail under power laws.

Lectures

• MIT 18.S096 (Fall 2013), Lecture 7 "Value at Risk (VAR) Models", Lecture 8 "Time Series Analysis I", Lecture 9 "Volatility Modeling": https://ocw.mit.edu/courses/18-s096-topics-in-mathematics-with-applications-in-finance-fall-2013/video_galleries/video-lectures/

Indian sources

• NSE Indices (index methodology, factsheets, TRI data): https://www.niftyindices.com
• India VIX methodology: NSE's India VIX white paper, linked from the India VIX page on https://www.nseindia.com
• Federal Reserve History, "Stock Market Crash of 1987": https://www.federalreservehistory.org/essays/stock-market-crash-of-1987

Code for this module Exercises m02_returns_stats (returns, drawdown, kurtosis, clustering diagnostics), m02_variance_ratio (2.3) and m02_tails (2.4, 2.6, 2.8); in the app: Exercises → returns_stats, and so on. From a terminal: cd exercises && .venv/bin/python -m pytest modules/M02-statistics-of-returns/tests (set COURSE_IMPL=solutions to run the reference implementations).